PRACTICAL ARITHMETIC
€t)e Cuskegee Knstitutc Series of Cms
EDITED BY
J. R. E. LEE
DIRECTOR ACADEMIC DEPARTMENT
TUSKEGEE NORMAL AND INDUSTRIAL INSTITUTE
Introductory Note
In presenting this volume the author endeavors to set
forth matter which will give training and drill in all of the
fundamental processes in arithmetic. The matter con¬
tained herein has all been taken by Mr. D. W. Woodard,
the author, from the industrial and business operations of
the Institute. He has visited every department of the
Institution, has examined all the books, and has had nu¬
merous conferences with every instructor. He has not
found a single practical, workable operation in arithmetic
that has not been exemplified in some of the work connect¬
ed with the Institution. The problems are therefore local
in their setting. The Accounting Department, the
Mechanical Department with its various construction
operations, and the Agricultural Department through its
planting, harvesting and productive endeavors, together
with the various industries for the training of young
women, have all furnished the material for the operations
in this volume.
Th is book in the present form is the Tuskegee Institute
Edition. It comprises one of the series of what is known
as "The Tuskegee Institute Series of Texts." This
series of texts covers various branches taught in the usual
secondary course. In this text and others that are under
way, claim is laid to concrete and practical application
of all the operations and principles set forth therein.
J. R. E. Lee, Editor.
II
PRACTICAL ARITHMETIC
TUSKEGEE INSTITUTE EDITION
PRACTICAL
ARITHMETIC
TUSK EG EE INSTITUTE EDITION
By
DUDLEY W. WOODARD
HEAD OF DIVISION OF MATHEMATICS
TUSKEGEE NORMAL AND INDUSTRIAL INSTITUTE
TUSKEGEE INSTITUTE, ALA.
19 11
Jnstitute ©regis
T'uskegee Institute, Alabama
1911
PREFACE
This book has been prepared in response to a long felt
need of the students of the Tuskegee Normal and Indus¬
trial Institute. At this institution, the attempt is made
to connect the arithmetic in a vital manner with the every¬
day interests and exercises of the students. The subject i9
presented as a necessary tool for doing certain things, for
solving specific problems.
Under this conception of the function of arithmetic,
the course centers about the problems. If this book has
any distinctive feature, it lies in the character of the prob¬
lems.
Attention is called to the very large number of problems
in which the data must be gathered at first hand by
teacher and student. In fact, it is impossible to carry
out the purposes of this book within the narrow con¬
fines of the class room.
In the gathering of problems for this work I have had
the hearty co-operation of the members of every depart¬
ment of the Institute and wish to express here my grate¬
ful appreciation of the ;ame.
D. W. WOODARD.
Ill
PRACTICAL ARITHMETIC
FUNDAMENTAL OPERATIONS
NUMBERS. UNITS
In making bread at the Institute Bakery, flour, yeast,
sugar, lard, salt, and water are mixed together. These
materials are mixed according to a recipe, which tells how
much of each kind of material must be used. Thus, the
recipe used by the bakers in making bread on a certain
day required 700 pounds of flour, 1 pound of yeast, 20
pounds of sugar, 10 pounds of lard, 5 pounds of salt, and
40 gallons of water.
In the statement just made, 700, 1, 20, 10, 5, and 40
are called numbers.
The symbols or characters, 7, 0, 1, 2, 5, 4, used in
writing these numbers are called figures or digits.
As you have already learned, the figures used in writing
numbers are:
123456 7 8 90
one two three four five six seven eight nine zero
Numbers like 40 and 5 are often called abstract or un¬
named numbers.
On the other hand, the expressions, "40 gallons" and
"5 pounds" are called concrete or named numbers.
1
F U N D A M ENTAL OPERATIONS
Other numbers are: 9 dollars, which tells how much
each student of the Institute pays a month for board; 39
miles, which tells how far Chehaw is from Montgomery
by railroad; 7 days, which tells how many days are in a
week; 25 cents, which tells the price per pound of a cer¬
tain grade of coffee sold at the Institute Commissary.
Now, one of each of the things named in the above
number expressions is called a unit. Thus, 1 pound, 1
gallon, 1 dollar, 1 mile, 1 day and 1 cent are units.
Exercise 1
1. Find out what units are used at the Institute Dairy
Barn in stating the amount of milk given by a cow in a
day.
2. What units are used at the Creamery in selling this
milk to customers?
3. Name the units used in the Dressmaking Division
in measuring cloth.
4. Point out on the yard stick, pocket rule, or tape
measure some unit lengths.
5. What units are used at the Paint Shop?
6. What units are used at the Poultry Yard in stating
how many eggs are bought, etc.?
7. Name some units used in the Cooking Division in
connection with recipes.
8. Find out what units are used at the Canning
Factory.
9. Name some units used at the Commissary.
10. Name some of the units used on the Farm, Truck
Garden, and Orchard.
11 Name any other unit not already mentioned.
READING AND WRITING NUMBERS
9
READING AND WRITING NUMBERS
Exercise 2
Read carefully the statements given below.
1. In 1910, 91,972,266 persons were counted as living
in the United States of America.
The number, 91,972,266, is read "ninety-one million, nine hun¬
dred seventy-two thousand, two hundred sixty-Mx.1' The names of
the orders or places occupied by each figure in the number are as
follows:
c
re
c
o
c
.2
*5
a
-S
<TJ
c
c
c
<v
o
f
03
qj
£
.2
-5
3
ri
C.
zz
c
c
O
c
£
h
X
<L>
h
X
z
h
9
1
9
7
2
2
6
6
2. A student working in the Brickmasonry Division
in one month earned $3.84.
The amount of money earned by the student is read "three dollars
and eighty-four cents." The period, called the decimal point, is
used to separate the number of dollars from the number of cents. In
the amount given, 3 states the number of dollars, 8, the number of
dimes, and 4, the number of cents. Observe that in reading numbers,
the word "and" is used only to separate that part of the name of
the number coming before the decimal point from that part following
the decimal point.
3. In February, 1910, the students in the Mattress-
making Division earned $52.45; in the Plain Sewing
Division, $27.50; in the Dressmaking Division, $47.05; in
the Ladies' Tailoring Division, $43.08; in the Millinery
Division, $42.70.
4. During the month of December, 1910, the students
of the Institute paid in cash on their board bills $3,443.98.
Of this amount, the boys paid $1,778.10, and the girls.
10
FUNDAMENTAL OPERA I IONS
$1,665.88. (Give the amount of money expressed by
each figure in each of the three numbers just given.)
5. During one year the Creamery handled 71,743 gal¬
lons of milk. For this time, 15.757 gallons of whole milk
and 31,851 gallons of separated milk were used by the
Hoarding Department.
6. The following is taken from the report of the Prin¬
cipal to the Trustees of the Institute for the school year
1909-1910:
"In the regular Academic and Industrial Departments of
the School, we have had during the past year an attend¬
ance of 1,662 students, 561 girls and 1,101 boys, from 35
states and 21 foreign countries. Besides the enrollment
in the main departments of the institution, there has been
an average attendance of 153 at the Children's House or
Training School; 98 in the Town Night School and 27 in
the afternoon cooking classes in the Town of Tuskegee; 10
in the night Bible classes taught in Phelps Hall, and 227
upon the Two Weeks' Short Course for farmers held in
January. Thus, we have been responsible for reaching
and teaching, all told, for greater or less time, 2177 per¬
sons. ''
(In numbers, 1662, 1101, and 2177, tell how many
of the students is expressed by each figure.
Exercise 3
Write in figures the numbers occurring below, using the
dollar sign and decimal point in the case of money.
1. In March, 1911, there were printed at the Institute
Printing Office fifteen thousand copies of The Southern
Letter, nineteen thousand, two hundred copies of The
Tuskegee Student, twelve hundred fifty copies of the
READING AND WRITING NUMBERS
11
Jo urnal of the National Medical Association, and one
thousand copies of the National School News.
2. In one year, eleven thousand, six hundred bushels of
sweet potatoes were grown on the Institute Farm.
3. The girls working in the Laundry earned six hun¬
dred forty-four dollars and seventeen cents in December,
nineteen hundred and ten.
4. On May thirty, nineteen hundred ten, the endow¬
ment fund of the Institute amounted to one million, four
hundred one thousand, four hundred forty dollars and
seventy-seven cents.
5. Find out what is meant by the "endowment
fund."
6. According to the thirteenth census of the United
States, the population of the state of Alabama was given
as two million, one hundred thirty-eight thousand, ninety
three.
7. Find out what is meant by "the census." When
was the thirteenth census taken? When will the next
census be taken?
ROMAN NUMERALS
A system of writing numbers, called the Roman system,
employs letters instead of the figures ordinarily used for
this purpose.
The letters, with their values, are:
I V X L C D M
1 5 10" 50 100 500 1000
The following will show how numbers are written in
this system:
12 FUNDAMENTAL OPERATIONS
II =2
XX
20
XCIX
= 99
III =3
XXII
22
CLXI
= 161
IV (IIII) = 4
XXXV
35
MDCXI
= 1611
VII = 7
XLVII
47
LXXIX
= 79
VIII =8
LXXXVII =
87
CCCXVIII
= 318
IX =9
MCMX1V =
1914
DXIII
= 513
Exercise 4
IVrite in the usual (Arabic) figures.
MCMXXXIV LXXVII DCXCIII
XLVI CCCXVIII MVIII
Express in Roman numerals.
76
54
85
39
111
93
48
1016
1724
1913
679
364
Bring into class three instances in which you have ob¬
served the use of Roman numerals.
ADDITION
Exercise 5
Give results quickly.
2 + 3
2 + 5
2 + 4
2 + 7
2 + 6
2 + 8
3 + 3
3+4
3 + 6
3+5
3 + 7
4 + 5
4 + 6
5 + 6
2 + 9
3 + 9
4 + 7
6+6
7 + 6
8 + 3
8 + 5
9 + 4
6 + 9
5 + 7
8+6
9 + 7
9+8
9 + 9
10+3
10 + 8
11+2
11+5
ADDITION
13
12 + 7
15 + 5
1 + 3 + 2
7 + 4 + 5
10 + 9
13 + 6
6+7 + 5
9+7 + 7
12+ 4 + 3
Add quickly
11 + 9
13 + 8
1 + 4 + 5
8 + 5 + 4
12 + 3
15+4
5 + 8+7
8+5 + 9
10 + 7 + 3
the following
12 + 9
17+5
5 + 3 + 5
7 + 6+6
13 + 4
16+3
9 + 9 + 2
2 + 9 +8
12 i 6+ 4
)l twins:
10+10
18+ 4
5 + 6+ 4
3 + 7+ 9
14+ 5
17+ 3
8 + 4+ 7
6 17+ 9
3 + 14^ 5
3 Omit unnecessary words in adding. For instance, in adding
5 this column, beginning at the bottom say:
6 7, 8, 10, 16, 21, 24.
2
1 In this example, the numbers, 3, 5, 6, etc., to be added,
7 are called addends, while the result, 24, is called the sum.
~2A~
If columns are added from the bottom upward, check re¬
sults by adding from the top downward.
4
5
7
8
3
3
2
4
2
4
8
2
3
6
1
6
6^
1
3
5
8
9
6
7
7
6
8
9
6
5
5
6
8
4
4
8
5
7
6
7
4
3
1
2
3
4
8
6
9
1
2
5
14
FUNDAMENTAL OPERATIONS
1
2
7
5
6
4
9
7
7
9
8
3
8
3
1
6
3
1
7
9
5
7
6
9
8
7
8
7
9
5
3
4
2
6
5
3
Exercise 6
1. During the month of March, 1911, the Creamery
received from the Institute Dairy Barn 6574 gallons of
milk and purchased from neighboring farmers 1674 gallons
of milk. How many gallons of milk were handled at the
Creamery during this month?
6574 gal. Adding: 4+4 = 8; put down 8; 7 tens + 7 tens =
1674 gal. 14 tens; 14tens=l hundred+4 tens; put down 4 in
8248 gal. tens' place of results; 6 hundreds-|-5 hundreds-f-
1 hundred = 12 hundreds; 12 hundreds-|-l thousand = 2 hundreds;
put down 2 in hundreds' place of the result; 1 thousand+6 thou-
ands +1 thousand = 8 thousands; put down 8 in the thousands' pla'^
of the result.
Then, the total number of gallons of milk handled at the Cream¬
ery during March, 1911, was 8248.
2. During the period mentioned in the preceding
problem, the sales of the Creamery on the retail wagon
routes were as follows: Route No. 1, $234.64; Route
No. 2, $157.30. Find the value of the dairy products
sold on these two routes for the month.
$234.64 Adding, the value of the sales on the two
157.30 routes for the month is found to be $391.94.
$391.94
In adding United States money, the addends are to be so
placed as to bring decimal point beneath decimal point,
thus having the figures of the same order in the same column.
ADDITION
15
3. On one day the hogs of the Swine Raising Division
were kept in ten groups on the farm. The record of the
division for the day gave the number of hogs in each
group as follows:
Group 1 130 hogs Group 6 130 hogs
2 17 7 50
3 94 8 148
4 80 9 110
5 130 10 104
Find the number of ho;js in the entire herd.
4. On March 12, 1911, the menus given below were
served the students boarding in Tompkins Hall. The
cost of each item is given.
Breakfast: rice, $4.80; butter, $12.60; syrup, $7.60;
coffee,$7.98; rolls, $14.12.
Dinner: sausage, $20.00; rutabagas, $10.50; corn,
$6.78; bread, $13.80; milk, $6.40; pie, $20.25.
Supper: ginger bread, $12.57; light bread, $12.00;
syrup, $7.60; tea, $5.00.
Find the cost of the food for each meal and for rhe
day.
5. Find out (through teacher) the cost of the various
food-stuffs used for the meals of students in Tompkins
Hall for some recent day, and compute the cost of the
same for the day.
6. In July, 1910, the cost of operating the Boarding
Department was as follows: provisions, $4,095.03; labor,
$885.16; other expenses, $478.68. Find the total cost of
operating the department for the month.
7. The cost of working the cabbage crop on the In¬
stitute Farm during April, 1910, was as follows: labor of
hired men, $11.93: labor of students, $58.79; team hire,
$16.80; fertilizer, $19.50. What was the cost of working
the crop for the month?
8. In 1910 the following was paid for student labor in
working the sweet potato crop of that year: Jan. and
16
FUNDAMENTAL OPERATIONS
Feb., $61.96; Mar., $53.45; Apr., $66.67; May, $108 34;
June, $368.30; July, $494.90; Aug. $201.99; Sept.,
$94.35; Oct., $106.50; Nov., $224.00; Dec., $29.55.
Find the amount paid students for working this crop.
9. The value of the seed used by the Agricultural De¬
partment during March, 1910, was as follows; corn,
$23.10; rape and rutabagas, $22.00; carrots and mangels,
$31.45; beets, $70.00; cantaloupes, $15.00; watermelons,
$4.38; turnips, $6.80. Find the total cost of these seeds.
10. For one month the students pursuing mechanical
trades in the Institute earned in the various divisions the
amounts given below:
Blacksmithing
. $151.81
Brick masonry
$303.46
Carpentry
. 339.22
Plumbing
168.74
Machinery
. 473.53
Harnessmaking .
86.35
Printing
. 113.25
Painting .
77.34
Sawmilling
50.95
Wh eel wrigh ting
84.43
Repair
. 113.84
Tailoring
138.39
Tinsmithing .
88.90
Shoemaking .
101.66
Electricity
. 120.01
Brickmaking
22.67
Foundry
33.04
Find the
total earnings
of the students
in the
mechanical divisions for the month.
11. Most of the employees of the Institute who trade
with its various departments use for this purpose coupon
books. The value of the trade carried on with the different
divisions of the Institute by means of these coupon books
during November, 1910, is given below:
Sales Room . . $154.27 Commissary . . $964.29
Dairy .... 142.25 Truck Garden . 30.01
Printing . . . 4.52 Dressmaking . 5.60
Carpentry . . 13.08 Goat Herd . . 4.50
Sawmilling . . 4.50 Fuel Account . 25.10
ADDITION
17
Hospital
44.90
Repair
2.60
Shoemaking .
16.95
Horse Barn .
40.97
Painting
.61
Poultry Raising .
4.05
Millinery .
6.00
Blacksmithing .
.80
Mattressmaking
3.85
Tinsmithing
10.61
Brickmaking .
.80
Plain Sewing
.25
Practice Kitchen
9.30
Farm ....
12.60
Brickmasonrv
.54
What was the value of the trade in coupons for the
month?
12. The daily receipts for the Institute Commissary
for the month of February, 1911. were as follows:
February Cash Coupons
1 $17.14 . . $ 18.37
2 15.82 . . 105.15
3 11.55 . . 59.21
4 ... 14.53 . . 80.33
5 42.30 . . 72.11
7 . . . 16.27 . . 38.90
8 : 15.36 . 27.20
10 24.40 . . 45.77
11 16.48 . . 31 84
13 38.43 . . 52.71
14 39.87 . . 32.50
15 ... 17.26 . . 47.20
16 16.13 . . 27.79
17 7.95 . . 17 68
18 22.25 . . 56 87
20 36.80 . 49.63
21 15.05 . . 28.55
22 13.04 . . 20.77
23 11.11 . . 15.25
24 16.26 . . 16.47
25 ... 16 57 . . 19.37
27 41.42 . . 86.73
28 14.95 . . 37.95
Find the total value of the sales for the month.
IS FUNDAMENTAL OPERATIONS
SUBTRACTION
Exercise 7
1. A student, having $8, paid $2 for a uniform hat.
How much did she have left?
To find out how much the student had left, we must take (sub¬
tract) $2 from $8. Now, $8—$2 = $6. Then, the student had $6
left, $'8 from which we take $2, is called the minuend; $2, which
is subtracted is called the subtrahend; $6, the result, is called the
remainder or difference.
2. The lace used in trimming a dress was bought in a
bolt containing 17 yards. When the dress was finished,
8 yards of lace remained unused. How many yards of
lace were used in trimming the dress?
3. In measuring a student for a skirt in the Dress¬
making Division, the skirt measure from the waist to the
floor was found to be 42 inches. The girl wished her
skirt to be 4 inches from the floor. How long should the
cloth for this skirt be cut, allowing 3 inches for a hem?
4. The skirt measure of another student from the
waist to the floor was found to be 39 inches. This stu¬
dent desired her skirt to be 5 inches from the floor. How
long should the cloth be cut, allowing 4 inches for a hem?
5. A student measured 43 inches from the waist to
the floor. How long should the cloth for a skirt for this
student be cut, allowing 4 inches for a hem and 3 inch¬
es for each of two tucks, and making the skirt when
finished 5 inches from the floor?
6. Find out the method used in the Institute Com¬
missary in making change. For instance, if your pur-
SUB FRACTION
19
chases amount to ,$1.68 and you give the clerk a $2 bill,
how does he count out to you the proper change?
7. Show how the change might be counted out to a
purchaser who bought $3.76 worth of goods and gave the
clerk $5
8. When the purchases amount to $13.33 and the pur¬
chaser gives the clerk three $5 bills, show how the change
might be counted into the hands of the purchaser.
Exercise 8
Supply the missing numbers.
3 +
= 5
2 +
= 6
4 = 7
5 H-
= 8
4 +
= 9
5 r =9
2 +
-11
3 +
= 10
6 i =12
5 +
= 12
4
= 13
6 =14
7 +
= 15
8 i
= 17
9 i =19
7 +
= 19
8 +
= 20
5 =18
13 +
= 16
12
= 19
14 =21
23 +
= 30
37 +
= 46
56 : =70
Give results
rapidly.
9-3
12-
9
13-
4
14- 6
8-5
13-
7
16-
6
15- 9
10-6
17-
7
16-
8
19-10
11-5
18-
8
15-
10
17- 6
12-7
18-
9
19-
8
18-10
14-9
15-
8
23-
7
37- 5
50-8
67-
8
59-
4
71- 7
35-9
88-
9
43-
7
101-98
7 + 8-
-5
9
5-7
3
5-
■6
10+ 2-7
3 + 9-
-8
5 +
7-5
16 h
8-
■7
23+ 7-9
17 + 6
-8
4 + 18-7
51 +
6-
-8
26+ 7-2
19-8 + 7
24-
7 + 9
53-
8
7
16- 9 + 6
20
F U N D A VIE N T A L O P E R A TIO N S
Exercise 9
1. During the school year 1908-1909, there were en¬
rolled in the Institute 1494 students. In 1909-1910,
1662 students were enrolled. How many more students
were enrolled in 1909-1910 than in 1908 1909?
To find how many more students were enrolled in 1909-
1910 than in 1908-1909, we subtract (take) 1494 from
1662 as indicated below.
1662 4 units cannot he taken from two units. Take 1 ten
1494 (10 units) and add to the 2 units, making 12 units. 12
108 units—4 units 8 units. Since 1 ten was taken from the
6 tens, 5 tens are left. 9 tens cannot be taken from 5
tens. Take 1 hundred (10 tens) from the 6 hundreds and add to the
5 tens, making 15 tens. 15 tens—9 tens 6 tens. Since 1 hundred
was taken from the 6 hundreds, 5 hundreds are left. 5 hundreds
—4 hundreds 1 hundred. 1 thousand—1 thousand--0. Then,
1662—1494" 168. Therefore, there were 168 more students enrolled
in 1909-1910 than in 1908-1909.
Another method of subtracting 1494 from 1662 is that
called the method of making change. ( See Exercise 7.)
1662 We are now looking for the number which when add-
1494 ed to 1494 will produce 1662. It is evident that the
168 figure in units' place of the number sought must be such
that when added to 4, the figure 2 will be in units' place
of the sum. According to this method, we proceed as follows:
4 ;-8=12, put down 8
1 - 9 <3 —16, put down 6
111 6, put down 1
1 O 1.
2. The Institute received a bill for a car of coal ship¬
ped from Bessemer, Alabama, in which the weights were
specified as follows:
SUBTRACTION
21
Gross 113,500 pounds
Tare 34,500 pounds
Net 79,000 pounds
Find out what is meant in this connection by the words
gross, tare, net. See actual coal bill furnished by teacher.
3. Find the number of pounds of coal received by the
Institute in the three cars mentioned below.
Gross Tare
Car No. 1. 115,600 36,700
Car No. 2. 123,400 39,600
Car No. 3. 109,000 35,200
4. The population of thirteen Southern States for
1900 and 1910 is given below. Which state gained the
greatest number of persons during the ten years? What
was the total increase in population for all of these states
together?
1900
1910
Alabama
1,828,697
2,138,093
Arkansas
1,311.564
1,574,449
Florida
528,542
752,619
Georgia
2,216,331
2,609,121
Kentucky
2,147,174
2.289,905
Louisiana
1,381,625
1,656,388
M ississippi
1,551,270
1,797,114
North Carolina
1,893 810
2,206,287
Oklahoma
790,391
1,657,155
South Carolina
1,340,316
1,515,400
T ennessee
2,020,616
2,]84,789
Texas
3,048,710
3,896,542
Virginia
1,854,184
2,061,612
5. On the following page is a reproduction of the
monthly statement given each student of the 1 nstitute.
The statement here reproduced is one that was given a
student for the month ending January 31, 1911.
Henry Davis
IN ACCOUNT WITH THE TUSKEOEE NORMAL AND INDUSTRIAL INSTITUTE
Statement for the Month Ending January 31, 1911
Debits ( IVhat the Student ogives the School )
Credits (What the School ou.es the Student
To Balance last Statement
Board and lodging for the month.
Medicine and Hospital..
Shoemaking
Tailoring ..
.Sales Room
Dressmaking
Sewing...
Millinery
Cash Drawn
Breakage and Fines
Indebtedness to School
By Balance last Statement
Cash paid ..
Work in Boarding Dept
in Teachers' Home
in Office.
Choir. _ _ .. ...
in Division: —
Blacksmithing ... Carpentry...
Dressmaking Klectncal ..
Farm .. Latin deri ng
Masonry.. Machinery...
Printing Painting
Sboemaking Tailoring
22 :i2
19 :i2
Balance due the Student
This bill is due when received; payment must not be deferred later than the 15th.
SUBTRACTION
23
What does "To Balance last Statement" mea1? What
does "By Balance last Statement'' mean? Verify the
above statement, that is, see if the student teally owes
the Institute the amount indicated opposite "Indebtedness
to School."
In subtracting United States money put down numbers so
as to bring decimal point beneath decimal point. M hyf
6. Another student for one month owed the Institute
for board and lodging $8.50. The Institute owed him at
the beginning of the month $7.86. This student earned
by work on the farm during the month $10.26. Make
out a statement showing the standing of the student.
7. A student for one month owed the Institute for
board and lodging $6 80, for medicine and hospital charges,
$5.85, for cash drawn, $.50. On the other hand, the In¬
stitute owed the student at the beginning of the month
$1.82. The student earned by work on the farm $3 20,
and by work for the Machinery Division, $1.00. How
did the account of this student stand at the end of the
month?
8. The statement of a student for one month showed
that at the beginning of the month, the student owed the
Institute $2.15. For board and lodging for the month,
she owed $8.50. She earned by work in the Boarding
Department, $2.75, by work in the Dressmaking Division,
$1.78, by singing in the Institute Choir, $ 90. What was
the standing of this student at the close of the month
mentioned?
9. Verify your statement for last month.
10. For the year ending May 31, 1910, the receipts of
the Institute lor current expenses and equipment were
$319,964.31. Of this amount, $118,062.37 came in the
FU\DAMENTAL OPERATIC)NS
form of donations from individuals and organizations.
How much was received from other sources than those
just mentioned?
11. In the report of the Principal of the Institute for
the year mentioned in the preceding problem, we find the
following statement: "1 he value of our plant, including
equipment and live stock, is now $1,279,248-/3, making
an addition of $163 613.94 for the year for permanent
physical plant." Find the value of the plant on May 31,
1909.
12. A hat made in the Millinery Division cost as fol¬
lows: shape, $.35; lining, $.06; straw, $1.25; quills, $1.25;
thread, $.03; labor, $.50. This hat sold for $4.25. Find
the gain.
13. Four students of the Cooking Division were given
$1.00 and told to prepare a luncheon for six persons. The
material used by the students in preparing the luncheon
was as follows: flour, $.07; tomatoes, $.08; peas, $.15;
salmon, $.15: eggs, $.05; lemons, $.03; lard, $.05; coffee,
$.03; sugar, $.05; butter, $.05; crackers, $.05; milk, $.07;
potatoes, $.03; baking powder, salt, and pepper, $.02.
H ow much of the $1.00 given the students w7as left?
14. On another day, five students of the Cooking
Division were given $1.50 with which to prepare a dinner
for six persons. For this purpose they used the following:
green peas, $.10; crackers, $.05; rice, $.05; beef, $.05;
vinegar, $.05; chicken, $.30; butter, $.14; lettuce, $ 05;
bread, $.10, coffee, $.05; sugar, $.15; eggs, $.05; milk,
$.05; flour, $.10; gelatine, $.15. How much of the
$1.50 given the students was left?
15. On January 1, 1910, the Institute oat crop then
on hand was valued at $5542.00 During the year 1910,
SUBTRACTION
25
$1993.21 was spent on the crop. The oats and hay rais¬
ed from the crop were valued at $8630.74. What was
gained on this crop for the year?
16. The cost of raising the sweet potato crop of
1910 was $3588.10. T he value of the sweet potatoes
raised was $8291.62. By how much did the value of the
crop exceed the cost of raising it?
17. The growing of the corn crop of the same year
cost $5433.42. The crop was estimated to be worth
$5675.20. Find gain.
MULTIPLICATION
Exercise 10
1. How much does a student pay for board and lodg¬
ing who enters the Institute on September first and stavs
until the close of the school year?
2. A student working in the House and Sign Paint¬
ing Division received 3 Cents per hour. How much did
he earn in one full working day?
3. In some repair work done in the Harnessmaking
and Carriage Trimming Division, 7 yards of buckram
costing 12 cents a yard were used. Find the cost of this
material.
Give results rapidly.
5/6
Here we are required to multiply 6 by 5, that is, to take 6 five
times. 6, the number multiplied, is called the multiplicand; 5, the
number by which we multipy, is called the multiplier; 30, the result,
is called the product.
3x6 5x4 6x2 9x11
2x7 4x3 5x6 10x11
4X6 6x3 7x4 llv 8
4x9 3x8 9x3 12x 7
8x4 6x7 7x7 lOx 9
5x7 7x8 6x6 12x 6
FUN DA VI EN PAL OPERATIONS
4x4
3x10
7x9
12 X 8
9x5
5x11
8x8
12 X 5
3x4 2 <
v Perform multiplication
first, then
addition )
6x7 ; 3
2x9 + 5
6x8 + 8
2X 7-9
5x7 + 8
3x8 + 5
7x7 + 7
6+ 9x7
8x9 + 3
8x7-6
5x6 + 4
9x 9—7
4x7-9
11x7-6 12x6-4
8x12-6
3x3x3
6x2x5
5x2x9
3x 4x6
2x3x8
2x4x8
1x9/9
3x 3x6
Exercise
11
1. The Bakery used on one day 4 barrels of flour.
What was the weight of this flour, allowing 196 pounds
to the barrel.
196 ft> If 1 barrel of flour weighs 196 pounds, 4 barrels will
4 weigh 4 times 196 pounds.
784 ft) The explanation of the multiplication of 196 by 4 is
as follows: 4X6 units---24 units. Put down 4 and keep the 2 tens
to add to the next product. 4X9 tens-—36 tens. 36 tens 2 tens ~ 38
tens. Put down 8 and keep the 3 hundreds to add to the next prod¬
uct. 4Xlhundred = 4 hundreds. 4 hundreds + 3 hundreds = 7 hun¬
dreds. Then, 4X196 = 784. Therefore, the 4 barrels of flour weighed
784 pounds.
2 The Institute bought at one time for the Foundry
7 tons of Number 2 pig iron at $14.50 per ton. The
freight charge on this shipment was at the rate of $2.35
per ton. Find the total cost of pig iron.
$14.50, price per ton of pig iron. $16.85
2.35, freightcharge per ton. /
$16.85, total cost per ton of pig iron. $117.95,total cost of 7 tons.
Note the position of the decimal point in the product ob¬
tained when $16.85 is multiplied by 7.
MULTIPLICATION
27
3. During October, 1910, a student in the Dressmak¬
ing Division made 8 uniform skirts. The price paid for
making one skirt at that time was $.15. Find the amount
paid the student for this work.
4. A student in the Brickmasonry Division worked 9
full working days in one month at $.35 per day. What
were his earnings for the month in this division?
5. If you put in full time at your work next month at
full pay, what will be your probable earnings for the
month? Show how you arrive at your estimate.
6. A family in Greenwood trading with the Institute
Creamery bought during one week the following: 7 quarts
of skimmed milk at $.02 per quart; 8 pints of whole milk
at $.04 per pint; 3 pounds of butter at $.28 per pound.
Find the amount spent by the family during the week for
dairy products.
Multiply as indicated
5x $649.08
6x $101.67
7X $8765.43
8x $5307.07
4X $3057.96
3 x $90706.59
10X5
10 X 10
10x$.05 10x$.08 10X$1.50
100x6 J 00x3 100x8
We see from the above that when an integer (whole
number) is to be multiplied by 10, 100, 1000, etc., the
7 x 234
6x5478
6x 857
8x1854
4X9754
3 x 7528
5x6507
4X9995
8x8734
9X6006
7X4008
5x5307
Exercise
1. Give
the products.
10x6
10X3
10x8
10x4
28
FUNDAMEN TAL OPERATIONS
product can be found by annexing as many zeros to the
multiplicand as there are zeros in the multiplier.
When United States money is to be multiplied by 10,
100, 1000, etc., the product can be found by moving the
decimal point in the multiplicand as many places to the
right as there are zeros in the multiplier.
Thus, 100x17 = 1700; 100x$3.25 = $325.00.
2. Announce immediately the products.
10x375 100 x 13 10 x $1.50
100x 55 1000x 97 100X $2.37
100x863 100x300 10 x $10.07
3. During the year 1910, the Blacksmith Shop used
80 tons of coal. This coal cost the Institute $2.35 per
ton at the mines. The freight charge on the coal
was $1.61 per ton. Find the total cost of the coal used
by the shop for the year.
$2.35, cost per ton of coal at mines.
$1.61, freight charge per ton.
$3.96, total cost of 1 ton of coal.
$3.96 If the total cost of 1 ton of coal was $3.96, then
80 the total cost of 80 tons was 80 times $8.96, which
$316.80 is *316-80-
Now, 80 = 8X10. Then the product, 80 X $3.96, can he found
by first multiplying by 8 and then by 10. Thus8X$3.96 =
$31.68; 10X $31.68 =$316.80. But the actual work necessary to
be done is indicated.
4. In December, 1910, a student in the Dressmaking
Division made 40 pairs of the cuffs worn by the girls on
their uniform dresses. For this work she received $.02
per pair. H ow much did the girl receive for this work?
MULTIPLICATION
29
5. In the same month, the Dressmaking Division sold
to students 20 uniform dresses at $2.00 each and 10 sets
of white cuffs and collars at $.25 per set. Find the
amount received by the division for these articles.
6. In making a set of harness for the dump carts used
on the Institute grounds, 10 pounds of "Union" harness
leather are used. This leather cost $.35 per pound. Find
value of leather used in one set of this kind of harness.
7. The Institute bought for the Commissary from the
Calumet Tea and Coffee Company of Chicago 20 five-
pound cans of cocoa at $.28 per pound, and 100 one-
pound cans of cocoa at $.29 per pound. Find the value
of this order.
8. The Buell Manufacturing Company of St. Joseph,
Mo., sold the Institute 60 blankets at $1.75 each. What
was the amount paid for these blankets?
9. During the school year 1908-1909, families living
in Greenwood bought of the Institute 132 tons of do¬
mestic coal at $6.50 per ton. Find the amount paid the
Institute for this coal.
To find the amount paid the Institute for the coal, we
multiply $6.50 by 132. Why?
(a) (b)
$6.50 $6.50
132 132
13.00= 2 x $6.50 1300
195.00= 30 x $6.50 1950
650.00 = 100 x $6.50 650
$858.00 = 132 x $6.50 $858.00
In the work marked (a) the operation is explained. In practice,
the work put down under (b) is all that is necessary.
30
FUNDAMENTAL OPERATIONS
10. The Sales Room sold to the Plain Sewing Divi¬
sion on November 21, 1910, the following: 51 yards of
domestic at $.10 per yard; 1 paper of pins, $.05; 8 yards
of sateen at $.15 per yard; and 55 yards of gingham at
$.U8 per yard. Find total value of these goods.
11. In making a set of single wagon harness at the
Institute Harness Shop, 16 pounds of leather costing
$.38 per pound were used. Find the cost of the leather
used for this purpose.
12. For making a set of light buggy harness, it is esti¬
mated that 15 pounds of oak harness leather are required.
This leather cost $.40 per pound. Find the value of the
leather in one set of such harness.
13. From September 1, 1910, to April 1, 1911, the
Upholstery Division made 228 pillows. Each pillow re¬
quired 1 yard of ticking, $.15, and 4 pounds of linters at
$.05 per pound. The cost of the thread, labor, etc., used
in making each pillow was estimated to be $.10. Find
the cost of making the pillows.
14. For the same period, 2011 pillow cases were made
by the same division. In making each pillow case, 1 yard
of pillow tubing, $.18 was used. The cost of the thread,
labor, etc., required to make 1 pillow case was estimated
to be $.06. Find the cost of the pillow cases.
15. On March 11, 1911, products of the Institute
Truck Garden were sold on two vegetable wagons by
students. The vegetables on each wagon were checked
on the departure of the wagon and on its return. In
this way, the amount of money to be reported by the
driver was found. The following is the record of the two
wagons on the day mentioned:
MULTIPLICATION
31
Wagon No. 1.
Wagon N
o. 2.
Out
Back
Out
Back
Turnip s
20 bunches,
6 bunches
12 bunches
3 bunches
Salad (Rape)
10
3
11
0 "
Onions
6
0
6
0 "
Radishes
4
0
4
0 "
Kale
4
2 '1
3
0
Rutabagas
10
0
S
0 "
Sweet potatoes
3 bushels
3 pecks
2 bushels
0 bushels
The sweet potatoes sold at $1.00 per bushel. The
other vegetables at 5f per bunch.
Find the value of the sales on each wagon and the total
sales for the two wagons.
16. On one day the Truck Garden sold to the Board¬
ing Department the following:
24 bunches spinach (" $.05
12 bunches lettuce Ca> .05
75 bunches salad Ca) .02
7 bushels rutabagas On .80
10 bunches onions On .05
Find the value of the sale.
17. The J. W. Butler Paper Company of Chicago
sold the Institute for use in the Printing Division 5 reams
of paper, each ream weighing 140 pounds, at $.06 per
pound. Find the cost of this paper.
(What is meant by a "ream" of paper?)
18. The Institute bought of the American Linseed
Oil Company 2 barrels of boiled linseed oil. One barrel
contained 51 gallons and the other barrel contained 52
gallons. This oil cost $.75 per gallon. Find what the
Institute paid the firm, a reduction of $1.55 being given
for cash payment.
32
FUNDAMENTAL OPERATIONS
19. The Institute bought of the Loeb Hardware Com¬
pany of Montgomery 225 pounds of lamp black at $ 13 per
pound and 5 gallons of paint at $2.25 per gallon. Find the
cost of this order.
20. The Institute purchased from the Vandiver Gro¬
cery Company of Montgomery, Ala., the following: 2
bags of rice, 200 pounds, at $.06 per pound; 2 barrels of
grits at $3.65 per barrel; 2 bags of Irish potatoes, 5 bushels,
at $.90 per bushel; 3 cases of baking powder, 6 dozen
cans, at $2.50 per dozen; 1 case of peas, 2 dozen cans, at
$1.75 per dozen; 2 boxes of chocolate, 24 pounds, at $.33
per pound. The freight on the above was $1.66. Find
total cost on the shipment.
21. During one month the Creamery bought from
farmers living near the Institute 434 gallons of milk at
$.18 per gallon. How much was paid for this milk?
Find the products.
375X 4876
530X73632
904X 7083
900X 5362
7673 V 8219
906 < $ 37.87
537 x 406.09
872 X 5367.83
608 X 702.03
3117 X 4268.93
DIVISION
Exercise 13
1. A uniform coat made in the Institute Tailor Shop
had on it 5 buttons. In spacing the buttons on the coat,
the tailor first located the top button, and then the
bottom button. Measuring the distance from the top
button to the bottom button, he found it to be 16
DIVISION
33
inches. He then located the other three buttons so
as to make the distance between any two consecutive
buttons the same. How far apart were the buttons on
this coat placed?
2. On another coat made in the Tailor Shop there
were placed 4 buttons. The distance from the first to
the last button was 15 inches. How far apart did the
tailor place the buttons on this coat?
3. A student in 'he Carpentry Division who received
$.30 per day for his labor worked 7 hours on one day.
H ow much did he receive for his work on that day?
4. A bolt of cloth received at the Dressmaking
Division contained 42 yards. How many uniforms can
be made from this cloth, allowing 8 yards to the dtess?
How many yards would be left over?
Give quickly the results.
12-^4 (read "12 divided by 4"). Here we are required to find
the number which when multiplied by 4 will give 12. We know
that 4X3-—12. Therefore, 12 -9— 4 = 3. 12, the number to be divided,
is called the dividend. 4, the number by which we divide is called
the divisor. 3, the result, is called the quotient.
15-
- 3
12-
- 6
18-
- 3
16-
- 8
14-
- 2
24-
- 6
20-
- 5
22-
-11
32-
- 4
42-
- 6
48-
- 8
56-
- 7
60-
-10
63-
- 7
72-
- 8
88-
- 8
77-
- 7
99-
-11
54-
- 9
70-
-10
81-
- 9
96-
-12
100-
-10
64-
- 8
49-
- 7
28-
- 4
60-
- 5
34
FUNDAMENTAL OPERATIONS
36- 4
108- 9
36- 6
144-12
36-12
121-11
38 — 5. In this case, we see that we cannot find an integer which
when multiplied by 5 will give 38. But we find that 7 is the number
which when multiplied by 5 will give the product nearest 38. 5x7 =
35. 38 — 35 = 3. Then, 38 — 5 = 7, with 3 remaining. 3, that
part of the dividend that is left, is called the remainder.
1. On one day 216 pounds of cream were churned at
the Creamery. Find the number of gallons of cream
churned on the day mentioned, allowing 8 pounds to the
gallon.
Since 1 gallon of cream weighs8 pounds, we shall have 1 gallon
of cream for every 8 pounds that we have in 216 pounds. To find
out how many times we have 8 pounds in 216 pounds, we divide
216 by 8 as follows:
8 will not divide 2 hundreds giving an integer
8)216
in the quotient, but will divide 21 tens, giving 2 tens
27 as quotient and 5 tens as remainder. Adding
the 5 tens to the 6 units, we get 56 units. 56 — 8 = 7
Then, the quotient is 27. Therefore, 27 gallons of cream were
churned on the given day.
2. Some painting done at Phelps Hall required *2
(one-half) gallon of white paint costing $1.90 per gallon
and gallon of yellow paint costing $1.70 per gallon.
Find the cost of the paint used on this job. (When a
number is divided into two equal parts each part is called
J/2 of the number.)
47 f 6
58-8
55-10
29- 9
32- 3
99-12
Exercise 14
$.95, cost of white paint.
$.95 + $.85=$1.80, cost of paint for job.
Note the decimal points in quotients.
2)$1.90
DIVISION
35
3. The Institute bought Ix3 (on< -third) dozen mor-
ta hoes for the Brickmasonry Division for $2.00. Find
the cost of one hoe.
(When a number is divided into three equal parts, each
part is called 13 of the number.)
4. Divide as indicated.
3872- 2 471- 3 5250
7761- 9 532- 8 7394
60832- 8 21252- 7 6372
84288-12 7340-10 6780
8453-16 5724-11 76394
6
5
4
10
10
Exercise 15
1. In January of one year 6,109 gallons of milk were
received from the cows at the Dairy Barn. Find the
average number of gallons received daily.
To find the average number of gallons received daily for the
month, we divide 6,109, the total number of gallons received during
the month, by 31, the number of days in the month.
The process of division is as follows:
197
Dividing 61 by 31, we obtain 1 as a quotient.
31)6109 1X31—'31. Subtracting 31 from 61, we get 30
as remainder. Bringing down 0, the next figure
300 in the dividend, we have 300 as the next partial
279 dividend. Dividing 300 by 31, we get 9 as a
219 quotient. 9X31- 279. Subtracting 279 from
217 300, we obtain 21. Bringing down 9, the next
2 figure in the dividend, we have 219 as the next
partial dividend. Dividing 219 by 31, we get 7
as a quotient. 7X31 -=217. Subtracting 217 from 219, we obtain
2 as remainder.
Then, 6109 gallons — 31 — 197 gallons, with 2 gallons as remain¬
der.
Therefore, the average number of gallons received daily for the
given month was about 197.
The result of division when there is a remainder is generally ex¬
pressed thus: 6109-i-31 = 197"3T-
FUNDAMENTAL OPERATIONS
To check division, multiply together the divisor and <|uotient and
add the remainder. If the result is equal to the dividend, the divi¬
sion is correct. In checking the division just performed, we pro¬
ceed as follows:
31 X 197 = 6107. 6107 + 2 = 6109.
2. The value of the work done in the Wheelwright
Shop for one year was $4500. Find the average value of
the work done per month.
3. Find the average daily sales of the Commissary for
February, 1911.
See Problem 12, page 17.
4. The sales of the Truck Garden products during
the year 1910 were as follows: January, $849.13; Feb¬
ruary, $517.70; March, $667.47; April, $1010.26; May,
$1201.26; June, $985.88; July, $1317.97; August, $857.03;
September, $672.94; October, $701.96; November,
$608.04; December, $301.48. Find the average monthly
sales.
5. The record of the eggs laid by the chickens and
ducks at the Poultry Yard for the week, January 24-30,
1911, is as follows:
January 24 87 eggs
25 63
26 79
27 79
28 81
29-30 133
Find the average number of eggs laid per day. At
this rate, about how many eggs were laid during the
month?
Di vide as indicated.
23079 — 39 40007-75 76552-96
17280-24 56258-54 90250:95
35008-48 22459-37 53659-76
98567^83 445445-89 72250 85
DIVISION
37
Exercise 16
1. In the summer of 1910, 397 dozen gallon cans of
peaches were put up at the Canning Factory. This
fruit was valued at $1885.75. What was the value per
To find the value placed upon a dozen cans
we divide $1885.75 by 397. Why?
The process of division is the same as that
given in Problem 1, Exercise 15.
Note that the decimal point in the quotient
is placed just above the decimal point in the
dividend.
2. The Institute paid $10.80 as freight charge on a
shipment of iron pipe from Birmingham, Alabama. This
shipment weighed 4500 pounds. Find the freight rate
per 100 pounds on this kind of goods.
3. The Institute received from Pheonix City, Ala.,
4 barrels of syrup, each weighing 375 pounds. The freight
rate on this syrup was $.20 per 100 pounds. What did
the freight on this syrup cost the Institute?
4. A dealer sold the Institute 3000 eggs at $7 per
100. Find cost of eggs.
5. The Brickmasonry Division, in connection with
some repair work, used the following material: 1300
bricks at $.79 per 100; 2 barrels of lime at $1.08 per barrel;
2 cubic yards of sand at $.80 per cubic yard; y barrel of
cement at $2.60 per barrel. The cost of the student
labor employed in the work was $1.44. Find total cost
of the job.
6- A vault was built in a cemetery in the town of
Tuskegee by students of the Institute. On this job were
"used 12 sacks of cement at $.65 per sack, 2 cubic yards of
dozen cans.
$4.75
397) $1885.75
1588
297 7
277 9
19 85
19 85
FUNDAMENTAL OPERATIONS
sand at $.80 per cubic yard, 2000 bricks at $.79 per 100.
The cost of students' labor was $4.20, and $.25 was paid
for hauling material. Find the cost of building the vault.
7. A car of coal received by the Institute contained
108,000 pounds of coal. How many tons of coal were in
this car, reckoning 2000 pounds to the ton?
8. The total number of gallons of milk received at the
Dairy Barn for the year 1910 was 59,590. Find the
average number of gallons received daily for the year.
Divide as indicated.
11025- 105
332869-- 367
3944384^ 563
6547328-7643
$1054.29^- 328
21280- 375
87621^ 998
2492963- 121
665417-9753
$6572.02^ 529
475000- 250
110032- 876
871061- 342
7061089-6431
$ 2983.53-4- 213
REVIEW
Exercise 17
1. On a certain day there were 12 pounds of buttef
on hand at the Creamery. On this day 66 pounds of but¬
ter were made and 14 pounds sold. On counting the but¬
ter before closing for the night, 63 pounds were found
at the Creamery. Was all the butter accounted for?
2. On another day there were 60 pounds of butter on
hand at the Creamery at the opening of business for the
day. On this day, 62 pounds of butter were made and
59 pounds sold. On counting the number of pounds of
butter left at the close of the day's business, 63 pounds
were found. Was all the butter accounted for?
3. Find out (through teacher) the amount of butter
on hand at the beginning of business, the amount
made, the amount sold, and the amount found at the
close of business on some recent day at the Institute
REVIEW
39
Creamery. Then find out if all the butter was account¬
ed for on the day under consideration.
4. On January 1, 1911, the Creamery started a new
record of the milk bottles taken from the Creamery by
the drivers of milk wagons and of those brought back.
The following is the record for January as kept at the
Creamery.
Route No.
1.
Route
No. 2.
Date
Out
Back
Out
Back
Jan. 1
43
48
22
17
" 2
45
49
73
28
" 3
58
68
21
14
" 4
51
42
24
22
" 5
41
53
10
10
" 6
45 •
53
22
20
" 7
52
65
18
17
" 8
53
5
26
27
" 9
40
41
23
25
" 10
55
60
26
20
" 11
53
51
23
25
" 12
48
44
27
13
" 13
44
60
19
26
" 14
62
52
26
23
" 15
43
47
19
17
" 16
39
45
20
16
" 17
41
46
16
" 18
63
52
25
19
" 19
46
47
18
21
" 20
54
48
18
" 21
51
60
17
5
40
REVIEW
Route No.
1.
Route
No. 2.
Date
Out
Back
Out
Back
Jan. 22
77
95
32
29
" 23
92
77
30
34
" 24
76
77
29
29
" 25
72
100
29
24
" 26
91
88
34
36
" 27
95
79
30
31
" 28
75
94
33
32
" 29
81
59
36
34
" 30
61
74
32
27
" 31
81
65
30
30
H ow did the bottle account of Route No. 1 stand at the
end of the month? Of Route No. 2? Of the Creamery?
5. The roof of the Dynamo Room was laid by the
members of the Tinsmithing Division. The material
used for this purpose was as follows: 14 boxes of tin
roofing at $15 per box; 100 pounds of solder at $.20 per
pound; G bundles of galvanized iron at $6 per bundle; 1
keg of nails, $3; 45 squares of roofing paper at $.35 per
square; 1 gallon of acid, $.50; 15 bushels of charcoal at
$.10 per bushel; 15 pounds of rosin at $.03 per pound.
Drayage and freight on above cost $85. The labor em¬
ployed on this work cost $177.85. What did this roof
cost the Institute?
6. The Institute paid $830 for 65 hogs. Find the
average price per hog.
7. During the first three months of 1911, 27 hogs
and 109 shoats, weighing in all 15,874 pounds, and valued
at $.08 per pound, were slaughtered at the Institute.
Find the value of these animals.
REVIEW
41
The J. W. Butler Paper Co. of Chicago sold the
Institute 10,000 shipping tags at $.85 per M (1000) and
allowed a reduction of l/\ (one-fourth) of the given
price. Find what the Institute paid the firm for these
tags.
9. In October, 1910, 1329 students were fed in the
Institute Dining Room at a cost of $5933.44. Find
cost per student.
10. Six girls of the Senior Class of 1911 were commis¬
sioned to prepare a dinner for six persons at an expense
of not more than $1.50. The material given to these
students for the dinner follows: ice, $.15; lard, $.03;
butter, $.14; flour, $.03; pickles, $.10; crackers, $.10;
eggs, $.10; chicken, $.35; potatoes, $.05; peas, $.10; salt,
$.02; sugar, $.15, bread, $.10; milk, $ 10. Material,
valued at $.10, was not used. Did these students stay
within expense limit?
11. The capacity of the Brewer brick machine at
Brick Yard No. 1 is 20,000 bricks per working day of
ten hours. How many bricks can be made by this
machine in one hour? How many bricks can be made
in a week, iunning full time?
12. In one kiln were burned 160,000 bricks. How
many full working days must the machine have worked
in order to turn out the bricks for this kiln?
13. The Institute shipped to the Burdell Floral Co. of
Bowling Green, Ky. the plants as given below, the price
per 100 being indicated in each case: 500 American can-
nas, $1.50; 300 Boston ferns, $3.00; 200 mixed verbenas,
$2.00; 100 whitmani ferns, $3.50; 200 coleus, $2.00; 200
42
REVIEW
red geraniums, $2.50; 100 wandering Jews, $2.00. Find
the value of the shipment.
14. The Institute bought for the Shoe Shop 1 roll of
scoured oak leather. There were 10 sides of leather in
the roll and 18 pounds to the side. Find the value of
this leather at $.43 per pound.
FACTORS AND MULTIPLES
Exercise 18
1. Name two numbers whose product is 10.
2. Name two numbers whose product is 14.
3. Name two numbers whose product is 22.
We find that the two numbers whose product is 22 are 2 and 11,
These two numbers, 2 and 11, are called factots of 22.
The factors of a number are the integers(whole num=
bers) which when multiplied together produce the given
number.
Thus, 2X3X5 — 30; then 2, 3 and 5 are factors of 30.
4. Give three factors of 12.
5. Give three factors of 36.
6. Give five factors of 60.
7. Give two factors of 56.
8. Give three factors of 66.
2X3X11—66. Then 2, 3, and 11 are factors of 66. The num¬
ber, 66, which is the product of 2, 3, and 11 is called a multiple of
each of those numbers.
The product of two or more whole numbers is called
the multiple of each of those numbers.
Thus, 21 is a multiple of 7, because 7 is one of the factors of 21.
9. Give two multiples of each of the following num¬
bers: 8, 9, 10, 6, 17, 20, 19.
10. Give three multiples of 11.
11. Give all the multiples of 3 as far as 30.
44
FACTORS AND MULTIPLES
12. Give two multiples and two factors of 15.
A number which can be exactly divided only by itself
and 1 is called a prime number.
A factor which is a prime number is called a prime
factor.
The following will be of assistance in finding the factors of num¬
bers:
A number is divisible by 2 if it ends in 0, 2, 4, 6, 8. Thus, 74
is divisible by 2. (Numbers divisible by 2 are called even numbers.
All other numbers are called odd numbers. )
A number is divisible by 3 if the sum of its digits is divisible by
3. Thus, 732 is divisible by 3, since 3 will divide 7^ 3 - 2.
A number is divisible by 5 if it ends in 0 or 5. Thus, 985 is
divisible by 5.
Exercise 19
Give the prime factors of the following numbers'.
1. 210.
The work may be arranged as follows:
2) 210
3) 105
5) 35
7
Then, the prime factors of 210 are 2, 3, 5, and 7.
2. 154 3. 165 4. 48
6. 247 7. 64 8. 100
10. 78 II. 108 12. 170
Exercise 20
1. Name a number that is an exact divisor of both 15
and 20.
2. Name a number that is an exact divisor of both
33 and 55.
5. 72
9. 230
13. 1728
FACTORS AND MULTIPLES
45
3. Name a number that is an exact divisor of both 24
and 42.
An exact divisor of two or more numbers is called a
common divisor of those numbers.
The greatest number that will exactly divide two or
more numbers is called the greatest common divisor of
those numbers.
4. Give the greatest common divisor of 12 and 18; of
20 and 30; of 22 and 77.
5. Find the greatest common divisor of 60, 84 and
132.
60 = 2x2x3x5 To get the G. C. D. of these three
84 = 2 X2X3X7 numbers, proceed as follows: 1. Get
132 = 2x2x3x11 the prime factors of each number. 2.
Write down the prime factors of the
smallest of these numbers, 60. 3. Strike out all of the factors of
60 which do not occur in each of the other numbers. The product
of the remaining factors will be the G. C. D. desired.
Thus, putting down the factors of 60 and striking out the factor
which does not occur in both 84 and 132, we have
2X2X3
Then, the G. C. D. of 60, 84, 132 is 2X2X3 or 12.
Find the G. C. D. of the following numbers:
6.
90, 126
11.
128, 320
7.
48, 96
12.
56, 72, 104
8.
13, 26, 34
13.
118, 138, 280
9.
100, 350, 500
14.
112, 231, 306
10.
71, 81, 101
1. Name a number that is a multiple of both 3 and 4.
2. Name a number that is a multiple of both 6 and 10.
46
FACTORS AND MULTIPLES
3. Name a number that is a multiple of both 8 and 12.
A number that is a multiple of two or more numbers
is called a common multiple of those numbers.
The smallest number that is exactly divisible by each
of two or more numbers is called the least common
multiple of those numbers.
4. Find the least common multiple of 4 and 6; of 5
and 12; of 9 and 12.
5. Find the least common multiple of 126, 294, 420.
126 = 2 X 3x3x7 To find the least common
294 = 2x3x7x7 multiple of these three numbers,
420 = 2x2x3x5x7 proceed as follows: 1. Get the
prime factors of each number. 2.
Writedown the factors of the largest number, 420. 3. Write
down such factors of the other numbers as do not appear in 420.
The product of all the factors thus written down will be the L. C-
M. lequired.
Thus, writing down the factors of 420, we have
2X2X3X5X7
In 126 there is one factor, 3, which does not appear in 420. In
294 there is one factor, 7, which does not appear in 420. Then,
theL. C. M. of 126, 294, and 420 is 2X2X3X5X7 X 3 X 7 or 8820.
Find the L. C. M. of the following numbers4.
6.
8,
20
12.
96,
144,
528
7.
16,
72
13.
13,
27,
61
8.
48,
108
14.
36,
108,
180
9.
144,
216
15.
55,
121,
143
10.
15,
60,
120
16.
42,
126,
378
11.
105,
150,
240
17.
11,
21,
35
COMMON FRACTIONS
Exercise 21
Students to bring to class room pocket rule, ste el quare, tailor's
or dressmaker s square, surveyor s tape, tape line—all avail¬
able instruments used in the trades for measuring length.
1. Point out on one of the measuring instruments
mentioned above the inch, foot, yard.
2. Find the mark which divides the inch into 2 equal
parts. What is each part called?
3. Find the mark which divides the inch into 4 equal
parts. What is each part called?
4. Find the mark which divides the inch into 8 equal
parts. What is each part called?
5. Students in trades requiring measuring instruments
on which the inch is divided into smaller parts will report
upon these instruments to the class.
6. How many inches in % of 1 ft? {%. of 1 foot means
1 ft.-f-4).
7. How many inches in h of 1 ft.?
8. How many inches in x/i of 1 yd.?
9. Find the number of inches in % of 1 yd.
10. Find the number of inches in of 2 ft.
2 ft. =2X12 in. = 24 in.
24 in.-^3=8 in.
11. Find the number of inches in % of 3 yd.
48
COMMON FRACTIONS
12. Find the number of feet in '4 of 4 yd.
13. Find the number of feet in of 4 yd.
14. Find the number of inches in 2 3 of 1 ft.
2 3 of 1 ft. means li of 1 ft. taken 2 times. Thus,
-3 of 1 ft. = 2X ' 3 of 12 in. = 2X4 in. =8 in. 2 3 of
1 ft. is usually written ~ 3 tt.
15. Find the number of inches in M ft.
16. Find the number of feet in 23 yd. How does this
result compare with the number of ft. in *3 of 2 yd?
17. Find the number of inches in -/i yd.
18. Find the number of pints in Y\ gal.
19. Find the number of ounces in 5 8 it).
l/z , / 3, Y\ , %8, etc., are called fractions.
The number above the line is called the numerator; the
number below the line is called the denominator. Thus,
in the fraction 23, 2 is the numerator and 3 is the de¬
nominator.
If the numerator is less than the denominator, as in %, the fraction
is called a proper fraction. If the numerator is greater than the
denominator, as in 4, the fraction is called an improper fraction.
% ft., as we have learned, may be regarded as ft. taken 3 times.
ft. is called a fractional unit. Now, ft. taken 3 times gives 9
in. Also, % of 3 ft. is 9 in.
Then, ft.=3X)^ ft■, and
34 ft.—3 ft.-: 4.
From this we see that a fraction may be regarded in two ways:
(1) as a fractional unit taken as many times as is expressed by the
numerator, and (2) as an indicated division. When we think of
as an indicated division, 3 is a dividend and 4 a divisor. In fact,
division is often indicated by writing the dividend above the divisor
in this way.
Reduction of fractions
40
Read the following fractions and explain them in the two
Ways mentioned above:
Hit. i ft), I bu.
s 7 4
t it, in. 32
4 gal. U in. U
REDUCTION OF FRACTIONS
Exercise 22
1. A bushel of corn weighs 56 pounds. How many
pounds are in -/i bu. of corn? Multiply both numerator
and denominator of this fraction by 2. Find the number
of pounds in the result. How does this result compare
with the number of pounds found in 34 bu.?
2. A bushel of beans weighs 60 pounds. How much
does t bu. of beans weigh? Multiply both numerator
and denominator of this fraction by 3. Compare the
number of pounds found in the result with the number of
pounds found in 5 bu.
3. How many inches in e yd.? Divide both numerator
and denominator of this fraction by 2. Compare the
number of inches found in the result with the number of
inches found in i yd.
4. In a ton of coal there are 2000 pounds. How
many pounds in H T.? D ivide both the numerator and
the denominator of this fraction by 5. Compare the num¬
ber of pounds in the result with the number of pounds in
IS 'T
so 1 •
From the preceding examples we have found that
Multiplying or dividing both the numerator and the de¬
nominator of a fraction by the same number does not alter the
value of the fraction>
50
COMMON FRACTIONS
Exercise 23
1. Change 5 8 to a fraction whose denominator is 16.
We see that the denominator 16 is 2 times the denominator 8.
Then,
s 2X5 x®
8 ~ o — 16.
2 x «
Reduce the following fractions to equivalent fractions having
the denominators indicated:
2
5 _...
G 1 2
7.
7
8 — 6 4"
12
_4
3.
3 ..
8 " 3 2
8.
5
6 - 2 4
13.
2
9
4.
6
6 12
9.
5
8 ~ 2 4
14.
1
G
5.
3
2 — 1 2
10.
3
10 — 6 0
15.
8
8 ■
6.
2
3 — 9
11.
1
4 1 6
16.
T
A fraction is reduced to its lowest terms when its nu¬
merator and denominator are prime to each other, that
is, have no common factor except 1.
Exercise 24
1. Reduce it to its lowest terms.
_1 6 16-7-4
2 4 24 4 6
4 4 -f- 2 2_
6 ~ 6 -f-2 3
Then, M—f
2 and 3 are prime to each other. it can be reduced immediately
to its lowest terms by dividing the numerator and the denominator
by their G. C. D., 8.
Reduction of mixed numbers
51
Reduce the following fractions to their lowest terms:
2.
2
4
9.
4
8
16. A
3.
1 6
4 0
10.
1 3
1 6
17. y
4.
8
2 0
11.
1 4
1 (5
is. n
5.
1 8
2 4
12.
2 0
3 2
19. -h
6.
6 4
1 4" 4
13.
2 2
4 8
20. ^
7.
5 6
14.
8
1 0
21. ^
8.
1 2
l r>
15.
2 1
3 G
22. n
REDUCTION
OF
MIXED
NUMBERS
On one day the Creamery sold 7 whole quarts of cream
and 3/4 of a quart of cream. In the record at the Cream¬
ery, this quantity of cream was written 7qt., which
means 7 qt. + -iqt.
A number like7?4, consisting of an integer (whole
number) and a fraction, is called a mixed number.
Exercise 25
Reduce l-/\ to fourths.
1= T
7 7 X | /
2. 8_ I 3 — 3 1_
4 I 4 4
-3 31
/ 4 — 4
Change the following to improper fractions:
51
6i
4i
2f
8}
92
101
4g
3tV
7-i r,
141
12i
371
871
62i
16!
33-J
661
1U
81
llli
2H
14?
106 g
58U
99 z
00
oo
52
COMMON FRACTIONS
Reduce V to a mixed number.
VVe have learned that a fraction is an indicated division. Then, -i-1-
means 11 : 4. Performing the division indicated, we get = 24 .
'Rjduce the following fractions to mixed numbers or integers:
1 6
3 3
3 2 1 2
10# 12 5
1 6 4
3__9 SLl
10 0 0 3 33
" "K " '7
ADDITION
Exercise 26
1. Find the sum of i and t.
■|=4"5 The L. C. M. of the denominators,
4 1 , 3 and 5, is 15. Reducing each frac-
s 15 tion to fifteenths, we find that +,• ■=
10,12 _2 2 17 10 ,4 12
15 + 15=15=11 5 1 5 , and 5—15.
10 fifteenths +12 fifteenths=22 fifteenths. Can you find the sum
of | and without reducing each fraction to the same denominator?
The L. C. M. of the denominators of two or more fractions is called
the least common denominator (L. C. D.) of these fractions.
Add the following fractions'.
ADDITION
53
10.
11.
12.
13. l'^e, if 2~, e'4
14. A, ,;V.. -A-
TC S - _7._
AO. 8 , 10, 40
16. The Institute bought of Carson Pirie Scott Com¬
pany of Chicago 8 bolts of gingham, the number of yards
in the 8 bolts being as follows: 31J4, 31 ;4, 28/2, 31/2,
33-/i, 30>4 , 30, 32*2. Find the total number of yards of
gingham bought.
311 = 311
311 = 331
281 = 281
311 = 311
331 = 331
301 = 301
30 =30
321 = 321
248V = 2511
To find the total number of yards purchased,
we must add as indicated. The fractional
parts of the numbers are first reduced to the
least common denominator and added. The
sum of the fractional parts of the numbers is
the sum of the integers, 248
is 248 —|— 4 . -
248 + ^ = 2511.
= 3f, or
3l.
The result
Then,
The eight bolts of gingham contained 251 yards.
17. The number of gallons of whole milk sold by the
Creamery on its two wagon
March, 1911, is given below.
routes for the month of
Date
Gal Ions
Date
Gallons
Date
Gal Ions
1
16-8
11
18
21
19
2
21
12
21
22
18
3
1858
13
20
23
17
4
18
14
20
24
16^
5
19 M?
15
21
25
©
C\)
6
17-. 8
16
21/2
26
19lA
7
19 K
17
18 h
27
15
8
17?4
18
19
28
18
9
22
19
23
29
18
10
20
20
145 o
30
17
31
16
COMVION FRACTION'S
Find the total number of gallons of whole milk sold on
the two routes during the month.
18. A skirt made in the Dressmaking Division was
39 inches long when finished. This skirt had one
tuck requiring \ Vi inches of cloth and a hem requiring
3-H indhes. How long should the cloth have been cut
for this skirt?
19. Another skirt was 38^2 inches long when finished.
How long was the cloth for the skirt cut, if 1,'j. inches
Were allowed for one tuck, 2 /2 inches for another tuck,
and 4j'4 inches for the hem?
20. A uniform skirt made for a student in the Nurse
Training School was 40 inches long when finished. This
skirt had a 5-inch hem and two 2-inch tucks. L2 of an
inch was allowed for turning the hem and 12 of an inch
for a seam at the top. How long was the cloth cut for
this skirt?
21. The sleevelets forming a part of the uniform just
mentioned measured 8inches when finished. 2 inches were
allowed for hem at each end and )\ of an inch for turn¬
ing each hem. How long was the cloth for each sleevelet
cut?
22. At the Blacksmith Shop the rim of a wheel meas¬
ured 125 aft. How long a piece of iron was used for the
tire of the wheel. -4 in. being allowed for welding?
Add the following:
23. 7 J, 8h
24. 91, 7IsG
25. 121, 8fr
26. 13A, 175
27. 211, 13 L HI
28. 25tV, 102-, 331
29. 331, 181 f;, 24-,5o
30. 67? 451, 1071
SUBTRACTION
55
SUBTRACTION
Exercise 27
1. From i take f
The L. C. D. of the two fractions is found to he
24. Each fraction is reduced to 24ths and the
difference found as indicated.
Subtract as indicated.
2.
3 5
4 — 8
7. i
2
— 3
12.
1 5 3
2 4 — 16
3.
1 1
4 — 16
8. n
8"
13.
9 4
10 — 5
4.
7 3
16 — 8
9. 1-6
3
— 32
14.
3 3 3
4 0 — "4
5.
1 1
3 — 12
10. i
1 y
— 6 4
]5.
s 1
9 — 6
6.
2 3
3 — 8
11. II
— TT
16.
2 1 5
6 4 — 16
17. 121 — 9!.
121 = 111 =llfl Show that 12f=ll|. Why is
91= 91 = 9i®2 12~3 changed to 11-| before the
2 It subtraction is begun? Explain
processs fully.
18. 13! -51 22. 40x6—22! 26. 561 -31/,
19. 25i -19A 23. 62,^- 17.2 27. 731 -151!
20. 100H-58U 24. 341 -171 28. 47H-39I
21. 981 — 76f 25. 6911-431 29. 18H-8II
30. Sugar that cost the Institute 5/8 f per pound
was sold at the Commissary for 67/3^ per pound. Find
the gain on one pound of sugar.
31. When a student was measured for a pair of
trousers, at the Tailor Shop, the measurement for the out¬
side seam was found to be 42y?". The tailor deducted
\l/i" for the rise in front and added Y\" for the fall in the
back of the trousers. ?■]'{" was allowed for the hem.
How long wa« the cloth cut in the front, at the outside
seam, and at the back of the trousers?
S6 COMMON' FRACTIONS
32. The measurement of the outside seam of another'
pair of trousers was found to be 41 x'\". 1 1 -j " was de¬
ducted for the rise in front and added for the fall in
the back and 2/4" was allowed for the hem. How long
was the cloth cut in the front, at the outside seam, and af
the back of these trousers?
MULTIPLICATION
Exercise 28
1. At the Institute Brick Yard, it is estimated that 3_t
of a cord of wood is required to burn a thousand bricks.
How many cords of wood were required to burn a kiln of
160 thousand bricks?
If to burn 1 thousand bricks requires 3j- cord of wood, to burn 160
thousand bricks requires 160 times as much, or, 16(>X:1i cord.
160X3 fourths 480 fourths (44~)
---J- = 120.
Then, it required 120 cords of wood to burn the kiln of 160 thousand
bricks.
2. According to the preceding problem, give a rule
for finding the product of an integer and a fraction.
The process of multiplying, when one of the facto.s is a fraction,
can often be shortened by first indicating the product and then
canceling, that is, striking out the common factors in the dividend
(numerator) and divisor (denominator.) Thus,
40
160X .3='«X3 = 4qx3 = 120
In this case the common factor 4 is struck out of 160 and 4. Upon
what principle does cancellation depend?
Multiplication
1 he Institute bought for the Shoe Shop from the
Atlanta Leather Company three calf skins, the total
weight of which was 6-4 pounds. This leather cost $1.35
per pound. How much did the Institute pay the firm
for the leather?
$1.35 To find the amount paid for the leather, we multi-
6 >4- P'y $T35by6'\\. Why?
810 6X$1-35=$8.10
101 Ti , r 3X$1.3S " $4.05 ^ 1
1W1 4 4X$1-3S = —-7^ — = - — $1.0li
•$'9.11 K .
64 X $1.35 = $8.10 +$1 .OtI = $9 11-4
Then, the Institute paid the firm $9.11 for the leather.
4. At the Institute Harness Shop, 17 pounds of
harness leather valued at $.35 per pound were used in
making a set of medium buggy harness. Find the value
of the leather used in making this set of harness?
5. In making some crates for the Piggery, the Carpen¬
try Division used $2.77 worth of material. On this job
three workmen were employed. One hired man worked
7/^ hours at $.25 per hour; another hired man worked
3Y hours at $.25 per hour; one student worked 5 hours
at $.05 per hour. Find total cost of job.
6. The materials used in making a suit at the Tailor
Shop were as follows: 3/4 yd. of black unfinished worst¬
ed at $3.00 per yd.; 1% yd. of black Italian lining at$1.24
per yd.; 1Y yd. of silk sleeve lining at $.55 per yd.; 34yd.
of vest lining at $.45 per yd.; 1 yd. of shrunk linen duck
at $.24 per yd.; 1 yd. of wire cord silesia at $.19 per yd.;
1 yd. of wigan at $.11 per yd.; ^ yd. Holland (linen) at
$.25 per yd.; Y\ yd. of padding at $.65 per yd.; l/i yd. of
hair cloth at $.40 per yd.; H yd. of twill pocketing at
58
COMMON FRACTIONS
$.21 per yd.; Y- yd. of waist band canvas at $.21 per yd.
The buttons used were estimated to be worth $.15. Find
total cost.
7. During November, 1910, a girl in the Dressmaking
Division finished 4 pieces of work for which she received
$.12 Y a piece. How much did the student earn in this
way for the month?
$ 12
By multiplying $.12^ by 4, we find the amount
received by the student for the 4 pieces of work.
48 4X12^=4X 7^+4X12
$.50 4X^=2;4X12 = 4S
Then, 4X12^=2-^48 = 50.
8. The uniform waist worn by the Institute girls in
the spring of 1911 cost as follows:. 8 yards of madras at
$.08>2 per yard; buttons, $.08; thread $.02X1; labor, $.25.
The waists were sold for $.65. Find gain on each waist.
9. The uniform skirt of a girl made in the Dressmak¬
ing Divis'on required 5 yards of percale at $.12/2 per yd.
Other items of expense in connection with the making of
the skirt were: 1 spool of thread at $.05; 2 hooks and
eyes, $.01; four (Vs dozen) buttons at $.10 per dozen;
the labor of one girl 9 hours at $.03 per hour. The
skirt sold for $1.00. Find the gain on this skirt.
10. In making a shirt waist, 2/2 yards of lawn at $.20
per yard were used. On this same waist, there were used
1 dozen buttons, $.10; 1 spool of thread, $.05; and 2 yards
of lace at $.15 per yard. The cost of making the waist
was $.35. Find the total cost of the waist.
11. The hats worn by the Senior girls in 1911 were
made in the Millinery Division. Each hat required the
MULTIPLICATION
following: 3 bolts of straw at $.62per bolt; 134 yards
of silk at $.50 per yard; wire, $.15; cheese cloth, $.08;
thread, $ 03. Find total cost of materials used in making
one of these hats.
12. The Tinsmithing Division made two refuse boxes
for use in the Boarding Department. Each box requir¬
ed 1/4 sheet of galvanized iron. Each sheet of such iron
Weighed 40 pounds. This iron cost $.04 per pound. To
make one of these boxes required the labor of one student
5 hours at $.03Y?. per hour. Find total cost of the two
boxes.
13. On one day six students worked 5 hours staining
some railing in the Shoe Shop. Three of these students
received $.02 Y per hour; one student received $.03 Y* Per
hour; each of the remaining two students received $.02
per hour. The gallon of stain used on the job cost $1.60.
Find total cost of the work.
14. The House and Sign Painting Division in some
work done at the Poultry Yard Used the following: 2
gallons of gray paint at $1.70 per gallon; 2 gallons of
slush paint at $1.00 per gallon; 1 gallon of No. 7 paint
at $1.70. On this job were employed 3 students 4/4
days, each at the rate of $.50 per day, and 1 man Y* day
at the rate of $2.50 per day. Find cost of the job.
15. To "hard oil" some woodwork in Cassedy Hall
'required 1Y2 gallon of hard oil at $1.70 per gallon. Y\
gallon of turpentine at $1.00 per gallon, and one box of
Washing powder, $.05. The labor employed in this work
cost $2.10. Find cost of work.
16. The Institute bought for the Printing Division 12
reams of paper, each ream weighing 75 pounds at $.06><4
per pound. Find cost of paper.
fr'O
COiVhMON FRACTIONS
17. The Institute shipped to the Virginia Nursery-
Co., Purcellville, Virginia, the following plants: 100 sal¬
vias at $.02 each; 75 verbenas at $.02 each; 50 white ge¬
raniums at $ 02/^ each; 25 red geraniums at $.02/2 each;
75 coleus at $.02 each. Find the value of this shipment.
18. The Creamery has two wagon routes on which
it sells dairy products to its customers. On Route No. 1,
two trips are made daily. At the beginning and end of
each trip, the products in the wagon are checked and the
quantity recorded. The following is the record of the two
trips made by the wagon on Route No. 1 on April 3, 1911.
Morning
Aft
ernoon
Out
Back
Out
Back
Whole milk
Gallons
7
2
Quarts
12
1
9
5
Pints
3
10
1
Halves
4
1
10
1
Cream
Quarts
2
l'/s
1
X
Skimmed milk
Gallons
15
4
Buttermilk
Gallons
9
Butter
Pounds
8
3
4
On this route the price of the whole milk was as follows:
gallons, $.28; quart, $.07; pint, $.04; half pint, $.02.
The cream sold at $.40 per quart; the skimmed milk, at
$.08 per gallon; the buttermilk at $.10 per gallon; the
butter at $.28 per pound. Find the value of the sales on
this route for the given day.
MULTIPLICATION
61
19. In the shop of the M attressmaking Division,
double mattresses are made 6 ft. 4 in. long and 4 ft. 6 in.
wide. In estimating the amount of cloth to be used, for
every foot and fractional part of a foot in the length, in.
is to be added for tufting. The same addition is to be
made to the width. The border (boxing) is cut 5 in.
wide. In making one such mattress ticking 30 in. wide
and costing $.15 per yard was used. There were also
used 45 pounds of linters (cotton) at $.04 per pound, 5
pounds of corn shucks at $.02 per pound, and tv\ ine, $.05.
One girl working one day for $.25 made the complete mat¬
tress. Give drawing to show how you would cut the
cloth. Find the cost of producing the mattress.
20. A single mattress made in the shop mentioned
above measured 6 ft. 4 in. long and 2 ft. 9 in. wide. The
following materials were used in making this mattress: 20
pounds of linters at $.04 per pound; 5 pounds of shucks
at $.02 per pound; twine, $.03. The boxing (border)
was cut five inches wide. The ticking used cost
$.15 per yard. One girl worked ^2 day at the rate of
$.25 per day in making the mattress. Making allowances
for tufting as in the preceding problem, find the cost of
producing this mattress.
Exercise 29
1. Find a scale (on steel square, tailor's square, pocket
rule, or other instruments) in which % in. is divided into
3 equal parts. Counting the number of such parts in 1
inch, we find that in 1 inch, there are 12 such parts.
Each of these parts is iV of an inch.
Then, 3 of = , or what is the same thing,
i \/ i// X—H
3X4 — 12
COMMON FRACTIONS
Suppose that we are required to find § X 5« that (s,
§ of I".
Now, we have already found that
-1- v -1"
3X4
^ L-//
— 12 •
Since
2
3
X
CM
Jl
— v ?
3 X 4
X
CM
II
Since
II
CO
X
iXT"
= 3Xtt"
Since u-fxl, we see that
To multiply one fraction by another fraction, we multiply the
two numerators together and the two denominators together and
write as result the product of the numerators over the product
of the denominators.
Give the products indicated. Cancel whenever possible.
2. k x6. 3^x1 10. Hx -!
3. fx! 7. tVXt 11. ifx 4
4. ixif 8. Axt 12. IX~h
5. TeXf 9. Hxt 13. 11X It
14. 5/^x7^ (Reduce each mixed number to an im¬
proper fraction before multiplying).
15. 51 x 61 19. lOA- Xll
16. 91x31 20. 51 x3!
17. 4-Hrx-t- 21. <rV x5l
18. SAxlvV 23. lit x4-}
23. In making an overcoat at the Tailor Shop, Y\ yd,
of chamois pocketing was used. This pocketing cost
$.12^2 per yard. Find value of the pocketing used on the
overcoat.
MULTIPLICATION
63
24. The Institute bought from the Ahrens and Ott
Mfg. Co., Louisville, Ky., 20% pounds of block tin at
$.36Vt. per pound. What was paid for this tin?
25. Bernard Frank & Co. of Montgomery, Ala.
sold the Institute 5 pieces of organdie containing 118^<4
yards at $.ll34 per yard. Find the cost of this cloth.
26. The cost of a hat made in the Millinery Division
was as follows: Wire shape, $.85/4; lining, $.26; straw,
2>2 bolts at $1.12/4 per bolt; thread, $.08^ ;velvetband,
$.37/4; 5 yards of silk ribbon at $.40 per yard; 2 hat pins
at $.37/4 each; labor of one student, 2 days at $.25 a day.
This hat was sold for $7.85. Find gain.
27. An individual sold the Institute for use in the
Canning Factory 2/4 pecks of figs at the rare of $.50 per
bushel. Find what was paid for these figs.
28. The Institute bought at one time of Schloss &
Kahn of Montgomery, Alabama, 250 pounds of oats at
$.62/4 per bushel, and 500 pounds of oats at $.44 per
bushel. Reckoning 32 pounds of oats to the bushel,
find the total cost of the above purchase.
Exercise 30
1. On one day 900 pounds of cotton seed meal were
used at the Dairy Barn as part of the feed for the cows.
Find the cost of this meal at $27.00 per ton.
2000 pounds =1 ton
1 pound = 2_oVo" ton
900 pounds = 900 X 2~oV"o ton = 2% ton
The cost of 1 ton of meal =$27.00
Then, the cost of 2% ton of meal = 2S-X$27.00 = $-2-~!<rfl-=$12.15
Therefore, the 900 pounds of meal cost $12.15.
(U
COMMON FRACTIONS
2. Other feed-stuffs used for the cows on the abcivt?
date were 5400 pounds of corn ensilage at $5 per ton,
2700 pounds of cotton seed hulls at $9.40 per ton, 100
pounds of bran, $1.50. Find total cost of feed of cows
for the day.
3. The Institute bought of the Jas. Clark, Jr. Electric
Co., Louisville, Ky., 30 sockets at $19.80 per 100, 500
feet of No. 14 rubber covered wire at $7.95 per 1000 feet,
150 feet of No. 10 rubber covered wire at $14.50 per
1000 feet, 228 feet of No. 6 rubber covered wire at
$30.80 per 1000 feet, 150 feet of lamp cord at $1.31 per
100 feet, 25 rosettes at $.05 each, 1 switch, $.77, 6 snap
switches at $.46 each, 420 porcelain knobs at $2.10 per
100, and 100 insulators, $3.99. Find total value of this
purchase.
4. The Institute sold an instructor a load of coal
weighing 1200 pounds. This coal was sold for $4.00
per ton. Find the value of the load of coal.
5. On one day the Brickmasonry Division repaired
the furnace of Heating Plant No. 2. There were used
for this purpose 250 bricks at $7.90 per 1000 and 1 bar¬
rel of mortar valued at $.40. The labor of the student9
employed in this work cost $1.20. Find cost of this re¬
pair work.
6. A recipe for corn bread requires the following: Y'l
cup of flour, /4 cup of meal, 2 tablespoonfuls of baking
powder, 2 tablespoonfuls of melted lard, 1 tablespoonful
of sugar, 1 teaspoonful of salt, r/8 pint of milk, 1 egg.
Find the cost of the materials required by this recipe at
current prices. (Students will secure from the Cooking
Division all necessary information, such as the number of
cups of flour to one pound, etc.)
COMMON FRACTIONS
es
1. A recipe for muffins follows: 1 cup of sweet milk,
l/i teaspoonful of salt, 1% cup of flour, 1 tablespoonful of
sugar, 1 yi teaspoonful of baking powder, and 1 tablespoon^
ful of melted butter. Find cost of the materials for this
recipe at curreht prices.
8. A recipe for biscuits requires 1 dup of flour, 1
tablespoonful of butter, cup of milk, % tea^-
spoonful of salt^ 2 teaspoonfuls of baking powder Find
cost of the materials for this recipe at current prices.
9. Students in cooking classes will report recipes and
show how they estimate the cost of same.
DIVISION
Hxercise 31
1. The heavy lines on some paper ruled At the frint-
irig Office divided the sheet into ciolumns re in. wide. The
lighter lines divided each of these columns into 3 equal
parts. What was the width of the smaller columns?
To find the width of the smaller columns, we divide 1% in by 3.
We have learned that to divide any number by 3 means to find f/i
of that number.
Then,
-■re in. -4- 3 = 3 of -re in.
3
10. 3
X —'n. = in.
3 16 16
Then each of the smaller columns was i% in. in width.
~3~ is called the reciprocal of 3>
In fact, the reciprocal of any number is 1 divided by that number.
Thus, the reciprocal of 8 is "g".
We see from the above that
To divide a fraction by an integer, multiply by the reciproc-
tal of the integer.
66
DIVISION
8.
5
9.
tW 4
10.
31 . 7
64 — /
11.
6
12.
A-5-14
13.
ii
Divide as indicated. Cancel when possible.
2. } -2
3. I -4
4. I -2
5. i%-5
6. ! -3
7. f — 4
14. 5T/3—8 (Red uce mixed number to improper frac¬
tion before dividing).
15. 91-11 19. 121- 7
16. 7f — 5 20. 33i —10
17. 31- 9 21. 151- 3
18. 8f —4 22. Ill- 8
23. 216J-5
Without reducing 2161 to an improper fraction, the work may be
performed as follows:
5)216f 216 — 5 = 43, with 1 as a remainder.
43Vff U-5=txi = 27o
24. 1121
25. 3761
26. 501f
27. 100^
28. 2111
29. 7061
30. 143i
31. 3607^
3
9
12
4
32. At the Institute Tailor Shop in locating the but¬
ton holes upon a coat, the tailor first decides upon the
location of the first and last buttons. On a uniform coat
made in the shop, the distance from the first button to
the last was found to be 1Z1/?". There were five buttons
on this coat, the distance between any two successive
buttons being the same. How far apart were the buttons
placed on this coat?
COMMON FRACTIONS
13. On another uniform coat the distance from the
first to the last button was 14?4"> There were 5 buttons
on this Coat. Find how far apart the buttons were
placed.
14. On a three-button coat, the distance from the
first to the last button was 11/4 inches. Find how far
apart the buttons were placed.
15 On another three-button coat, the distance from
the first to the last button Was 10 v/\ inches. How faf
apart were the buttons placed?
16. In a two-horse wagon made in the Institute shops
the width of the bottom of the body was 41%//. The
front cross bar was 47// long. The bottom was nailed to
the front cross bar so as to be the same distance from
each end of the bar. Find the distance from the end of
the bar at which the mechanic should begin to nail the
bottom. See wagon.
17. Find out (through teacher) what is a mortise and
tenon joint. At the Wheelwright Shop, in making a
wheelbarrow, it Was necessary to locate a Vb" mortise in
a 2" handle. Show how this mortise is located.
18. On the 1/4" sill of a wagon there is a }4" mortise.
Explain how this mortise is located on the sill.
19. Secure (through teacher) other examples of
mortise and tenon joints from the actual Work of the In¬
stitute Shops. Show in each case how the mortises and
tenons are located.
Exercise 32
1. A student in the Wheelwright Division was given
a working draft (drawing) of a milk wagon according to
68
DIVISION
which he was to build the wagon. On this drawing Y\
in. represented 1 ft. The width of the door of the wagon
appeared as 1^2 in. How wide did the student actually
make the door of the wagon?
If Mm. on the drawing represented 1 ft., then, for every >4 in. in
l/^in. there was 1 ft. in the actual width of the door. To find the
width in ft. of the door, we must divide 1 ^2 in. by ~/\ in.
II . 3 3 . _3
±2 -r- 4 = 2 — 4
Since 1 — 4 ,
l-j-4: = 4, and
l-f = iof 4=!
2
3 3 3,43 4
Then, 2 - 4"~ 2 3 ~ f X 3
The actual width of the door of the milk wagon was 2 ft.
We see from the solution of the preceding problem that
To divide a fraction by a fraction, invert the terms of the
divisor and multiply.
2. The height of the same door was represented on
the drawing by 2Y\ in. Find the height of the door.
3. On the working draft of a mail wagon built in the
Institute Shops, the length of the wagon was represented
by 10/^ in. and the width, by in. On this drawing,
1/4 in. represented 1 ft. Find the length and width of
the mail wagon.
4. The Institute bought for the Paint Shop 379
pounds of linseed oil at $.89 per gallon. Find the
amount paid for this oil, reckoning 7/^ pounds of linseed
oil to the gallon.
5. The Mattressmaking Division received two bolts
of white sheeting, one consisting of 41/2 yards and the
other, 34 yards. Find the number of sheets that were
made from this sheeting, 2/4 yards being used for each
COMMON FRACTIONS
69
sheet. Find the cost of each sheet, if the sheeting cost
$.23 per yard and the thread, labor, etc., cost $.10 per
sheet.
6. The Printing Division made 500 letter heads,
measuring 8/^'Xll", for use in one of the offices in the
Institute. The paper from which these letter heads
were cut came in sheets 17//X22// weighing 20 pounds
to the ream, and costing $.14 a pound. How many sheets
were used in making the 500 letterheads? Find the cost
of the paper so used. Make drawing to show how the
sheets were cut so as to have no waste. See specimen of
paper furnished by teacher.
7. Daily record blanks made by the Printing Division
measured 8^2//Xl4.// The sheets from which these
blanks were cut were 28" long and 11" wide, weighed 20
pounds to the ream, and cost $.10 per pound. Find the
cost of the paper used in making 2500 of the record
blanks.
8. The absent and tardy blanks used in the Academic
Department in 1911 measured . Th ese blanks
were cut from stock measuring 17//X22.// This paper
weighed 16 pounds to the ream and cost $.08 per pound.
Find the cost of the paper used in filling an order for
10,000 of these blanks.
9. The paper kept in stock at the Printing Office on
which The Southern Letter is printed measures 24//X36,//
weighs 70 pounds to the ream, and costs $.08 per pound.
Measure a copy of The Southern Letter and compute the
cost of the paper required by an issue of this monthly for
which 15,000 copies were printed.
10. M easure one of the monthly statements given to
students of the Institute. Secure (through teacher)
sufficient information from the Printing Office to allow
you to compute the cost of the paper in lU,000 of these
blanks.
70
common fractions
Exercise 33
1. A reduction of %. of the list price was given ofl
some goods purchased by the Institute. The amount
paid for the goods Was $300.15, What was the list price
of the goods?
The Institute paid ^4 of the list price for the goods. Explaifi.
34 of list price of goods = $300.15
34 list price of goods = "3 of $300.15— $100.OS
T of list price of goods — 4 X $100.05 = $400.20.
Then, the list price of the goods was $400.20. What is meant by
the "list price" of goods?
2. The weight of 1 cu. in. of cast iron is about if of
the weight of 1 cu. in. of wrought iron. A piece of
machinery cast at the Foundry weighed 97^3 pounds.
What would the same piece of machinery weigh if made
of wrought iron?
3. The threaded Dart of a screw is y%" long. On this
Screw there are 28 threads. How many threads are there
on a screw of the same kind whose threaded part is V
long?
4. Another screw whose threaded part is long has
10 threads. How many threads are there on a screw of
the same kind whose threaded part is V long?
5. If "H- of a number is 121, what is the number?
6. If tV of a number is 75, what is the number?
7. If ~T2 of a number is 4.0/4, what is the number?
8. If f of a number is 23%, what is the number?
9. If iV of a number is 2, what is the number?
10. If I of a number is /3, what is the number?
AREAS AND VOLUMES
AREAS
Using the steel square or the dressmaker's square, draw
on the board a figure of four sides, making each side 1
foot long and taking care to "square" each corner by
means of the instrument.
Such a figure, having four equal sides and four square
corners (right angles) is called a square-
The amount of surface in this figure is called 1 square
foot.
Just as cloth is sold by the yard, coal by the ton, milk
by the gallon, etc., so certain other goods are sold by the
square foot, as, the slate blackboards in the Academic
Building, the stained glass in the windows of the Chapel,
and certain kinds of leather used in the Harnessmaking
Division.
A figure, like the drawing below, which has four sides
and four right angles (squared corners) is called a rectangle
Is a square a rectangle?
| This figure represents a rectangle 4
feet long and 3 feet wide. ( % in. rep-
resents 1 foot.) The horizontal lines
' divide the rectangle into three strips
each 1 foot wide. The vertical lines
divide each of these strips into 4 square feet. Then,
there are, in all, 3x4 sq. ft. or 12 sq. ft. in the rectangle.
The number of square units—square inches, square
n
areas and volumes
feet, etc., in any figure (surface) is called the area of that
figure. Thus, ift the above figure, the area is 12 square
feet.
The area of a rectangle is given by the product of the numbers
that express its length and width in the same units.
1 he length and width of a rectangle are called its
dimensions.
Exercise 34
1. A piece of calf skin in the Shop was fouftd to DC
48" long and 30" wide. This leather cost $.40 per sq. ff»
Find the cost of the piece of calf skin.
48" = 4'
30" *= l\'
4X2*2 X 1 s<|. ft. — 10 sq. ft., the area of the skin.
Since 1 sq. ft. of this leather cost $.40, then 10 sq. ft. of the
leather cost 10X$-40 or $4.00^
Therefore, the piece of calf skin cost $4.00.
2. Measure the slate boards in Room 24, Academic
Building. This slate cost $.16 per sq. foot. Find the
cost of the slate out of which the boards of this class room
are made.
3. The back of a buggy seat built in the Institute
Shops measured 18"x30". In cutting the leather for this
back, there were added to the length 9" for pleating and
6" for finishing; there were added fo the width 6" for
pleating and 5" for finishing. This leather cost $.27 x/i per
sq. ft. Find the cost of the leather used for this back.
4. The seat cushion of the same buggy was 28" long
and 17" wide. In cutting the leather, there were added
to the length 8" for pleating and 4" for the finishing;
AREAS AND VOLUMES
73
thefe were added to the width 5" for pleating, and 5" for
finishing. The leather of which this seat cushion was made
was the same as that mentioned in the preceding problem.
Find the cost of the leather used for this cushion.
5. The dash board of the same buggy was 20" long
and 16" wide. Both sides of a dash board are covered
with leather. In Cutting the leather for each side, 2r>
Was added to the length and 4" to the width for finish¬
ing. Find the Cost of the leather used to cover the dash
board, this leather being worth $.25 per sq. ft.
6. Class will visit Carriage Trimming Shop and esti¬
mate cost of leather used in trimming a carriage in the
shop at the time of visit,
7. To find the cost of the flooring of a room, proceed
as follows: Find in square feet the actual area to be
covered; then add to this result %. of the area found.
This gives the number of sq. ft. of lumber required. Find
the cost of the lumber required to floor your class room at
current prices.
8. Secure (through teacher) information concerning
the method used at the Institute in estimating the cost of
plastering. Compute the cost of plastering your class
room.
VOLUMES
Examine one of the ordinary bricks made in the Insti¬
tute Brick \ ard.
How many measurements are necessary to give you an
idea of the size of the brick?
How many measurements are necessary to give you an
idea of the size of orte of the faces of the brick?
A solid of the shape of a brick, all of Whose faces are
rectangles, is called a rectangular solid.
74
AREAS AND VOLUMES
In estimating the cost of the brick-work in a given
structure, it is, of course, necessary to know the number
of bricks required. One method used by brickmasons is
to reckon a certain number of bricks to each cubic foot of
the structure to be built.
We shall now proceed to find out what is meant by a
cubic foot.
Observe the cubic foot of wood exhibited by teacher.
How many edges has it? Measure the length of each
edge. What figure does each face make? What is the
area of each face?
Every solid of this shape is a cube. Then, what is a
cube? What is a cubic inch? A cubic yard?
Construct by means of wooden cubic inches (supplied
by teacher) a rectangular solid that is 5" long, 4" wide,
and 3" high. You thus obtain a rectangular solid with 3
layers of cubic inches. Each layer contains, as you can
find by counting, (4x5) cu. in., or 20 cu. in. Then,
the three layers contain (3x4x5)cu. in., or 60 cu. in.
The number of cubic units—cubic inches, cubic feet,
etc., in any solid is called the volume of the solid. Thus,
the volume of the solid just constructed is 60 cu. in.
The volume of a rectangular solid is given by the product of
the numbers that express its length, width, and thickness in the
same units.
The length, width, and thickness of a rectangular solid
are called its dimensions.
AREAS AND VOLUMES
75
Exercise 35
1. At $7.90 per M ( 1000), what is the cost of the
bricks in one of the walls of White Memorial Hall that is
20' long, 18" thick, and 20' high. Count 22 bricks to 1
cu. ft.
18"^ ii'
1^X20X20X1 cu. ft. —600 cu. ft., the volume of the wall.
600X22 bricks = 13,200 bricks.
13,200 ^-1000^ 13^, the number of thousand bricks in
13,200.
l3iX$7.90 = $104.28. cost of 13| thousand bricks.
Then, the bricks in the wall cost $104 2$.
2. The truss plates used in the construction of Tomp¬
kins Hall were cast at the Institute Foundry. Each plate
is 2"x22"x28." One cu. in. <>f cast iron weighs about
U of a pound. At $.02 a pound, what is the value of
one of these plates?
3. The four foundation plates for the Institute Watef
Tank were also cast at the Foundry. Each plate meas*
ures 2"x28"x28." At $.02 a pound, what is the value
of the four plates?
4. The frame for- a manhole Cast at the Foundry
measured i"X26"X26." Find the cost of this frame at
$.02 per pound, deducting 186f cu. in. for the hole in the
frame and adding 20 pounds for the lip of the frame.
5. What is the cast iron mentioned in the preceding
problems worth per cu. ft ?
76
AREAS AND VOLUMES
6. How many cu. in. in a 16-pound sash weight cast
at the Foundry? If such a mass of iron were cast in the
form of a rod 2" square at the ends, how long would the
rod be?
7. Find out (through teacher) the dimensions of a
pattern of simple shape recently cast at the Foundry,
and estimate the value of the same.
8. A farm wagon built in the Institute shops had a
bed 1' 6" long, 3' 2" wide, and 10" high (inside measure¬
ments). Find the capacity of this wagon in cu. ft. How
much does it lack of holding a cu. yd.?
9. Another wagon had a bed 8' long, 3' 2" wide, and
15" high. By how much does its capacity exceed 1 cu.
yd.?
10. Class will visit the Wheelwright Shop and compute
from actual measurement the capacity of wagons under
construction.
REVIEW
Exercise 36
1. The Senior girls in Practice Cottage used the fol¬
lowing supplies for the week beginning Dec. 30, 1910:
2 pounds of pork at $.12i per pound; 2 dozen oysters at
$.10 per dozen; 2 cans of pears at $.25 a can; 1 pail of lard,
$.35; 10 pounds of sugar at $.062" per pound; 1 quart of
syrup, $.10; 1 box of corn flakes, $.10; 1 dozen eggs, $.30;
1 cake of chocolate, $.25; 1 bottle of flavoring, .$05; 1
peck of potatoes, $.35; 1 sack of flour, $.40; i peck of
meal, $.25; 1 \ pounds of bacon at $.20 per pound; 1 chick¬
en, $.40; 2" dozen onions, $.10; 3 bars of soap at $.05 each;
1 broom, $.40; 1 gallon of oil, $.15; 1 box of starch, $.05;
1 box of bluing, $.05; 2 cans of tomatoes at $.08 each; 2
cans of peas at $.071 each; 1 box of macaroni, $.07. Find
the cost of these supplies.
2. On one day, 400 dozen biscuits were made in the
Bakery. In making these biscuits, the following materials
were used; 280 pounds of flour at $.03i per pound;
cans of milk, 10 gallons to the can, at $.08 per gallon; 5
pounds of salt at $.01 per pound; 40 pounds of lard at $.12
per pound; 10 pounds of baking powder at $.11 per pound.
Find the cost of the materials used in making the biscuits.
78'
REVIEW
3. The standard sizes of flat paper used in the Print--
ing Division are given below. The numbers give the
width and length in inches.
Flat Foolscap 13X16
Cap 14 X ^
Crown 15X19
Demy 16X21
Folio Post 17 x 22
Medium 18x23
Double Flat Foolscap ......16x26'
Royal 19 x 24
Double Cap 17x28
Super Royal...... . 20x28
Double Demy 21x32
Double Demy, Oblong 16X42
Imperial ... -^3x31
Double Medium 23 x 26
Double Medium, Oblong 18x46
Elephant 23 x 28
Colombier • ■ ■ ■ 23 x 34
Atlas , ,••••' 26 x 33
Double Royal 24 x 38
Double Elephant "....27x40
Antiquarian! . ... '. 31 X 53
Secure specimens of the letter heads, blanks, etc., used
in the various departments of the Irfstitute. In each case
find out by actual measurement the size or sizes of paper
named above from which the letter head or blank can be
cut without Waste. Make drawings to show how you
would cut the paper.
4. The Cudahy Packing Co., Memphis, Tenn., sold
the Institute 150 pounds of bacon at $.10i a pound; 125
pounds of shoulders (pork) at $.111 a pound: 688 pounds
of lard at $.08f a pound. Find total amount paid for
these supplies.
REVIEW
79
5. The Institute bought for the Truck Garden 50
bushels of seed potatoes at $1,872 per bushel. Find the
cost of these seed potatoes.
6. Th ree bales of broom corn were purchased by the
Institute. Two of these ba es, weighing together 650
pounds, cost $.07y per pound; the third bale, we ghing
372 pounds, cost $.061 per pound. Find the amount
paid for the three bales of broom corn.
7. A piece of calf skin in the Shoe Shop contained
7//2 sq. ft. If a pair of uppers for shoes requires 2/^ sq.
ft. of leather, how many pairs of uppers can be cut from
this piece of calf ^kin?
8. It is estimated that for each pair of half soles for
women's shoes, a piece of leather Syi" X7is required.
How many pairs of half soles of this kind can be cut from
a piece of leather ll"X60/;. Make drawing to illustrate
your result.
9.. At $.16 per Sq. ft., find the amount paid for the
slate boards of Room 12, Academic Building.
10. An estimate was made at the Carpentry Shop on
the cost of flooring 2 rooms and a hall of a house in
the town of Tuskegee. Each of the rooms measured
16/X20/; the hall,12/x34/. The flooring specified in
this estimate cost $2.40 per 100 sq. ft. The moulding
for each room and the hall cost $.50 per 100 feet. (In
finding the amount of moulding needed, the entire distance
around each room and the hall was counted.) Other
items in the estimated cost were: 50 pounds of nzils,
$.1.75; sand paper, $.50; labor, $1.50 per "square"
80
REVIEW
of floor laid (1 square = 100 sq. ft.). For supervision
and waste, tV of the cost of the above was added. Find
total cost of job according to this estimate. (See
Problem 7, Exercise 34.)
11. The Institute bought of the Pittsburgh Plate Glas9
Co. of Atlanta the following pieces of stained win¬
dow glass: 16 lights, each 13" Xl8"; 50 lights each 14" X
36". This glass sold at $.10 per square foot. Find the
value of the order.
12. Find the cost of the following materials used in
the Carriage Trimming Division in making the back of a
buggy: 1 piece of leather, 30" X45" at $.21 per sq. ft.;
1 piece of buckram, 30" long, at $.42 per yard; 1 piece of
sale duck, 16" long, at $.65 per yd.; Yi yd. mole skin at
$.50 per yd.; 40 clinch buttons at $.30 per gross.
13. A tank made at the Tin Shop measured 24" X 24" X
30". Find the number of gallons that it will hold
(231 cu. in. to 1 gallon).
14 A cheese vat made for the Creamery in the Tirf
Shop measured 12"X 23" X42". Find the capacity of this
vat.
15. The inside measurements of a wagon bed built irt
the Institute shops were 16" X40^2 "X9' 8". Find the
capacity of this wagon bed in cu. ft. How much does
this wagon lack of holding 2 cu. yd.?
DECIMAL FRACTIONS
The Institute pays the freight charges on most ship¬
ments of goods purchased by it.
At one time a barrel of linseed oil was received from
St. Louis and the freight charges paid by the Institute
amounted to $1,046 for every 100 pounds in the weight
of the barrel.
Now, as we have already learned, the figure 4 gives the
number of cents in the amount of the money mentioned.
The figure 6 states thenumber of milts. (10 mills —1 cent.)
What part of a dollar is 4 cents?
What part of a dollar is 1 mill?
What part of a dollar is 6 mills?
On a shipment of corn from Montgomery, Ala., the In¬
stitute paid freight charges at the rate of $.099 per cwt.
(cwt. is the abbreviated form of hundred weight, which
means 100 pounds).
What part of a dollar does the 9 next to the 0 express?
What part of a dollar is expressed by the 9 on the right?
How does the amount expressed by the first 9 compare
with that expressed by the second 9?
82
DECIMAL FRACTIONS
At the Machine Shop, it is estimated that 1 cu. in. of
wrought iron weighs .2816 lb. (read "two thousand eight
hundred sixteen ten-thousands").
In this number, .2816ft).,
the figure 2 expresses i^oft).,
the figure 8 expresses too"ft).,
the figure 1 expresses ToVofb.,
the figure 6 expresses tooooR).
Then, .2816 = i%^too^toVo"-I-totot i W</V• .2816
is simply another way of writing i^oVst.
Fractions whose denominators are 10, 100, 1000, etc.,
are called decimal fractions. These fractions can always
be written with the decimal point as in the case of i~oVro.
READING AND WRITING DECIMALS
Exercise 37
Read the following:
1. 367.425763
This number is read "three hundred sixty-seven and four hun¬
dred twenty-five thousand seven hundred sixty-three millionths. " The
names of the orders or places occupied by each figure are given below.
EhDhschhmS
367-4 25763
Note that the decimal fraction takes its name from the place occu¬
pied by the figure on the right.
READING AND WRITING DECIMALS
83
2. 43.09
8,
20.36
3. 5673.935
9. 203.6
4. 60.009
10. 7231.4006
5. 3.1416
11. 52.016
6.
.2036
12. 7.37193
7. 2.036
13. 5001.52316
Write with the decimal point.
14. Fifty-six and seventy-three thousandths.
15. Three hundred seventeen and eighty-seven ten-
thousandths. *
16. Five thousand sixteen and eight hundred ninety-
three ten-thousandths.
17. Thirty and five thousandths.
18. Seven thousand seven hundred six and eight thou¬
sand three hundred-thousandths.
19. Forty-seven ten-thousandths.
20. Seven hundred and seven hundredths.
21. Four hundred six and nine hundred forty-four
thousandths.
22 Six and twenty-eight millionths.
84
DECIMAL FRACTIONS
REDUCTION OF DECIMALS
Exercise 38
ge to
common
fractions in
lowest terms.
1.
.125
.125=
125
1000=
— i
8
2.
.25
8.
.1875
3.
.35
9.
.307
4.
.75
10.
.0325
5.
.001
11.
.4375
6.
.3125
12.
.735
7.
.975
13.
.625
14.
.161
,16| =
16f
100
50
3 i.
100 6
15.
.33*
19.
.llli
16.
.661
20.
.141
17.
.12*
21.
.871
18.
.621
22.
.09-A-
37 370 3700 t, „ Q_
c;nrP S7— = = -'\ve see that .37=.370=.3700 —
•6/—100 1000 10000
.37000.
Zeros may be annexed to the right of a decimal
without altering its value.
REDUCTION OF DECIMALS
85
Exercise 39
1. Write .07 as thousandths. Read result.
2. Write .38 as thousandths. Read result.
3. Write .016 as ten-thousandths. Read result.
4. Write .9 as thousandths. Read result.
5. Write .1153 as hundred thousandths. Read result.
6. Write .3007 as millionths. Read result.
7. Write .4900 as hundredths. Read result.
8. Write .50700 as thousandths. Read result.
Exercise 40
1. Reduce to a decimal.
8) 3.000 we have learned that a fraction is an indicat-
.375 ed division. To reduce § to a decimal, we carry
out the division indicated.
- ■
3^-8=3000 thousandths^8 = 375 thousandths,
375 thousandths=.375.
Note that, in the above, when 3.000 is dividied by 8, the decimal
point in the quotient comes directly beneath the decimal point in the
dividend.
2. How may any common fraction be reduced to a
decimal?
3. Reduce I to a decimal.
6)5.000 Dividing as in the preceding example, we find
8333 that ^ — .833^ However far the division is
carried in this case, there is always a remainder.
Often the result is written in this way: ^=.833 +
86
DECIMAL FRACTIONS
Reduce to decimals.
4.
1
4
9.
8
14.
5
T
5.
3
4
10.
2
3
15.
8
9
6.
1
2
11.
7
"1 2
16.
3 7
6 4
7.
3
8
12.
1 S
3?
17.
4
1 1
8.
3
1 6
13.
1 1
1 6
18.
3
5
19.
M
23.
.21
27.
11.071
20.
.031
24.
.37*
28.
42.011
21.
.151
25.
.611
29-
5.011
22.
.12?
26.
.005*
30.
12-h
ADDITION AND SUBTRACTION
Exercise 41
1. At the Dairy Barn the milk received from each cow
is weighed on scales by which the weight is given in
pounds and tenths of a pound. On one day a cow gave
17.8 pounds of milk in the morning and 16.7 pounds of
milk in the afternoon. Find the weight of the milk given
by the cow for the day.
17.8 pounds In adding 17.8 to 16.7, we place the num-
16.7 pounds ^ers so as to bring decimal point beneath de
2^7^ pounds c'mal point. Why? Adding, we find that on
the day mentioned, the cow gave 34.5 pounds.
2. The record of a cow at the Dairy Barn for the first
week in April, 1911 was as follows:
MORNING AFTERNOON
April 1. 19.6 pounds 18.2 pounds
2. 20 15.4
3. 21 17.7
4. 18.7 15.5
5. 19 16
6. 19.4 17.2
7. 18.1 17
ADDITION AND SUBTRACTION 87
On what day did the cow give the greatest quantity of
milk? Find the number of pounds of milk given by
the cow in this week.
Add the following:
3. 73.07, 97.016 35.9, 607.036.
4. 500.706, 1976.31, 406.096, 53.8, 9763.8721,
43.5094.
5. 3.17i, 81.702, 306.57*.
6. 171.011, 301,541, 517.61.
7. 4762.093, 711.9364, 59.4008, 1765.02,
983.41278.
8. A wheel for a pulley on a washing machine was
made in the Machine Shop. The stud pin of this wheel
had a diameter of 1.28". The hole into which this stud
pin was forced was made .002" less in diameter. What
was the diameter of the hole?
1.280" T° diameter of the hole, we subtract .002//
.002" from 1 .28//, getting as a result 1.278 inches. Why
I.278" 's t'le zero annexed t0 the minuend? What
effect has the annexing of the zero upon the value of
the minuend? How would you check the result of the subtraction?
What is meant by the "diameter" of the hole?
9. One foot of three-inch pipe used in the Plumbing
Division will hold .3672 gallons of water, while one foot
of four-inch pipe will hold .6528 gallons of water. How
much more water is held by one foot of four-inch pipe
than by one foot of three-inch pipe?
10, In putting f" studs in machinery, two tools are used
at the Machine Shop in boring the holes: the reamer
drill and reamer. The reamer is 1" in diameter, while
the reamer drill is .001" less in diameter than the reamer.
Find the diameter of the reamer drill.
II. In repairing a typewriter, a reamer yi" in diameter
was used. The reamer drill used in connection with the
88
DECIMAL FRACTIONS
reamer had a diameter .001" less than that of the reamer.
Find the diameter of the reamer drill.
12. The engine in the foundry was built in the Insti¬
tute Machine Shop. A hole in the disc on the crank
shaft of this engine is 1H" in diameter. The crank pin
which was forced into this hole was .002" greater in di¬
ameter. Find the diameter of the crank pin.
13. In another "force ' fit made in the Machine Shop,
the diameter of the stud pin was 2", while the diameter
of the hole into which the pin was forced was .OOS^ less.
What was the diameter of the hole?
14. The tap drill used in making a iV screw bores a
hole .240" in diameter. How much is left for the thread
on both sides of the hole?
15. A pipe used in the Plumbing Division was found to
be . 154" in metal thickness. The external diameter of
the pipe was 2.315". Find the internal diameter.
16. Another pipe was found to have an internal diame¬
ter of .624" and an external diameter of .841". What
was the metal thickness of this pipe?
Subtract as indicated.
17. 37-29.06
18. 317.81-276.734
19. 4*8.021 — 56.681
20. 300-196.5432
21. -A-.0798
22. 51-3.927
23. .9-.3216
24. .03i —.001.
MULTIPLICATION
Exercise 42
1. The Institute received from the National Tube Co.,
McKeesport, Pa., a shipment of pipe weighing 108,000
pounds. The freight on this pipe was at the rate of
MULTIPLICATION
m
$.736 per cwt. Find the amount paid by the Institute as
frieght charges on this pipe.
$.736 10800-c 100=^=108, the number of cwt. in 10800 lb,,
108 Since the freight on 1 cwt. of pipe was $.736, then,
5888 the freight on 108 cwt. vas 108X$.736.
736
$79,488 108X$.736= 108X $736
1000
_ 108 V $736 = $79488
1000 1000
= $79"ro-o\= $79,488.
Which is the nearer $79,488: $79.48 or $79.49? Then, how much
did the Institute actually pay in freight charges on the pipe?
2. The record of the Brickmasortry Division shows
that a student in one month worked 9.8 days at the rate
of $.35 per day. Find the earnings of the student for
the month in this division.
$.3 5 To the amount earned by the student dur»
9.8 ing the month, we multiply $.35 by 9.8. Why?
^80 qrV« «_Q 8 v$35_98v $35
315 ' X100'~10X 100
$3,430 98 $3S_ = $3430
10 100 1000 * 1 000
Then, the student received $3.43 for his work during the month.
From the solutions of the above problems, we see that
When two numbers containing decimals are multiplied to¬
gether, the number of decimal places in the product is equal
to the sum of the number of decimal places in the factors.
3. A reproduction of the pay roll of the Wheelwright
Division for the month ending May 22, 1911 is given on
page 90. Under Scl. (School) is indicated whether the
student attends day or night school, under Time is given
the number of days worked by the student; under Rate,
the amount received per day. 1 he amount given each
student is omitted. Find the total amount paid the
students of this division for the month.
90
DECIMAL FRACTIONS
Tnske^ee Normal arid Industrial Institute
Report of Students' Work In Wheelwright ---Division
For the Month Ending May 22 1911.
NAME
Alphabetically
Adams, Prentice _
Allen, George
Burris, Seymour, _
Chisholm, Primus,
Cooley, William..
Demps, James
Fish, Milous
Harris. Pinkard..
Hawkins, Irving-.
Hicks. Joseph
Johnson. Clarence
Jones. Albert
Jones. J. B
Jordan, Lewis
Moore. Charles
Nesby. Edward
Owens. Jessie
Pryor. James
Thomas. Howard_
Wafer, Henry.
Watt, Governo
Wells, Perry..
Wright, Elbert
Wright, Ernest
KIND 0E
WORK
TIME
SCL.
Vehicle',..D.. .. 7.3-
RATE
D.
. D
. D-.
. N..
.D--
.D ..
-. 9.4.
.. 5...
7.6.
14.7
__ 8.5.'
.. 6.8.
__D.. -- 3.1.'
1). v
I) 9.1
__ D.
9.1
-D-
_ N __ .14.9.
--D-.' ..7.1
_.D-\--8.2.
_.D--'..6.2-
_.D_.
__D__ i-
. D__
_ N._
_ D__
. D_.
D_.
-.6.2.
.15 ..
..8.5.
..8.2.
..6.7 .
...20
...33
...33
...25
...25
...23
24
35
25
. $.27
....26
....23
....22
....38
....25 .
....20 .
....27
'1...33
....35
....29
Approved by..R. R. Taylor
Edw. D. NelsOn....ln Charge
MULTIPLICATION
91
4. During one month, five special agricultural students
Were employed at the Truck Garden. The number of
days worked by these students were, respectively, as fol¬
lows: 18.5 days, 18.3 days, 14 days, 18.5 days, 19.5 days.
Each student received $.71 per day. Find the total
earnings of these studenrs.
5. One student (post-graduate) worked in the Truck
Garden the same month 18.7 days and received .$77a
per day. What did he receive for this work?
6. During the school year 1910 1911, the Institute
purchased most of its coal from the Bessemer Coal Iron
and Land Co., Besseinrr, Ala. In accordance with an
agreement made with the Institute, this company sent in
a bill for premiums due to undercharges made on shipments
during September, October, and November, 1910. The
shipments and premium rates, as stated in the bill, were
as follows'.
September - - 72.95 tons $.0884 per T.
October - - - 553 90 tons (s $.1384 per T.
November - 1114.35 tons (a/ $.1160 per T.
Find total value of the premiums paid.
7. Find out(through teacher) at the Plumbing Division
what is meant by an "offset." Locate an offset in some
building.
8. To find the length of pipe to be used in a "45°"
offset, plumbers multiply the length of the offset by
1.414. Find the length of pipe required for a 45° offset
of 12".
9. Find the length of pipe required for a 45° offset
of ISi".
92
DECIMAL FRACTIONS
10. Give the products: 10x37.478; 100x89.6;
1000x476.32.
11. Judging from the products just found, how does
multiplying a number by 10, 100, 1000, etc., affect the
position of the decimal point?
Multiply as indicated.
12.
10 X .03
18.
563.07x9.542
13.
100x7.09
19.
52.901 x.0018
14.
100x372.7
20.
42.3/^x764.02 >2
15.
1000x52.304
21.
94.737x5.067
16.
1000x1107.0325
22.
70.008x3.005
17.
10000x376.942
23.
4.01^X7.32-^
DIVISION
1. Divide 120 by 8. Multiply both dividend and di¬
visor by 6, and then perform the division. Multiply both
dividend and divisor by 10 and then perform the division.
2. How does multiplying both dividend and divisor by
the same number affect the quotient?
3. In one month a cow at the Dairy Barn gave 670.8
pounds of milk. Find the value of this milk at $.19 per
gallon. (8.6 1b. make 1 gallon).
DIVISION
93
To find the number of gallons in 670.8 pounds, we divide 670.8
by 8.6. Before dividing, we multiply both dividend and divisor by
10. Thus, 10X670.8=6708, and 10X8.6=86.
Now, 670.8^8.6 = 6708 -86. Why?
78
Checking result, we find that
86^fino8 78X8.6 = 670.8.
~7^,0 Then, in 670.8 lb. of milk there are 78 gallons,
boo
ggg 78x$. 19 = $14.82.
Therefore, the value of the milk given by the
cow during the month was $14.82.
4. Divide 3.5154 by .93.
Here we multiply both dividend and divisor by 100.
This multiplication we know, will make the divisor an
integer.
100x3.5154 = 351.54. 100 x.93 = 93
3.78 3.5154-.93 = 351.54-93. Why?
93)351.54 Explain the division as indicated.
279 Account for the position of the
72.5 decimal point in the quotient.
65.1_ Check: .93x3.78 = 3.5154.
7.44
7.44
In practice, the decimal point in 72.5, etc., would be
omitted.
In the division of decimals:
Multiply both dividend and divisor by such a number
(10, 100, etc.) as will make the divisor an integer. Then
divide, giving the quotient the same number of decimal places
as are possessed by the dividend as changed.
94
DECIMAL FRACTIONS
5. The following is a record of the number of pounds
of milk given at the Dairy Barn by two cows, Black
Beauty and Hulda, for the year 1910.
BLACK BEAUTY HULDA
January
254.9 ft>
311.4 ft>
February
812
318.4
March
740.5
366
April
679.5
305
May
664.5
303.8
June
756.8
186.5
July
634.3
658.2
August
689
767.4
September"
483
656
October
458
514
November
379
479
December
351.1
377.2
Reckoning 8.6 pounds of milk to the gallon, find how
many more gallons were given by Black Beauty than by
Hulda. Find the average number of gallons per day
given by each cow during the year.
6. The Institute bought 500 sacks of corn, weighing
in all 56,224 pounds at $.67 per bushel. The firm alj
lowed a reduction for freight amounting to $.20 per cwt.
Find the net cost of this shipment of corn.
7. The Washburn Crosby Milling Co., Louisville,
Kv., sold the Institute 200 sacks of flour, 24 pounds to
the sack, at $5.3U per barrel. The amount paid by the
Institute for this flour was $132.50. How many pounds
were reckoned to the barrel according to this bill? (Orj
dinarily 196 pounds of flour are regarded as> 1 barrel.)
DIVISION
95
8. The Institute bought 1 car of hay, weighing
22,680 pounds, at $15. 25 per ton. A reduction of $22.45
for freight was allowed on the shipment. What did this
hay cost the Institute?
Di vi de as indicated.
9. 1.0368-8.64 14. 536.09-.0038
10. 1782.5-3.875 15. 41.7362-3 006
11. 372.897-.0378 16. 57.649-100.07
12. 47.638-98.63 17. .0006-.034
13. 506.81-976.345 18. 54.3-86.475
19. Divide (a) 18.6 by 10. (b) 3.87 by 10. (c)
56.87 by 100. (d) 373.9 by 100. (e) 1756.7 by 1000.
(f) 3.72 by 1000.
20 How is the position of the decimal point affected
when a number is divided bv 10? By 100? By 1000?
21. The Institute bought of Winter LoeD Co., of
Montgmery, Ala., 10 barrels of granulated sugar, weigh¬
ing in all 3573 pounds, at $4.90 per cwt. Find the
amount paid for this sugar.
22. Find the amount paid by the Institute for 4190
pounds of hay at $.72/4 per cwt.
23. For printing the Institute catalogue of the year
1910-1911, 46 reams of "'hite book paper were purchased.
This paper cost $5.60 per cwt. Each ream weighed 60
pounds. The paper and packing weighed 3^03 lb., on
which the Institute paid freight at the rate of $1,055 per
cwt. The cost of hauling this paper from the depot to
the Printing Office was $1.00. Find the total cost of this
paper.
96
DECIMAL FRACTIONS
14. For covering the catalogue of the year mentioned,
1500 sheets of cover paper were purchased at a cost of
$4.00 per 100 sheets. The Daper was shipped in a
package weighing 300 pounds. Freight charges paid
by the Institute were at the rate of $.93 per cwt.
The hauling of this paper from the depot cost $.25. Find
the total cost of this cover paper.
15. The feed used at the Dairy Barn for one month
was as follows:
98,965 pounds cotton seed hulls («; $ .47 per cwt.;
128,732 pounds of rape (?; $ .25 per cwt.;
20,400 pounds of cotton seed meal (£<> $1.35 per cwt.;
10,800 pounds of shorts @ $1.50 per cwt.;
900 pounds of corn meal («; $2.00 per cwt.;
600 pounds of bran (<v $1.50 per cwt.
Find the value of the feed used at the barn during the
month.
16. During the same month, the feed used at the
Horse Barn was as follows:
34,547 pounds of chops(oats and corn)
@ $ 2.00 per cwt.;
41,260 pounds of hay @ $23-00 per T.;
674 bushels of oats^ @ $ .50 per bu.;
219 bushels of corn (a) $ .75 per bu.;
2900 pounds of bran @ $ 1.50 per cwt.
Find the value of the feed used at the Horse Barn
during the month.
DIVISION
97
27. In 1911, the cows at the Dairy Barn were divided
into three classes. No. 1 cows gave over 20 pounds of
milk a day. No. 2 cows gave from 12 pounds to 20
pounds of milk a day. No. 3 cows gave less than 12
pounds of milk a day.
The record of Baker, an average No. 1 cow, for the
week beginning March 5, 1911 was as follows:
MORNING AFTERNOON
March 5.
14.1 pounds
11.7 pounds
6.
15
10.7
7.
14.7
11
8.
13 7
11.2
9.
13.1
11.1
10.
15
12.2
11.
14
11.6
For each day of the given week, the feed of all No. 1
cows was as follows: 30 pounds of cotton seed hulls; 5
pounds of cotton seed meal; 3 pounds of shorts; 2 pounds
of bran; 50 pounds of rape. Find the cost of this cow's
feed for the week at the prices given in preceding problems
of this exercise. Find the value of the milk given by this
cow during the week at $.19 per gallon. Compare the
value of the milk with the cost of the feed for the week.
y.S DECIMAL FRACTIONS
v 28. The record of Gorti, an av< rage N o 2 cow, for
?he same week was as follows:
MORNING AFTERNOON
March 5.
11.6 pounds
6
6.
8.3
7
7.
8
7
8.
9
7
9.
8
7
10.
9.5
7
11.
9
9
For each day of the week, the f< ed of all No. 2 cows was
as follows: 30 pounds of cotton seed hulls; 4 pounds of
cotton seed meal; 2 pounds of >horts; 1/2 pounds of bran;
50 pounds of rape. Compare the value of the milk given
by this cow during the week with the cost of the feed
consumed by her during the same time.
29. The record of Agnes, an average No. 3 cow, dur¬
ing the same week was as follows:
MORNING AFTERNOON
March 5. 5 pounds 4 pounds
6. 5 6
7. 4 4
8. 4 4.2
9. 4 4
10. 4.2 3.6
11. 4 4
For each day of the week, the feed of all No. 3 cows was
as follows: 30 pounds of cotton seed hulls; l.'i? pounds
of cotton seed meal; 1*2 pounds of shorts; l2 pound of
bran; 50 pounds of rape. Compare the value of the milk
produced with the cost of the feed of this cow for the
week.
DIVISION
99
30. The Institute bought of the Loeb Hardware Co.
of Montgomery, Ala. the following:
1 keg of No. 2 front horse shoes, $4.25; 1 keg of No. 3
hind horse shoes, $4.25; 1 keg of No. 4 hind horse shoes,
$4.25; 6 bars of IP' round iron, 88 pounds, at $2.45 per
cwt.; 6 bars of round iron, 50 pounds, at $2.55 per
cwt., 6 bars i" round iron, 30 pounds, at $2.75 per cwt.,
6 bars of W" round iron, 20 pounds, at $2.95 per cwt.
Find the cost of this order.
31. Schloss & Kahn of Montgomery sold the Institute
.17 sacks of fertilizing salts, weighing in all 2610 pounds,
at $5 per ton. Find the amount paid for the salts.
32. In the office of the Institute Business Agent, the
method used in estimating the value of a load of coal at a
given price per ton is as follows: Suppose that it is requir¬
ed to find the value of a load of coal weighing 1725 at $4
per ton. (1) Point off three decimal places in 1725, get¬
ting 1.725. (2) Divide $4 by 2. $4-^2 = $2. (3) Find
the product of 1.725 and $2. 1.725X$2 = $3,550. This
product, $3.55, gives the value of 1725 pounds of coal at
$4 per ton.
Explain how this procedure gives the desired result.
33 The I nstitute purchased from the Bessemer Coal,
Iron and Land Co. of Bessemer, Ala. 2 cars of coal. One
car contained 81,000 pounds of coal and the other car
contained 59,400 pounds of coal. This coal sold at $1.40
per ton. The freight on the shipment was at the rate of
$1.80 per ton. Find total cost of the two cars of coal.
100
DECIMAL FRACTIONS
34. The Roden Coal Co. of Marvel, Ala. sold the
Institute one car of coal containing 80,500 pounds at
$2.85 per ton. The freight on this coal was at the rate
of $1.61 per'ton. Find total cost of the coal.
35. On one day 64 head of cattle, weighing altogether
36,745 pounds, were purchased by the Institute, the price
being $2.75 per cwt. Find the cost of the cattle.
36. On another day 13 head of cattle, weighing 6305
pounds, were purchased at the rate of $2.80 per cwt.
Find the amount paid for the cattle.
BUSINESS FORMS
Exercise 43
The tin cans used at the Canning Factory in 1911
were purchased from the American Can Company. On
pages 102, 103, 104, and 105 are reproduced (1) the order
given by the Business Agent of the Institute, (2) the
reply of the firm, (3) the bill for the goods, and (4) the
freight bill.
1. The students will make a careful study of the corre¬
spondence and the bills.
2. Verify the "extensions" on the bill of the goods, that
is, see if the figures given under "amount" are correct.
3. Find out what is meant by the statements and signa¬
tures within the enclosed space on the hill: "Extensions
O. K. C. N. P.," etc.
4. Verify the freight bill.
5. Secure from your trade instructor (1) the kind
and quantity of materials used in connection with some
work of the division, (2) the name of the firm handling
these materials, and (3) the prices charged by this firm
for the same. With this information, bring into class a
letter written to the firm ordering the materials designated.
6. Make out a bill in proper form for the same.
7. Secure (through teacher) and study carefully actual
bills of goods purchased by the Institute. Verify the
extensions in each case.
8. On the regular forms provided for that purpose,
make out a bill for some goods sold by your industrial
division or for some services performed by the same.
9. The class will visit the Institute Commissary and
observe the business forms used in the ordinary transac¬
tion of its business.
BUSINESS FORMS
BOOKER T. WASHINGTON WARRENLCGAN
Principal treasurer
The Tusxegee
Normal and Industrial Institute
FOR THE TRAINING OF
COLORED YOUNG MEN AND WOMEN
Tuskegee Institute, Alabama
ERNEST T. ATTWELL
BUSINESS AGENT
March 27, 1911.
Tne American Can Company,
Soutn Atlantic District,
AtlanLa, Ga.
Gent1emen:
As per quotation left with the
writer "by your Mr. F. W. Uatnright,
pl-ase ship us the following:
15.000 #10 Cans, with solder hemmed
caps, with 2- 7/16" opening.
10,000 #3 Cans, with solder hemmed
caps, wi th 2= 7/16" opening.
5,000 #1 cans, with solder hemmed
caps,with 2- 7/16" opening .
We figure that the above will make
upa carload shipment. However, if it
does not, we would be pleased to have
you reduce the number or add thereto
in the same proportion as above,
in order to make up a carload.
Kindly advise us in the matter by
re turn mai 1.
Very respe c tf u 1 ly yours,
E. T. Attwell
Business Agent.
BUSINESS FORMS
103
AmehicaiN Cain Company
South Atlantic District
Marietta St. and Jones Ave.
e. k. philip
manager
Atlanta, Ga.
Apr i 1 6, 1911.
Mr. E. T Attwe11, Business Agt.,
Tuskegee N. & L Institute,
Tuskegee Institute, Ala.
Dear Sir:
We duly receivea your valued order
of the 27th ult. for a oar load of #2, 3
and 10 Standard Packers' Cans, with 2-
7/16" opening and Solder Hemmed Gaps,
to be shipped assorted in oar from our
Baltimore Factory.
This specification will more than
fill a 36-ft,, car and will come pretty
near f11 ling a 40-f t. car. As we under¬
stand it, however, you desire us to
cut, the specification down on each of
the sizes m "the same proportion as or¬
dered, so as to makeup a36-ft. car¬
load and we are notifying our factory
accord ingly.
Thanking you for the order, which
we assure you will be shi ppea prompt 1 y
andfollowed with tracer, we are,
F. L.
Yours truly,
E. R. Philip
Manager.
s
0i
o
American Can Company
Maryland Trust Building
Baltimore
April 10, 1911.
Sold to Titskegee N<ormal & Industrial Institute, E. T. AttwelL Busines Agettt,
Address Tuskegee Institute, Ala,
Shipped to American Can Company, or order, TuskeQee N. & I. Institute,
Address Tuskegee, Ala.
Via PRR care of E. & S. Despatch at 85• l-2cent rate
Terms: FOB Baltimore, Md. S. D. vs B. L. Bank of Tushegee, Tuskegee, Ala.
ALL CLAIMS FOR DEFECTS OR SHORTAGE MUST BE PRESENTED WITHIN THIRTY DAYS FROM RECEIPT
OF SHIPMENT. GOODS RKTURNED WITHOUT OUR AUTHORITY ARE AT SHIPPER'S RISK.
Invoice Number
District Order
Customer's Order
Car
Freight
44-A No. 309
371 Comp.,
2
P. R. R. 26598
Collect B. L. 25
Quantity
Description
Price
Amount
14.000
8,300
4,500
27,068
No. 10 Reg. Cans 2- 7-16 in., Qpg.
No. 3 " "2- 1-16 in,,
No. 2 " " 2- 7-16 in., "
2- 7-16 in.. Hemmed Caps
42.SO M
17.25 M
13,50 M
1.70 M
NO 2009...
..DATE.
Apr.
15, 1911.
EXTENSIONS
0. K...
..C. N
P.
RECEIVED 0.
K
.. C. G.
Kelley
PRICES AND
PURCHASES 0.
K
-E. T. A.
F 595,00
143.18
60.75
46.02
$ 844.95
Paid by Draft
Acct. Canning Div.
FREIGHT BILL
form 188 Part 1 10-19-10 50m 0-298
da ie of issue
April 19, 1911.
consignee
0. N. Tuskegee Normal & Industrial Institute
freight-bill number
812
issuing station
destination and route, if fok beyond issuing station
TO THE1A/ESTERIN RAIL1A/AY OF ALA.
OR.
For Charlies on
Articles Transported
billing station
Pot. yds.
way-bill number and date
A. W. 49 7-12-1911
car initial and number
P. R. R. 26592
shipper and original point shipment connecting line reference original car, initial & number
A.C.C.Balt.
number of packages, articles and marks
1 Car Bulk Tin Cans
weight
15000
85'
freight charges
total
128.25
Received Payment for the Company__
4-22
1911
DRAYAGE
W. H. Ea&e
In case claim is made for Loss, Damage or Overcharge, this Freight
Bill and Bill of Lading must be presented therewith.
Demurrage Charge commences *
Agent. TOTAL TO COLLECT
19
REVIEW
Exercise 44
1. Below is reproduced a "job ticket ' used in the
Printing Division At sixty cents per day of 10 hours, find
the amount due the student for his work on this day.
At the same rate, what amount should be charged against
each job indicated by the numbers, 500, 489 and 511?
Name Kindelan
Printing Division : : Tuskegee Institute
JOB TICKET
Date . July IS. 19n._
i Came 6 i Hours 8
TIME <
' Left 4 t Overtime.:
%emarks
State whether the worlt is Composition, Lock-up, Presswork, Binding. Dist.. Etc. Hrs.
500 _ Folding 2 %
48Q Stitching 1
511 Feeding Job Press 3/4
Errands 1
CORRECT
A. A. Thomas
REVIEW
10?
2. Two barrels of washing powder purchased b\ the
Institute were shipped from New York to Tuskegee. The
total weight of the two barrels was 560 pounds. The
freight charge on this powder was $9.00. On investiga¬
tion it was found that the freight rate on this class of
goods from New York to Tuskegee was $1,059 per cwt,
The Institute filed a claim for overcharges. Find the
amount of the claim.
3. The Institute purchased from the Conklin Tin
Plate and Metal Co. of Atlanta the following supplies
for the Tin Shop: 7 bundles of galvanized iron, weigh¬
ing 1118 pounds, at $3.95 per cwt.; 6 bundles of galvan¬
ized iron, weighing 923 pounds, at $3.65 per cwt.; 4 bundles
of galvanized iron, weighing 581 pounds, at $3.35 per
cwt.; 2 boxes of tin at $24.00 per box; 100 pounds of soldef
at $.26/i per pound; 5 gallons of muriatic acid at $1.25
per gallon. The freight paid by the Institute on this
shiprnent was as follows: 110 pounds at $.864 per cwt.;
108 pounds at $1,098 per cwt.; 840 pounds at $.719 per
cwt.; 2622 pounds at $.536 per cwt. Find the total cost
of these supplies.
4. At the Paint Shop *28 pounds of white lead were
used. This white lead cost $8.50 per cwt. Find the
Value of the lead used.
5. A recipe for cake follows: /i cup of butter, 3/4
cup of sugar, 2 eggs, >2 cup of milk, 1% teaspoonfuls of
baking powder, 1 >2 cups of flour, 1 teaspoonful of spice,
1 teaspoonful of vanilla flavoring. Find the Cost of the
materials for this cake at current Commissary prices. Se¬
cure from Cooking Division all necessary information cot.'
cerning the weight of 1 cup of butter, etc.
REVIEW
6. The following is a recipe for chocolate custard:
cup of milk,yk cup of sugar, 1 egg, 2 ounces of chocolate,
% teaspoonful of vanilla, 1 speck of salt, cinnamon to
taste. Find the cost of the materials for this custard at
current prices.
7. A recipe for cottage pudding follows: 2 tablespoon-
fuls of butter, ^/z cup of sugar, 1 egg, 3A cup of milk, 2
teaspoonfuls of baking powder, \ l/2 cups of flour, K tea-
spoonful of salt. Find the cost of these materials at cur¬
rent prices.
8. The Institute purchased for the Dressmaking Di¬
vision 366/4 yards of lawn at $.12 :/2 per yard. What
was the value of this lot of materia]?
9. The Easter waist worn by each of the Senior girls
in 1909 required 3 yards of material costing $.11 *-2 per
vard. The thread used was estimated at $.02/4; the
buttons, at $.09. The Dressmaking Division charged
$.20 for the making of each waist. This waist sold for
$.70. Find the gain on each waist.
10. The material used in making a hat in the Mil¬
linery Division was as follows: l1^ vards of bobbinet at
$1.37>2 per yard; 4 yards of lace at $.45 per yard; 18
inches of silk at $.62 ^ per yard; 2 yards of straw at $4.00
per dozen vards; 9 roses at $5.00 per dozen; 1 plume,
$6.00; 1 wire shape, $3.50; 1 spool of linen thread at
$1.50 per dozen spools. Find the cost of the material
used in the making of this hat.
11. The Institute bought from the Alabama Machinery
and Supply Co. of Montgomery, 437 12 feet of -U-inch
pipe at $4.60 per hundred feet. Find the value of this
pipe.
REVIEW
109
12. An individual sold the Institute a cow weighing
535 pounds at $2.12^ per cwt. Find the amount paid
for this animal.
13. One wall gi White Memorial Hall is 64',Iong, 37'
high, and 18" thick. " In this wall there are 18 win¬
dows, each 3'XS'. At the time of the construction of
this wall, the Brickmasonry Division estimated the cost
of laying 1000 bricks as follows: labor, $4.00; 1 bar¬
rel of lime, $1.25; Y-z cu. yd. of sand, $.40; 10
pounds of mortar stain, $.23; bricks, $7.90 per M.. Al¬
lowing 22 bricks to the cubic foot, find the cost of con¬
structing the wall.
14. In constructing a pit at the Institute Greenhouse,
a brick wall 107' long, 2' high, and 8/; thick was built.
Using the information given in the preceding problem,
find the cost of constructing this wall.
15. In installing a boiler for heating purposes, the
Brickmasonry Division built a four-walled brick founda¬
tion 17' long, 9' 6" wide, and 2' deep. The walls were
24" thick. Find the cost of the brick used in this foun¬
dation at $7.90 per M.
16. On Jan. 5, 1911, Schloss & Kahn of Mont¬
gomery, Ala., sold the Institute the following: 3 sacks of
navy beans, 480 pounds, at $2.75 per bushel: 1 barrel of
grits $4 00; 2 sacks of rice, 200 pounds, at $.05/4 per
pound; 3 cases of macaroni at $1.90 per case; 5 cases of
lump starch, 250 pounds, at $.03^2 per pound; 5 sacks of
salt at $.50 per sack; 2 cases of Royal Baking Powder,
4 dozen cans, at 12.50 per dozen. Make out the bill in
proper form.
practical applications
in the Tinsmithing, Painting, Carpentry, and othef
divisions of the Institute* it is often necessary in estimat¬
ing the material required in certain operations, to compute
the areas of figures which are not rectangles. For in¬
stance, in calculating the quantity of tin required to covet
a roof, etc., the area qf figures other than rectangles must
frequently be found.
We shall now1 consider some of the figures commonly
met with in such Calculations.
Triangle? Parallelogram
T rape^oid
A triangle is a figure bounded by three straight lines.
A parallelbgrarrt is a four-sided figure (quadrilateral)
In which the opposite sides are parallel, that is, they'
never meet however far they are produced<
AREAS
111
A trapezoid is a four-sided figure in which two sides are
parallel.
A straight line is perpendicular to another straight line
when it makes a right angle with it.
The base of a figure is the side upon which it is sup¬
posed to stand.
The altitude or height of a figure is the perpendicular
distance to the base from the vertex or side opposite the
base.
A
D
In the parallelogram ABCD, DC is the base and AE is
the altitude. The triangle ADE is equal to the triangle
BCF. Then, the parallelogram ABCD is equivalent to
the rectangle ABFE. The area of the parallelogram is
equal to the area of a rectangle having the same base and
altitude. The area of a rectangle equals the product
of the base and altitude.
The area of a parallelogram is given by the product of the
112
PRACTICAL APPLICATIONS
two numbers which express its base and altitude m the same
unit.
F B
In the figure, the triangle ABC is Yi of the parallelo¬
gram ABEC which has the same base and altitude.
1 hen, the area of the triangle is of the area of a par¬
allelogram having the same base and altitude.
Th e area of a triangle is given by y? the product of the num¬
bers which express its base and altitude in the same unit.
B C
The trapezoid ABCD is divided by the line BD (called
a diagonal) into two triangles, ABD and BCD. These
two triangles have the same altitude BE. The area of
the trapezoid is equal to the sum of the areas of these two
AREAS
113
triangles. Thus if BC = 3 ft., AD=10 ft., and BE =
4 ft., the area of the trapezoid is equal to /zXl0x4xl
sq. ft. + >2 X3X-±X 1 sq. ft. = !-_> (10 + 3) X4 X 1 sq. ft. = 26
sq. ft.
Th e area of a trapezoid is found by taking half the sum of
its two bases (expressed in a given unit) and multiplying the
result by the altitude (expressed in the same unit).
Exercise 45
1. The lower part of a partition in the Repair Shop is
a rectangle measuring' 12/x24/. The upper part is
a triangle with a base of 24' and an altitude of 1CK.
On one day this partition was painted. The paint
used cost $1.75 per gallon. The man who did the
work received $1.96 per day. Find the total Cost of the
job, if a gallon of paint will cover 500 square feet of this
kind of work, and a man Can cover 800 square feet of the
same in 1 day.
2. The tin roof of Tompkins Hall was laid by the
Tinsmithing Division. According to the manner in
which the tin was laid, 28 pieces of tin (20//X28//) were
required to cover 1 square (100 sq. ft.). This tin cost
$15.10 per box of 112 sheets. In Covering each square,
there were also used 5 pounds of solder, costing $.22/4
per pound, and sheathing paper costing $.25. The labor
cost $1.50 per square. The class will actually measure
roof and estimate the cost of covering the roof.
3. Deducting I" from the length and from the width
of each sheet for fastening, show that the number of
sheets allowed for each square in the preceding problem is
correct.
114
PRACTICAL APPLICA TIONS
4. Find the cost of painting this roof at current prices.
5. Observe the shape of the ceiling in the kitchen of
Tompkins Hall. Give a sketch of it. For convenience
in calculation, the ceiling may be divided into the following
figures:
1 rectangle, 42/x86/;
2 rectangles, 2'x9)4';
2 rectangles, 11)4'X14/^';
1 rectangle, 15 7-2'X 15^?';
2 triangles, base, 14/^', altitude, 3/2';
2 triangles, base, 9)4', altitude, 9)4'.
Exercise 46
1. The plans for a dwelling erected in Greenwood in
1911 were made in the Architectural Drawing Division.
Th is dwelling contained the rooms as given below:
SIZE OF ROOM
Kitchen
12'X14'X11'
Library
131'x 161'X11'
Parlor
13^x16^x11'
Bed Room
12'x 14'X10'
Bed Room
14'xl6'6"xl0'
Bed Room
13'6"xl4'6"xl0'
Bed Room
13'6"xl5'6"xlO
Bath Room
6'6'/X7'6'/X10'
Study
7'3"xl0'6"xl0'
Hall
10'X 22'x 11'
Hall
10'x 18'x 10'
AREAS
115
The dining room of this house is 11' high and contains
a bay window. For convenience, the floor of the dining
room may be considered as composed of 1 rectangle 14/4'
X 15>2", and 1 trapezoid, whose altitude is 3' and whose
two bases are respectively 12'G" and 4'IQ". The walls
of the dining room are: 14^2'Xll', 15}4'Xll/(2 walls),
1'Xll' (2 walls), 4/10//Xll/ (3 walls).
Find the cost of the plastering done on this entire
house, making no deductions for openings. Add 30
square feet for closets in the second bed room.
2. Find the cost of painting the floors of the dining
room and the study at local prices for such work.
3. Find the cost of covering the floors of the bath
room and kitchen with linoleum. Secure (through
teacher) the necessary information concerning the widths
and prices of linoleum in local stores. Give drawings
showing how you would lay the linoleum.
4. Find the cost of covering the floors of the four bed
rooms with matting at local prices. Give drawings to
show how you would lay the matting. Two closets at
one end of the second bed room give a space 18//X48//.
5. Find the cost of covering the floors of the library
and parlor with carpet at local prices. Give drawings
6. Suggest some way of treating the floors of the two
'halls and estimate the cost of the same at local prices.
116
PRACTICAL APPLICATIONS
N7. The roof of the house: under consideration was
covered with shingles. This roof consisted of the follow¬
ing figures:
From the above are to be deducted for dormer windows
1 triangle with a base of 12' and altitude of ll'; 2 trian¬
gles, each with a base of T and an altitude of 1%'\ 2
rectangles Allowing 1000 shingles to the square
(100 sq. ft.), find the quantity of shingles necessary to
cover the roof of this house. Find the cost of these
shingles at current prices.
In the Blacksmith Shop iron tires are put on the wheels
of the vehicles built in the Institute Shops. In estimating
the amount of iron required for the tire of a wheel, it is'
necessary to find the circumference of a circle.
A circle is a plane figure bounded by a curved line every
point of which is at a given distance from a point within,
called the center.
2 triangles, base 33', altitude 23^;
2 trapezoids, bases 40' and 7', altitude 23';
4 trapezoids, bases 12' and 7', altitude 7';
2 trapezoids, bases 10%' and 2', altitude 10/^'.
THE CIRCLE
The bounding line of a
circle is called the circum¬
ference.
The diameter o f a
circle- is a straight line
drawn through the center
and terminating in the
circumference.
A radius of a circle is a straight line drawn from the
center to the circumference.
THE CIRCLE
117
The circumference of a circle is found by multiplying the
diameter by 37".
In the Machine Shop, where threat accuracy is often necessary
3.1416, instead of 3-1-, is used in finJing the circumference of a circle.
The area of a circle is equal to the square of the radius
multiplied by 3y.
The "square" of a number is equal to the product obtained by
taking the number twice as a factor. Thus, the square of 3 = 3X3
= 9. The area of a circle whose radius is 2" is 2X2X—7?-Xl sq-
in., or 12sq. in.
Exercise 47
1. The diameter of the front wheels of a wagon made
in the Institute Shops was 42//. The diameter of the rear
wheels was 48/;. The iron of which the tires for these
wheels was made was \l/\" wide and thick. For
welding each tire a length equal to the thickness of
the iron is allowed. The weight of 1 lineal foot of the
iron mentioned is 1.56 pounds. Find the cost of the
iron used in making the four tires, the price of the iron be-
ng $2.30 per cwt. and the freight on the same being
$.224 per cwt.
2. At the Blacksmith Shop three circular bands were
made for a vessel in which fruits are scalded at the Canning
Factory. The material of which these bands were con¬
structed was 1%" wide and /i" thick. The diameter
of each band was 32^//. Allowing %" for welding each
band, how long a bar of iron was required to make the
three bands? This iron weighs 1.04 pounds per lineal
foot and cost $2.55 per cwt. (including freight). Find
the cost of the iron used in the construction of the three
bands.
3. The bottom rim of the vessel mentioned was made
of the same material. Unlike the three bands, this rim
lies "flat." The outside diameter of the rim was 31 Vz".
In estimating the length of iron for this rim, the diameter
to be taken was measured from center of stock to center
of stock. Allowing l/\'' for welding, find the cost of
the material in this rim.
118
PRACTICAL APPLICATIONS
4. The two wheels of one of the Institute dump carts
have a diameter of 5' and are fitted with tires 2,'j " wide and
V?" thick. This iron weighs 4.17 pounds per lineal foot
and costs $2.86 per cwt. Allowing y?" for welding, find the
cost of the material in the tires of the two wheels.
5. A measuring wheel used at the Blacksmith Shop
makes 24;/ to the revolution. What is the diameter of
this wheel? Find on a scale the length of this diameter
to the nearest eighth of an inch.
6. At the Machine Shop ten slots were cut in the rim
of a circular disc 3" in diameter. Each slot was tV'
wide. These slots were equally spaced on the rim. Find
the distance on the circumference of disc between any
two successive slots.
7. Find the area of the face of a disc which is 8" in
diameter.
8. The pressure of steam against a piston 12// in
diameter is 85 pounds to the square inch. Find the total
pressure upon the piston.
LUMBER MEASURE
The wood work on a one-horse farm wagon was done
in the Wheelwright Shop. Before we can compute the
cost of the materials used in the construction of this wag¬
on, it will be necessary to find the number of board feet
in the lumber used, for the Institute buys its lumber at
given prices per 1000 board feet.
A board 1 foot long, 1 foot wide,- and 1 inch thick
contains 1 board foot of lumber. (See board foot exhibit¬
ed by teacher.)
The number of board feet in a piece of lumber is equal to
the product of the numbers which express its length in feet, its'
width in feet, and its thickness in inches. A thickness less than'
1 inch is to be reckoned as 1 inch.
Persons who deal in lumber usually use the word "foot" instead
of "board toot".
LUMBER MEASURE 119
1 he coupling pole of the one-horse farm wagon requir¬
ed a piece of lumber measuring 2" X3 U " X 12'. Then,
in this piece of lumber there were
2 X 3 '4 X J* bd. ft. ==6^2 bd. ft,
11
Hxercise 48
1. The farm wagon mentioned above required in its con¬
struction the following pieces of lumber:
FRONT GEARING
No. of pieces Measurements Kind of wood
2 1-^"x4^"x9' Oak
1 2^"x3"x53" Oak
1 2i.;"x2i,"x2(r Oak
1 3" X 3/4" X 41" Oak
1 2^"x2"x51" Oak
2 i;4"xiM"x33" Oak
1 1M"x2>2"x46" Oak
1 l->i"x2"x46" Oak
2 l"x3"x 12" Oak
REAR GEARING
1 2^"x3"x53" Oak
1 2 >2"'x 3 >2" x 49" Oak
2 2"x3V2"x42" Oak
2 I"x3"xl2" Oak
COUPLING POLE
1 2"x3/4"xl2' Oak
BODY
2 1^"x3>4"x12' Oak
1 1-%"x4"x50" Oak
1 1-H"x2j4"x50" Oak
1 IH"X2>A"X12" Oak
3 I"xl2"xl2' Oak
2 1"X12"X40" Poplar
2 l"x 12' X12' Oak
14 I"x2"xl2" Oak
120
PRACTICAL APPLICATIONS
1 he spokes for the wheels cost $3.25; the hubs, $1.10;
the rims, $1.75. The labor in the Wheelwright Sho,p
cost $4.02. The iron work, including labor, in the Black¬
smith Shop cost $18.00. The painting of the wagon cost
$4 00. The oak used cost $23 per M; the poplar, $65
per M. Find the total cost of producing this wagon.
2. Class will visit Institute Sawmill and LumbtrYard.
PERCENTA G'E
Exercise 49
1. The Montgomery Fruit and Produce Co sold in
Montgomery for the Institute 39 crates of peaches at
$1.75 per crate and charged as commission -10% (read 10
per cent) of the total amount received for the peaches.
Expressage on this fruit cost the Institute $6.82. Find
the net amount received by the Institute for this fruit.
Per cent means by the hundred.
Then, 10% means tW, or .10.
5% means Too, or .05.
Commission is the amount charged by an agent or fiim
for buying or selling for another.
The solution of the preceding problem follows.
39X$l-75-—$68.25, amount received for 39 crates of peaches at
$1.75 per crate.
10% of $68.25—. 10 X $68.25-—$6,825
Then, the commission charged by the firm was $6.83
$8.56, expressage
6.83, commission
$15.39, total charges on transaction.
$68'25 $15.39-~=$52.86, net amount received by the Institute.
2. McCollough Bros, of Atlanta, Ga. received from
the Institute 42 crates of peaches. 1 he firm sold 21
crates at $2.25 each and 18 crates at $2.00 each. 4 crates
were lost in repacking. Expressage on the shipment was
$18.48. The firm charged 10% commission. Find net
amnunt rerpived bv the Institute.
122
PERCENTAGE
3. M. P. Wilcox of Montgomery received 5 crates of
peaches from the Institute which were sold at $2.25 a
crate. Find the net amount received by the Institute,
after paying 10% commission and deducting $1.10 for ex-
pressage.
4. J. J. Payne of Atlanta received 36 crates of
peaches from the Institute which were sold at $2.50 a
crate. Expressage on the shipment was $16.28; the
commission charged was 10%. The agent returned to
the Institute 44 empty crates for which he received $.10
each. How much did the agent remit to the Institute?
Exercise 50
Express the following as common fractions in lowest terms:
1.
12%
7.
18%
13.
CO
2.
25%
8.
15%
14.
62 >v
3.
75%
9.
45%
15.
33 H
4.
60%
10.
110%
16.
66^'
5.
80%
11.
200%
17.
16-'.;'
6.
6%
12.
12/2%
18.
w
Express
as decimals.
19.
3.5%
3-5% =
3 . S —
10 0
035
20.
5.8%
22.
0.8%
24.
.75%
21.
3.7%
23.
0.05%
25.
y^/o
Express
as per cents.
26.
.325
.325
— 3 2 S
10 0 0
— 3 2 . S —
1 0 0
32.5%
27.
.98/
30.
.5
33.
.075
28.
.101
31.
.065
34.
•oi x
29.
.333
32.
.005
35.
.575
v/o
PERCENTAGE
123
Exercise 51
1. In the cupola at the Foundry, pig iron is melted to¬
gether with scrap iron. For ordinary purposes, such as mak¬
ing window weights, etc., pig iron constitutes 25% of the
mixture. What per cent of the mixture is scrap iron?
At one time 700 pounds of iron were required for certain
castings of the kind just mentioned. How much pig iron
and how much scrap iron were used on this occasion?
In the above problem, 700, the number of which a
certain per cent is to be taken, is called the base.
25%, which states the number of hundreds to be taken,
is called the rate.
The result of taking a certain per cent of a number is
Called the percentage.
2. The amount of coke used in the cupola is 10% of
the weight of the iron to be melted. How much coke
was used to melt the 700 pounds of iron mentioned in the
preceding problem?
3. Machine castings contain 75% pig iron and 25%
scrap iron. Iron blocks cast at the Foundry for use in the
M achine Shop are 2" square at the ends and 3' long. 1
cu. in. of casting weighs .26 pound. The scrap iron
cost $.25 per cwt. and the pig; iron, $16.85 per ton (in¬
cluding freight). Find the cost of the iron required for
one of these blocks.
4. The Babbitt metal used in the Machine Shop as a
lining for certain parts of machinery consists of 3.7% cop¬
per, 89% tin, and 7.3% antimony. This metal is sold in
five-pound bars. Find the number o' pounds of copper,
of tin. and of antimonv in each bar.
124
PERCENTAGE
5. On one day 182 pounds of cream were churned at
the creamery. A test showed that 32% of this cream
was butter fat. Find the number of pounds of butter fat
in the cream.
6. The Creamery received from the Dairy Barn on
one day, 1736 pounds of milk testing 4.5% butter fat.
On the same day neighboring farmers sold the Creamery
73 gallons of milk testing 4% butter fat. Find the total
number of pounds of butter fat in the milk received from
these two sources. (8.6 pounds of milk make 1 gallon.)
7. A rule used at the Creamery in estimating the
number of pounds of butter that can be made from whole
milk is as follows: Multiply the number of pounds of
butter fat in the milk by 1.17. According to this rule,
how many pounds of butter ought to be obtained from
150 gallons of whole milk testing 4.5% of butter fat?
(8.6 lb to 1 gallon.)
8. To estimate the number of pounds of butter that
can be obtained from cream, proceed as follows: Mul¬
tiply the number of pounds of butter fat in the cream by
1.20. On one day J 50 pounds of cream testing 35%
butter fat were churned at the Creamery and 69 pounds
of butter were obtained. How does this result compare
with that which should have been obtained according to
rule?
9. On another day 274 pounds of cream testing 30%
butter fat were churned and 97 pounds of butter were
obtained. Compare this result with that given by rule.
10. Make similar comparisons of recent results in
butter making obtained at the Creamery.
PERCENTAGE
125
Study carefully the bill reproduced on page 126.
Observe that the price of the "cementico'' is $.09 per
pound, and, at that rate, the value of the purchase is
$27.00. But a reduction of 45% of $27.00, amounting
to $12.15, is given. The price, $.09 per pound, is fixed.
Instead of changing this price, the firm gives a reduction
of 45% of the same.
Such a reduction on the list price of goods is called a
trade discount.
After the freight has been deducted, we see that the
Institute owes the firm $13.35.
The terms on which goods are sold name the conditions
of payment. Notice that on the bill under consideration,
the terms are expressed thus: "60-2-10". This means
"60 days net, 2% discount in 10 days, that is, payment of
$13.35 is expected within 60 days of date, or a further
discount of 2% of $13.35 will be given for payment with¬
in 10 days of date on bill.
Th is last discount, which is a reduction for payment
within a specified time, is called a time discount.
This particular bill was paid by the Institute within 10
days of date of bill.
2% of $13.35 = $.267
The Institute was allowed a further reduction of $.27.
Then, the amount actually paid by the Institute for the
"cementico" was $13.35 —$.27, or $13.08.
United States Gypsum Co.
Customer's Order No. Manufacturers of Our Order No.
Req. 205
Sold to
| Address
T erms
If. o. b
GYPSUM PRODUCTS
CHICAGO, ILLINOIS
Tuskegee N. & 1.
Ins ti-tute,
E-77305
Date Shipped
5-12-11.
Shipped to Tuskegee N. & I.
Ins tit/U te.
Tuskegee Inst,. Ala. Station Tuskegee Inst.t Ala.
60-2-10 Via C & E i& W & A
Mi 11
CAR INITIAL
CAR NUMBER
WMAKEALL REMITTANCES IN CHICAGO OR NEW YORK EXCHANGE TOCHICAGO OFFICE, 200 MONROE STREET
3-100# drums white cementico. .09
Less 45%
Less frt 500 cwt.
Jute bads included in this Invoice vill be purchased at 10 cents each if
returned promptly to mill from which shipped in good order, freight paid
$27.00
12.15
$14.85
1.50
$13.35
PERCEN I'AGE
127
Exercise 52
1. The I nstitute bought from the American Woolen
Co. of New York 2 pieces of dark blue cloth, containing
together 81Y? yards, at $1.80 per yard^ and 2 pieces of
light blue cloth, containing together 117/4 yards, at
$1.22^ per yard. Terms 7% discount 4 months; 8% dis¬
count 2 months; 8/4% discount 30 days; 10% disccunt
10 days. The Institute made payment within 10 days.
Find the amount paid.
2. The Crane Co. of Birmingham, Ala. sold the In¬
stitute 603 feet of 2-inch black pipe listed at $.36 per
foot. A discount of 74.5% on list price was given. Find
the amount paid by the Institute.
3. Bernard Frank and Co. of Montgomery, Ala. sold
the Institute 10 bolts of cloth consisting of 338 yards at
$.10 per yard. Terms: 2% 10 days; 60 days net. The
Institute took advantage of the discount. The pack¬
age of goods weighed 150 pounds on which the In¬
stitute paid freight at the rate of $.307 per cwt. Find
total cost of cloth.
4. The Institute bought of the Westinghouse Lamp
Co. of Bloomfield, N. J. 100 tungsten lamps at $.70
each, 100 tungsten lamps at $1.10 each, 48 tungsten
lamps at $1.45 each, 250 carbon lamps at $.20 each,
and 175 carbon lamps ac $.30 tach. The discount
on the above was 17/4%. An additional discount of
10% was allowed on the tungsten lamps to cover possible
breakage. Find the amount paid by the Institute.
5. The Institute bought of L. Dannen >aum's Sons of
Philadelphia, Pa. 60 pieces of braid at $.62/4 each.
Terms: 6% 10 days; 5% 30 days. The Institute pa d
within 10 days. Find the amount of the payment.
128
PERCENTAGE
6. The Pittsburg Plate Glass Co. ■ lanta, Ga.
sold the Institute 15 boxes of window g, he price of
which, as listed, was $453.50. Discounts ' % and 10%
were given. Find the amount paid the or the glass.
In this problem, after the first discount of 90% has been taken, the
amount remaining is reduced by a discount of 10%. The last re
suit gives the amount paid by the Institute.
7. The Crane Co. of Birmingham, Ala. sold the In¬
stitute the following:
16 /4" tees, 5 pounds, at.$.28 per pound, less 45%—5%;
30 l"X/^"tees, llyi pounds, at $.28 per pound, less
45%—5%; 24 1" tees, 16 pounds at $.28 per pound, less
45%—5%; 228 feet of y?" galvanized pipe at $.08/4 per
foot, less 55%; 160 feet of 1" galvanized pipe at $.16/4
per foot, less 61%; 208 feet of 3" black pipe at $.75/^
per foot, less 71%. Find the amount paid the firm.
8. The Institute bought of the Electric Appliance
Co. of New Orleans, La. the following: 100 glass in¬
sulators at $50.64 per M; 500 feet of No. 6 weather¬
proof wire, 56 pounds, at $16.60 per cwt.; 500 feet
of No. 4 weatherproof wire, 84 pounds, at at $16.60 per
cwt; 500 pounds of No. 8 weatherproof wire, 41 pounds,
at $16.60 per cwt.; 500 feet of No. 10 weather¬
proof wire, 26 pounds, at $17.60 per cwt; 25 soc¬
kets at $.33 each, less 40%; 125 fuse plugs at $2.75
per 100; 25 dry cells at $.20 each; 3 bells at $.28 each;
4 push buttons at $.06 each; 125 oak side brackets at
$17.50 per M; 500 feet of No. 10 rubber covered wire at
$29.50 per 1000 feet, less 50%>250 feet of No. 8 rubber
covered wire at ,$40.00 per 1000 feet, less 50%; 250 feet
%" circular loom at $.06 per foot, less 33*/i%; 250 feet
of No. 18 fixture wire at $10.10 per 1000 feet, less 50%;
500 feet of No. 18 lamp cord at $25.30 per 1000 feet, less
50%—10%.
PERCENTAGE
129
After the discounts indicated were taken, further dis¬
counts for payment within 10 days were allowed: ^2 of
1% on the weather proof wire; 1% on the rubber covered
wire; 2>2% on the sockets; 1% on the lamp cord; 2% on
all other goods. Find the amount paid by the Institute
to the firm in settlement of this bill.
Exercise 53
1. Employees of the Institute who trade with its various
departments use largely for this purpose coupon books.
One such book is good for $20 in trade, and costs $20,
but a rebate of $1 is given the purchaser when the book
has been used. What per cent of the cost of the book is
the rebate? What is meant by ' rebate"?
$20;=cost of coupon book.
of cost of coupon book*
_z_ = .05 = 5%
Then, the rebate is 5% of the cost of the book.
Note that in the preceding problem, the base, $20, and the per¬
centage, $1, are given and the rate is to be found. Since the per¬
centage is equal to the product of the rate and base, it is seen that
the rate ts found by dividing the base by the percentage.
2. At the Creamery the number of pounds by which
the butter exceeds the butter fat contained in the
cream from which it is made is called the over run.
The attempt is made to keep the weight of the over
run always about 20% of the weight of the butter
fat in the cream. On one day 210 pounds of cream test¬
ing 30% butter fat were churned and 74 pounds of butter
Were obtained. What per cent of the weight of butter
fat in the cream was the over run?
130
PERCENTAGE
30% of 210 lb. =63 lb., the weight of the butter fat.
74 lb. 631b. =11 lb., the over run.
Since 631b. = weight of butter fat.
1 lb. —of the weight of the butter fat.
11 lb. =-§--3- of the weight of the butter fat.
Then the over run was XX of the weight of the butter fat.
ix = H^ 63 — .1746 -
1746 = -XXA s xx-a 6 = 17 46c/,
' ' u 10000 — 100 ''w/',
Then, the over run was about 17.5% of the weight of the butter
fat.
3. From 196 pounds of cream testing 35% butter fat,
84 pounds of butter were obtained. What per cent of
the weight of the butter fat was the over run?
4. From 216 pounds of cream testing 38r/r butter fat,
99 pounds of butter were obtained. What per cent of
the weight of the butter fat was the over run?
5. At the Poultry Yard in January, 1911, the eggs in
the 8 incubators then in use were tested with the follow¬
ing results:
Incubator No. of eggs No. of eggs No. of eggs No. of
put in.
broken in turning
Infertil
e eggs with
dead germs.
No. 1.
400
2
71'
1
2.
378
8
24
3
3.
163
1
18
1
4.
215
0
29
5
5.
261
0
88
16
6.
226
3
27
4
7.
89
0
16
6
8.
96
1
31
2
What
per cent of
the eggs not b
roken
was infertile?
What per cent of the eggs not broken contained dead
germs?
PERCENTAGE
131
6. The uniform dress of a student made in the Dress-
snaking Division costs as follows: yards of cloth at
$.12^2 per yard; 1 dozen buttons, $.10; 1 spool of thread
3-05; 2 hooks and eyes, $.01; labor, $.50. This uniform
was sold for $2.00 Find the gain per cent. (In reck¬
oning gain per cent or loss percent, the cost is always the
base.)
7. A pair of shoes made in the Shoe Shop sold for
$5.00. The cost of making the shoes was as follows:
trimming, $.30; bottom stock (soles, heels, etc.), $1.25;
uppers, 2h sq.ft. of leather at $.35 per sq. ft.; incidentals,
$.08; labor, $1.75. Find the per cent of profit (gain)
made on this pair of shoes.
K. In May, 1911. there were 13.300 peach trees in rhe
Institute Orchard of which 5346 were bearing. What
per cent of the peach trees was bearing at this time?
THE EQUATION
It will be found of advantage in solving many problems
to know something of the equation.
3+9=2x6
x-\- 7 = 20
A statement, like the above in which two expressions
(numbers) are said to be equal is called an equation.
In the second equation ^ stands for the number which
when added to 7 produces 20. This number we know to
be 13. for 134- 7 — 20.
The teacher will show by actual balance or scales the
truth of the following:
132
THE EQUATION
(1) The same number may be added to or subtracted
from both sides of the equation without altering the
equality.
(2) Both sides of an equation may be multiplied or
divided by the same number without altering the equality.
Find the numbers represented by the letters in the follow¬
ing equations.
Exercise 54
*=35—17=18.
Check: 18+17=35
2. *-8 = 10
Adding 8 to both sides of the equation, we have
*= 10+8 = 18
Check: 18—8 = 10
3. *+21 = 50
4. 9 = 17
5. *-30= 5
6. n- 7.3 = 8.7
7. * + 19.4 = 31.2
8. p+ .03 = 7
9. 3*+17 = 47 (3* means 3 times *)
Subtracting 17 from both sides, 3^=47 —17, that is,
3*=30
Dividing both sides by 3, jr=10
Check: 3X10+17=47
10. 4* + 7 = 27 13. 6£+ 8=«25
11. 3y — 5 = 22 14. 17*-.3 = 30.5
12. 5*—23 = 17 15. 5.6m + 3.7 = 40.9
PERCENT AGE
133
Exercise 55
1. In machine castings made at the Foundry, 75% of
the mixture is pig iron. Find the weight of a casting
containing 45 pounds of pig iron.
75% of wt. of casting = 45 lb.
1% of wt. of casting = of 45 lb. = lb.
100% of wt. of casting = 100 X yf lb. = 60 lb.
But 100% of weight of the casting is what we are trying to find.
Then, the weight of the casting is 60 pounds.
By making use of what we have learned concerning equations, we
may solve the problem as follows:
Let ;r = no of pounds in wt. of casting
Then, .75* = 45.
Dividing both sides by .75, x = 45^-.75 = 60
Then, the casting weighed 60 pounds.
2. The Institute paid $58.59 for a bolt (21 yd.) of
unfinished worsted, 7% discount being given for payment
within 10 days. At what price per yard was this cloth
listed?
Let * = no. of dollars in the price 21 yd. as listed.
.07* = no. of dollars in the discount,
x—.07^ = 58.59 the no. of dollars actually paid
x — .07*= lx—.07* = ,93x
.93* = 58.59
Dividing both sides by .93, x =63
Then, the 21 yd. of cloth, at the list price, would cost $63.
$63-^ 21 =$3, list price per yd. of worsted.
3. A casting contained 12/^ pounds of scrap iron.
This scrap iron was 25% of the weight of the casting.
Find the weight of the casting.
134
PERCENPAGE
4. A man received $9.00 on an investment in t.be
Tuskegee Co-operative Building and Loan Association,
which was 6% of the money invested. How much had
the man invested with the association?
5. How much must one invest in the association in
order to be assured of an income of $150?
6. For a pair of half soles sewed on the shoes, the
price charged at the Shoe Shop is $1.00. This gives the
Shoe Shop a profit nf 17H% on the cost of job. Find
the cost of the job.
7. One dozen "jumbo blocks" (sole leather) cost the
Institute $6.37, after a discount of 2% had been given.
Find the list price of this leather at that time.
8. A commission merchant of Montgomery, Ala. sold
12 crates of peaches for the Institute. After deducting
$2.50 for expressage, and 10c/r as commission for selling,
the merchant sent the Institute $19.10. At what price
per crate did the merchant sell the peaches?
9. All milk received at the Institute Creamery is "run"
through the separator, a machine which separates milk
into cream and skimmed, milk. The butter fat in the orig¬
inal milk flows out in the cream, the amount of butter fat
in the skimmed milk being so small as to be negligible in
practical calculations. After the separation, the cream
and skimmed milk are recombined to form whole milk
or cream containing any desired per cent of butter fat.
On one day 10 gallons of milk testing 4.5% were made
by mixing together skimmed milk and cream testing 45%
of butter fat. Find the number of pounds of skimmed
milk and of cream used for this purpose.
PERCENTAGE
135
8.6 lb.=wt. of 1 gal. of milk testing 4.5% butter fat.
10> 8.6 lb. = 86 lb. = wt. of 1 gal. of milk testing 4.5% butter fat.
4.5% of 86 lb. =3.87 lb., wt. of the butter fat in the 1 gal. of milk.
Since we are to regard the skimmed milk as having no butter fat,
we see that the 3.87 lb. of butter fat to be found in the 10 gallons of
the mixture must come wholly from the cream testing 45% Then,
we are required to find the amount of cream testing 45% butter fat
which contains 3.87 pounds of butter fat.
Let x = no. of lb. of cream required
.45* = 3.87
* =3.87 -.45 = 8.6
Then, 8.6 pounds of cream testing 45%, butter fat were used.
86 lb. -8.6 lb. =77.4 lb., the number of pounds of skimmed milk
required.
10. During one summer the Institute shipped daily to
the Riverside Dairy of Columbus, Ga. 10 gallons of
cream testing 20% butter fat. Cream of this kind weighs
8.4 pounds to the gallon. On one day, the shipped cream
was formed by combining cream testing 52% butter fat
and skimmed milk. How much of the cream testing
52% butter fat and how much skimmed milk were mixed
together to obtain the 10 pounds of cream testing 20%?
11. On another day the 10 pounds of cre^m testing
20% were made by combining cream testing 40% and
skimmed milk. How many pounds of cream testing 40%
and of the skimmed milk were used? (Give results to
the nearest ounce.)
12. On another day cream testing 48.5% butter fat
and skimmed milk were used to make the 10 pounds of
cream testing 20%'. Find the quantity of cream testing
48.5% butter fat and of skimmed milk used for this
purpose.
136
percentage
13. The whole milk sent out from the Creamery tests
4.5% butter fat. At one time 20 gallons of such milk
were made by mixing together cream testing 39.5% but¬
ter fat and skimmed milk. Find the quantity of cream
and of skimmed milk required.
RATIO AND PROPORTION
In the compounding of medicines in the Institute Drug
Room, in the mixing of fertilizers on the Farm, in the
making of belt dressing at the Machine Shop, etc., care
is exercised, in the case of any given mixftjre, to maintain
certain prescribed relations between the amount of any
one ingredient and the whole, and between the amount of
any one ingredient and that of any other ingredient.
For instance, in 1911, all cows at the Dairy Barn giving
more than 20 pounds of milk daily were allowed for the
day's feed 30 pounds of cotton seed hulls, 5 pounds of
Cotton seed meal, 2 pounds of bran, 3 pounds of shorts>
and 50 pounds of rape. Now, the total weight of this
feed for the day was 90 pounds.
The wt. of the cotton seed hulls = g-g. of the Wt. of the whole feed*
" " " " " " mtal = A "
V " " " bran = im> '
" " " " shorts = 93o~ " ''
,. „ rape =££""
Also, the weight of the bran was |- of the Weight of the cotton seed
ttieal, etc.
Whatever the amount of feed mixed at one time, whether a
quantity sufficient for 1 COW or for 58 COWS, the relation between the
weight of any ingredient and the whole feed, and the relation between the
Weight of any one ingredient and the Weight of any Other ingredient were as
given above, that is, these relations never changed.
Such a relation, like those indicated above, between
two numbers of the same kind is called a ratio.
138 RATIO AND PROPORTION
The ratio of one number to another number is found
by dividing the first number by the second.
The ratio of 3 ft.-to 6 ft. =A = JL= c
6 ft. 6 2
The ratio of 12 lb. to 4 lb •— ^ '— = 3
4 lb.
Note that the ratio is between rtumbers of the same kind, that is,
numbers that refer to the same unit, and that a ratio is always
abstract.
A ratio may be expressed in two ways. The ratio of
5 to 7 may be written as j or 5:7. In the ratio, 5 -7,
the first number, 5, is called the antecedent; the second
number, 7, is called the consequent.
Exercise 56
Express the following ratios first as common fractions in low-
est terms and then as decimals
(3 places):
1. 10 : 12 5.
3.5
: 7
9.
.03 : 1.6
2. 7 ft. : 14 ft. 6.
2.1
: .35
10.
2 >2 : 8
3. 8 lb. : 22 lb. 7.
56 :
72
11.
3tt : Vh
4. 3 ft. : 48 in. . 8.
36
: 6
12.
5 . 2
6 • 3
Exercise 57
1. Six acres of strawberries belonging to the Institute
were fertilized with the following mixture: 3 parts nitrate
of soda, 4 parts muriate of potash, and 2 parts acid
phosphate. 900 pounds of this mixture were applied to
the acre. How many pounds of nitrate of soda, of muri¬
ate of potash, and of acid phosphate were used on the
6 acres?
According to the above statement, to every 3 pounds of nitrate of
soda, there were used 4 pounds of muriate of potash, and 2 pounds
of acid phosphate.
31b. +4 lb.+2 lb.— 9 lb.
RATIO AND PROPORTION
139
Then, in every 9 pounds of the mixture, there were 3 pounds of
titrate of soda, 4 pounds of muriate of potash, and 2 pounds of acid
phosphate.
6X900 lb. =5400 lb., the weight of the mixture for 6 A.
5400 lb.-^9 lb. —600, the no. of tirrile that 9 lb. occurs in 5400 lb.
600X3 lb. = 1800 lb.> the weight of the nitrate of soda used.
600 X4 lb. = 2400 lb., the weight of the muriate of potash used.
600X2 lb. = 1200 lb., the weight of ihe acid phosphate used.
2. A fertilizer used at the Truck Garden consisted of
1 part muriate of potash, 2 parts acid phosphate, and 4
parts cotton seed meal. 25 acres planted in cabbage
were fertilized with this mixture,, 500 pounds being used
per acre. The muriate of potash cost $45 per ton, the
acid phosphate, $14 per ton, and the cotton seed meal,
$27 per ton. Find the cost of the fertilizer used on the
25 acres of Cabbage*
3. The same fertilizing mixture was used on 10 acre's
■of onions, 12 acres of Irish potatoes, and 18 acres of corn*
500 pounds were used on each acre. Find the cost of the
fertilizer used on each of the crops named.
4. A fertilizer used on the orchard consisted of 1
pound of Cotton seed meal to2lA pounds of muriate of
potash. Fin^i the cost of a ton of this fertilizer at the
prices given in the preceding problem.
5. A cover Crop used on the Orchard consisted of rye
and oats sowed in the ratio 1 : 2. 1/. bushels of th;s
mixed seed were useJ on each acre. 30 acres were
planted in this seed. Fmd the amount of each seed re¬
quired.
140
RATIO AND PROPORTION
6. Trees in the Orchard were sprayed with the follow¬
ing mixture: 2 pounds of arsenate of lead dissolved in
100 gallons of water and 1 pound of lime sulphate dis¬
solved in 60 gallons of water. At current prices, what
would 10 barrels of this mixture cost? (31/^ gal. = 1 bbl.)
7. A liquid preparation used in the summer as a belt
dressing at the Machine Shop consists of the following: 4
pounds of bees wax, 5 pounds of pitch, 3 pounds of resin,
and 13 pounds of neat's-foot oil. Find the number of
pounds of each ingredient in 50 pounds of the dressing.
8. A solid preparation used in the winter as a belt
dressing at the Machine Shop consists of the following:
6 pounds of beeswax, 5Y* pounds of pitch, 6Y pounds
of resin, and 1 pound of neat's-foot oil. How many
pounds of each ingredient are in 50 pounds of the prep¬
aration?
A proportion is a statement that two ratios are equal.
Th us, 3 : 7 = 9 : 21, is a proportion.
Find the value of x in the following:
Since this proportion is an equation, we can multiply both sides by
15 without destroying the equality.
Exercise 58
1. x _ 3
15" 5
3
x — 9
Check:
2. _x _ 5
27_ 9
4. * 2
.006— 3
3.
X
s_
4
5. * : 12 = 9: 22
16
RATIO AND PROPORTION
14i
6.
X
7
9. ^
2 =
8
7.
X
5
10. X
13=
7
8.
X
6
11. x
3.5 =
.07
6.4= .15 : 3.2
* : 6 = 3! : 5i
In the proportion, 5 : 7=15 : 21, the first and last terms, 5 and 2l,
are called the extremes; the second and third terms, 7 and 15, are
called the means. The product of the extremes is 5 X 21, or, 105.
The product of the means is 7 X 15, or, 105. From this we see
that, in a proportion, the product of the extremes is equal to the
product of the means.
12. x : 8 = 9 : 4
The product of the extremes is 4x; the product of the means is
8X9, or 72.
4x-72
x~18
13. 5 = 6: 13 16. *
7 — 21
14. *: 4.2 = 11:.6 17. *_A
.33~11
15. *:*=*:* 18.
7! 2
Exercise 59
1. On Jan. 18, 1911, in constructing the concrete
floor of the Institute Reservoir, there were used 55 sacks
of cement. (.95 cu. ft. to 1 sack.) The mixture used*
consisted of sand, gravel, and cement, 5 cu. ft. of cement
being used to 27 cu. ft. of sand and 27 cu. ft. of gravel.
Hew many cu. ft. of sand and of gravel were used on
the day mentioned? The cement cost $.65 per sack; the
sand, $.80 per cu. yd; and the gravel, $1.00 per cu. yd.
Find the cost of the material used. j
142
RATIO AN0 PKOPOKTION
55 X-95 cu. ft =52.25 cu. ft., the quantity of cement used on
fhe given day.
Since 27 cu. ft. of sand were mixed with 5 cu. ft, of cement, then,
the number of cti. ft. of sand used with 52.25 cu. ft. of cement must
hear the same ratio to 27 that 52.25 bears to 5.
Then, if x represents the number of cs». ft. of sand used with
52.25 cu. ft- of cement,
x _52.25
21 ~ 5 "
Multiplying both sides of the equation by 27, we obfafn
*= —
5
Then, the?e were 282.15 cu. ft. of sand used with the 52.25 cu,
ft. of cement. Also, there were 282.15 cu. ft. of gravel in the mix-
lure. Why?
55X$-65 2s$35.75, cost of the cement.
282.15-^27—10.45, no. of cu. yd. in 282.15 cm. ft,
10.45,X$.80— $8.36. cost of the sand.
J0.45X$1.00 = $10.45, cost of the gravel.
$35.75+$8.36+$10.45= $54.56, total cost of material used if?
constructing the concrete $oor of the reservoir on Jan. 18", 1911.
2. In putting the finishing layer of concrete on the
floor of the Reservoir, a mixture Consisting of cement and
sand in the ratio 1 r 2 was used. On one day 7 sacks of
cement were used in connection with this work. Find
the cost of the sand and of the cement used on the given
day at the prices mentioned in the preceding problem.
3. Cement Mocks used in the construction of Tomp¬
kins Hall were made of 3 parts of sand to 1 part of ce--
ment. Find the cost of the material used in the making
of a dozen- blocks each measuring S^X lS 'xlS".
RATIO AND PROPORTION
143
4. In a drawing of the Institute Chapel, the height of
a 24' window was represented by 4", According to this
scale, what length represented the height of the 113r
tower?
5. At the Creamery 9 pounds of cream testing 50%
butter fat are mixed with 91 pounds of skimmed milk to
produce 100 pounds of whole milk testing 4,5% butter fat.
How many pounds of skimmed milk must be used with 6
pounds of such cream in order to produce whole milk testing
4.5% butter fat? How many gallons of whole milk would
be in the mixture? (8.6 lb. to 1 gal.)
6. At the Machine Shop it is estimated that 1 cu. in,
of cast iron weighs .2607 lb., and 1 cu. in. of wrought
iron, .2816 lb. A piece of machinery made of wrought
iron weighs 36 pounds. What would the same piece
weigh if made of cast iron?
7. Patterns used at the Foundry are made of poplar
and pine. Find out (through teacher) the ratio of the
weight of 1 cu. in. of poplar to 1 cu. in. of cast iron.
Secure the same information concerning pine and cast iron.
Weigh certain patterns at the Foundry, and on the basis
of the information that you have obtained, compute the
weight of the casting for each pattern.
PRACTICAL APPLICATIONS
All plane figures bounded by straight lines, such as
triangles, quadrilaterals, etc., are called polygons.
A prism is a body
whose two ends are
equal and parallel
polygons and whose
sides are parallelo¬
grams.
We have already
dealt with one kind of
prism under the name
of rectangular soli d.
(Page 73.)
Locate prism-shaped
structures in the shops
and on the Institute
grounds.
It fs often necessary to find the volume of prisms#
as, for instance, in computing the capacity of one of the
prism-shaped silos on the Institute Farm, in which feed for
stock is kept. It can easily be seen that, if a prism is 1
inch in height, the number of cubic inches in the volume
of the prism is equal to the number of square inches in
its base. Then,
The volume of a prism is given by the product of the
numbers which express the altitude and area of the base in
corresponding units.
If the area of the base is expressed in square inches and the altitude
in inches, the base and altitude are said to be expressed in correj
sponding units. Other sets of corresponding units are: square foot
and foot, etc.
PRACTICAL APPLICATIONS
145
A body having a uniform diameter with two circles as
its ends is called a cylinder^.
Many tanks made in the
Tin Shop are cylindrical in
shape.
Locate other cylinders in
the shops and on the Insti¬
tute grounds.
As in the case of the prism,
it is often necessary to find
the volume of a cylinder, as,
for example, in estimating
the number of gallons held
by the Institute reservoir.
The volume of a cylinder is
given by the product of the
numbers which express the altitude and the area of the base in
corresponding units.
The area of the curved surface of a cylinder is given by the
product of the numbers which express the altitude and tht cir¬
cumference of the base in the same unit.
This is easily seen from the fact that at the Tin Shop in making
a cylinder of the kind that we are considering, the curved surface is
cut in the form of a rectangle. The base of the rectangle becomes the
circumference of the base of the cylinder and the altitude of the
rectangle becomes the altitude of the cylinder.
Exercise 60
1. Each of the three gables on Tompkins Hall meas¬
ures 35' at the base and has an altitude of 10'. The
brick work of these gables is 13" thick. Find the cost of
146
PRACTICAL APPLICATIONS
the bricks required to build these gables at $7.90 per M,
allowing 22 bricks to the cubic foot.
2. A tank in which fruits are washed at the Canning
Factory is 4/93/~" long, 19 " wide, and 14 1 s" deep. Find
the capacity.
3. Sides for the Ames engine used by the Institute are
cast at the Foundry. Each such plate is y'%" thick. The
face of the plate is a trapezoid with bases 15" and 10/4",
and altitude 12". On every plate there are four projec¬
tions each ^"Xl"Xl5's". At one time 12 of these
plates were cast. Find the cost of the iron in these 12 plates
if the castings were made entirely of scrap iron valued at
$.25 per cwt. Allow .26 lb. to the cu. in.
4. One of the Emery dormitories is 109'8" long and
40'2" wide. The height of the walls to the top of the
cornice is 29 6". The two gables have an altitude of 18'.
The wall of the first story is 18" thick; that of the second
story, 12" thick. On the first floor there are 25 win¬
dows each 3/4"x6/2// and 3 doors each 6'X7'. On the
second floor are 27 windows and 2 doors of the same
size as those on the second floor. There are 6 chimneys
each 24//x24//x47/6//. The foundation walls of the
building are 18" thick and have an average depth of 3/4'.
Find the value of the bricks in this building at $7.90
per M. (Figure the chimneys as solid).
5. A set of reinforced concrete steps on the right of
Tompkins Hall consists of 22 steps. Each step is 12/
long, 15" wide (on an average), and 6" thick. At the
time of the building of these steps, it was estimated that
the labor and material required to cover 1 sq. ft. of sur-
PRACTICAL APPLICATIONS
147
face with concrete 6r/ thick cost $.35. In addition to the
concrete, there were used 22 steel bands each 12 long.
This steel cost $.17 per foot.
On either side of the concrete steps there is a brick
wall of curved shape. One wall was 16" thick, 23' long,
3 high at one end and 10' high at the other end The
second wall was 16" thick, 33' long, 4' high at one end
and 15' high at the other end. The estimated cost of
building these two walls was $14.50 per 1000 bricks laid.
Find the cost of the steps and walls together.
6. A gasoline tank made in the Tin Shop for use in
the Painting Division was 26" in diameter and 33" in
height. Find the number of gallons held by this tank,
allowing 231 cu. in. to the gallon.
All measurements are inside measurements unless otherwise specified.
7. The milk urn in the kitchen of Tompkins Hall is
41 >2" deep and 26^" in diameter. Find the capacity of
this urn in gallons.
8. The coffee urn in the same place is 30/4 " deep and
29/^" in diameter. How many gallons of coffee will this
urn hold?
9. An angle plate used in the Machine Shop was
cast in the Foundry. This plate consisted of two flat
pieces of iron meeting at a right angle and joined by
two quarter-cylinders of iron. One piece measured
1"x9/'2"x 11"; the other piece measured I"x9^2"xl0".
The radius of each quarter cylinder was 2-H ; the
thickness (height), . This casting consisted of
75% pig iron and 25% scrap iron If the pig iron
cost $16.85 per ton and the scrap iron $.25 per cwt.,
find the value of the iron in one of these plates, allowing
.26 lb. to 1 cu. in.
148
PRACTICAL APPLICATIONS
10. Each of the semi-circular arches over certain win¬
dows of Tompkins Hall has an inner radius of 6 and an
outer radius of 6'18". These arches are 24" thick. Find
the number of bricks in each arch.
11. *1 he engine used in the Foundry was built in the
Institute Shops. The cylinder for this engine was cast
in the Foundry. The outer diameter of this cylinder is
7/^", the inner diameter, 53/s". The length of the cylin¬
der is 8Y\" - Each of two flanges on this cylinder had an
inner diameter of 7^//, and an outer diameter of 11" and
was 1 in thickness. Find the weight of the iron
in this casting. Find the value of this iron at the prices
given in Problem 9.
12. The angle plates used in the roof of Tompkins
Hall were cast at the Foundry. Each plate consisted of
4 parts each l"x3"xllH"> and two parts each l/i"x
8%"xllY\" • A hole in one of the latter parts was \Y"
in diameter and 1/^^deep. This casting consisted of 25%
pig iron and 75% scrap iron. Find the cost of the iron
in the 32 plates which were used on the roof.
13. The pumping engine of the Institute water plant
has a water cylinder 8}4" in diameter with a 10-inch
stroke. How much water is delivered at each stroke?
14. A meter registers the number of strokes made
by the piston in the water cylinder. Find out
(through teacher) the number of strokes recorded by this
meter within a given length of time and calculate the
number of gallons pumped during the period.
15. Each of two hot water tanks in White Memorial
Hall is 20" in diameter and 5' long. How many gallons
of hot water can be held in these tanks?
PRACTICAL APPLICATIONS
149
16. Find out (through teacher) the measurements of
one of the Institute street sprinklers and compute the
number of gallons that it will hold.
17. Find the number of square feet in the surface of
the body of this sprinkler. Estimate the cost of
painting the same at local prices for this kind of work.
18. Twenty trash cans of galvanized iron were made
in the Tin Shop. Each can was 18" in diameter and 30"
in height. Two laps on the side of each side of the can
required 2". The bottom was cut out of a square 20"X
20". Find the value of the iron in these 20 cans, the
weight of 1 sq. ft. of this material being 1.656 pounds
and the cost of the iron being $3,886 per cwt (including
freight).
19 A tank made of galvanized iron was 10" in di¬
ameter and 20" high. One lap on the side required 1",
and 1/4" were added to the height for finishing at top
and bottom. The bottom was cut out of a square 12"X
12". This material weighed .9062 pounds per <q ft. and
cost $4,486 per cwt. (including freight). Find the value
of the iron used in the construction of the tank.
KEEPING A BANK ACCOUNT
[Exercise 61
1. Describe in detail the process of opening an account
with the Savings Department of the Institute. Why is a
new depositor required to register his signature?
2 Study carefully the deposit slip reproduced on page
151.
3. Study carefully the check and stub reproduced on
page 152. What is the purpose of the stub? (See one
of the check books issued by the Savings Department
of the Institute.) What is meant by indorsing a check?
4. Study carefully the form of bank book issued by
the Savings Department of the Institute. What en¬
tries are made on each left-hand page of the book? What
entries are made on each right-hand page of the book?
What is meant by "balancing the book?"
5. Secure blank deposit slip and show how you would
enter upon it the following, representing a deposit made
at one time: 1 ten-dollar bill, 3 one dollar bills, 7 silver
dimes, 5 silver dollars, check for $2.38, check for $9.50
6. Make out a deposit slip for the following: 3 two-
dollar bills, 4 five-dollar bills, 17 silver dollars, check for
$13.70, check for $7.06, check for $41.16.
7. Make out a check payable to your teacher for
$3.78. Have it endorsed properly.
8. Make out a check to the Institute for the amount'
due on your last month's account.
9- Find out what is meant by a certified check. What
is the purpose in having a check certified?
10 Find out all you can about the postal savings banks
of the United States Government.
KEEPING A BANK ACCOUNT
151
DEPOSITED WITH
Savings Department
OF THE
Tuskegee Normal and Industrial Institute
By Matheuj fVinsloiv
Tuskegee Institute, Ala., Feb• 1S> 1911
PLEASE LIST EACH CHECK SEPARATELY
CURRENCY
Dollars
Cents
15
GOLD
SILVER .
3
10
CHECKS
12
35
8
TOTAL t
1 38
45
NO 56
July 10,
19
11
Henry Anderson
FOR Rent
Bal. bro't Ford.
Dollars
130
Cents
76
Ami deposited
Total....
Amt. this Check
Bal. car'd Ford.
12
50
118
26
NO^- TUSKEGEE INSTITUTE. ALA.„ July 101 1911,
Savings Department Tuskegee N. & I. Institute
TUSKEOEE INSTITUTE. ALABAMA
Henry Anderson
PAY TO THE ORDER OF
T^el-ve o no. i adc $ 12^o
John H. Smith
KEEPING A BANK ACCOUNT
153
INTEREST
Money paid for the use of money is called interest.
Exercise 62
1. Find the interest on $750 for 3 years 6 months at
4%.
$750, principal
.04, rate
$30.00, interest on $750 for 1 year at 4(Jq
3*2, no. of years
1M)0
90 00
$105.00, interest on $750 for 3 yrs. 6 mo. at 4%
In computing interest, allow 30 days to the month and 360 days to
the year, except in cases where exact interest is to be found, in
which cases 365 days are counted as 1 year.
Find the interest on
2. $500 for 2 yrs. 3 mo. at 4%.
3. $675 for 1 yr. 9 mo. at 5%.
4. $1525 for 3 yrs. 2 mo. at 3%.
5. $3050 for 2 yrs. 5 mo. 10 davs at 4}4%.
Find the exact interest on
6. $735 from Sept. 3 to Dec. 5, 1909 at 6%.
7. $900 from Mar. 8 to Aug. 6, 1910 at 4%.
8. $840 from Jan. 16 to Feb. 26, 1911 at 5%.
9. $1075 from Nov. 29, 1910 to Jan. 6, 1911 at 6%.
10. Does the Savings Department of the Institute pay
interest on its deposits?
11. Secure (through teacher) information concerning
the interest paid by banks of the town of Tuskegee.
12. Look among the advertisements in newspapers and
magazines in the Institute Library and note the rate of
interest paid on deposits in various banks. Report the
same to class.
$ 200
On the 8th day of May 1911
Jan.
1911.
Tuskegee, Ala.,_
!Uje promise to pay to the order of
Savings Department Tuskegee Normal and Industrial Institute
the sum of Two-hundred.
no dollars
100
Value received, negotiable payable at_
Tuskegee, Ala.
And_-a>e-_do hereby waive..oar..claim for the exemption of any real or personal property, salary
or wages, which is now or may hereafter be under the Constitution and Laws of this or any other
state of the United States, wherein we may be residing at or after the maturity of this note ex¬
empted from levy, sale or condemnation, on execution or other process of any court issued for the
collection of the debt evidenced by the foregoing promissory note. And we furthermore agree
to pay a reasonable attorney's fee for the collection of this note if not paid at maturity.
3 »
rt>
O "2
5 3
ST O
n 3
3S»-
a!
Witnesses
No.
Richard S. Williams
Chas. M. Wright
Henry Abbott
[L. S.]
[L. S.]
[L. S.]
o ore
3 <■<
2 E
X a.
STUDY OP A BUSINESS ENTERPRISE
1SS
Fxercise 63
1. Study carefully the note on opposite page. I ind out
the rate of interest charged by the Savings Department
on such loans. Secure full information concerning such
transactions.
2. On a blank form like the one on the opposite page
make out a note for $150, dated March 1, 1910 and due
May 1, 1910.
3. Secure (through teacher) information concerning
the lending of money by the banks of the town of Tuske-
gee.
STUDY OF A BUSINESS ENTERPRISE
Exercise 64
The class will make a careful study of the Tuskegee
Co-operative Building and Loan Association as (1) an
enterprise in which money can be invested with a guaran¬
tee of a given income and (2) a source of help in the
building of homes.
REVIEW
Exercise 65
1. Students in cooking classes will report to the arith¬
metic class menus covering breakfast, dinner, and supper.
Estimate the cost of the materials required to prepare the
above for five persons at current Commissary prices. Ex¬
plain in detail your calculations.
2. Students not in cooking classes will compute the
cost of some operation being carried on at present in their
industrial divisions, as, for instance, the cost of making a
buggy, etc. Give detailed statement.
Exercise 66
1. The Institute bought 675 pounds of charcoal at
$.08 per bushel. Reckoning 22 pounds to the bushel,
find the amount paid for the charcoal.
2. An individual sold the Institute 4 head of cattle,
weighing altogether 1925 pounds, at $2.80 per cwt., and
one hog, weighing 205 pounds, at $.07 per pound. Find
the total amount received by the individual.
3. A wheel made in the Wheelwright Shop had a dia¬
meter of 4'. The diameter of the hub was 6/4"; the
REVIEW
157
depth of the rim, lyz". How long were the spokes cut
from the outside of the hub to the inside of the rim? (See
wheel).
4. The diameter of another wheel made in the same
shop was 42". The diameter of the hub of this wheel
was 8>4"; the depth of the rim, 1 Y\". How long were
the spokes cut from the outside of the hub to the inside
of the rim?
5. The diameter of a wheel was 36". The diameter
of its hub and depth of its rim were 4^"and 1/i" re¬
spectively. How long were the spokes cut from the
outside of the hub to the inside of the rim?
6. The Institute bought of G. A. Miller, Statington,
Pa., the slate for 11 blackboards in the Academic Building.
The lengths of these boards were, respectively, 27'8",
19'11", 27'10", 19'8", 22'7", 25', 25'3", 25'4", 24T0",
8'8", 11'6". The width of each board was 4'. This
slate sold at $.16 per square foot. The freight on this
shipment, which weighed 5700 pounds, was at the rate
of $1,431 per cwt. Find the total cost of this slate.
7. The tin roof of the building containing the Electric
Plant of the Institute consists of the following figures: 1
rectangle 12'x26'; 2 trapezoids, each with bases 12' and
63' and altitude 25'; 2 trapezoids, each with bases 76' and
26' and altitude 25'. Find the cost of painting this roof
at current prices.
158
REVIEW
8, The roof of Dorothy Hall consists of the following:
Number of Triangles Base Altitude
2 49' 24'
5 28' 19.1'
1 3U.5' 24.5'
1 24.5' 3.5'
2 26.5' 4.8'
2 12' 18.3'
2 16.6' 15.8'
2 1.5' 14.3'
2 6 5' 15.3'
4 50' 25.3'
# 26.5' 16.5'
2 27' 40'
2 6.25' 13.4'
2 6.5' 23.9'
2 5' 19'
4 14.5' 19'
2 3.5' 23.2'
Number of Parallelograms
Base
Altitude
2
28'
19.1'
1
30.5'
24.5'
2
40'
5'
Number of Trapezoids
Bases
Altitude
2
37' and 51'
22.8'
Find the rlumbef of square feet of surface in the roof,
Find the cost of painting this foof at Current prices.
9. J. £>. Ransom and Co. of Nashville, Tenn. sold the
Institute the following: 207 feet (B. M.) of poplar at
$65 per M; 221 feet (B. M.) of poplar at $75 per M;
580 feet (B. M.) of poplar at $85 per M. The firm
allowed a discount of 2°/o for payment within 10 days-
Find the amount paid by the Institute.
REVIEW
15!)
10. The woodwork of a wheelbarrow made in the In¬
stitute Shops required the following pieces of lumber
(oak):
2 pes. 2 >2 " x 2 ?4" X 5'
2 pes. 2" X 2/J4"x 14/;
2 pes. 2" x2'4"xl2"
2 pes. 2>2"X2^4"X50"
1 pc. 1" X 12"x28"
1 pc. 1" X 12" X 24"
2 pes. 1" X 12"X 30"
The iron wheel used cost $1.00. The iron work in
the Blacksmith Shop cost $1.00. In constructing this
wheelbarrow, 1 student of the Wheelwright Division
worked 3 days at $.35 per day The oak of which the
wheelbarrow was built cost $23.00 per M. Find total
cost of producing this wheelbarrow.
11. The Institute purchased from Penick and Ford of
New Orleans, La. 2 barrels of molasses, containing 125^
gallons, at $.33 per gallon. A discount of 1 }4% was
given for payment within 10 days. According to agree¬
ment the Institute also deducted for freight charges on
the shipment. The weight of the two barrels of molasses
was 1506 pounds. The freight rate was $.21 per cwt.
Find the amount paid the firm by the Institute.
12. The Institute bought of the Westinghouse Lamp
Co. of Bloomfield, N. J. 50 tungsten lamps at $.80 each
and 50 tungsten lamps at $.70 each. The trade discount
on these purchases was 17/4%. An additional discount
of 10% to cover possible breakage was allowed. How
much did the firm receive for these lamps?
160
REVIEW
13. The Institute purchased for use in the Machine
Shop 53 feet of belting at $6.72 per foot. Discounts on
this price were 60%—10%—10%. Find the amount paid
the firm for this belting.
14. J. J. Payne of Atlanta, Ga. sold for the Institute 7
crates of peaches at $2.25 each and 17 crates at $2.00
each. Expressa^e on the fruit cost the Institute $10.56.
The dealer charged the Institute as commission 10% of
the value of the sales. Find the net amount received by
the Institute for this fruit.
15. The total income of the Institute for year ending
May 31, 1910 was $210,309.32. Of this amount
$14,457.25 was received from students in the form of en¬
trance fees and tuition fees (including fees received at
the Training School ). What per cent of the income
of the Institute did the students contribute in this way?
16. For the same year $4,500 was received from the
State of Alabama. What per cent of the year's in¬
come came from the State?
17. In the construction of the Senior Practice Cottage,
the following framing material was used:
SILLS
NO. OF PIECES
SIZE NO. OF PIECES SIZE
SIZE
1
5
4
6"x8"—20' 5 6"x8"—14'
6"x8"—18' 4 6"x6"—14'
6"x8"—16'
JOISTS
7
36
20
54
8
8
2"x 10"—10' 5 2"x6"—20'
2"xl0"—16' 11 2"x8"—16'
2"xl0"—14' 5 2"x8"—20'
2" x 6" —16' 5 2"x8"—18'
2" X 6" —14' 5 ' 2"x8"—14'
2"x6" —22'
REVIEW
Hi]
392
10
12
STUDS
2"x4" —10'
PLATE AND SUB-SILL
2"x4"—IT 9 2"x4"—18'
2"x4"—16'
8
POSTS
4"x6"—10' 60 4"x4"—10'
30
8
8
RAFTERS
2"x8"~-24' 26 2"x6"—20'
2"x6"—18' 8 2"x6"-16'
2"x 6"—14' 16 2"x6"—12;
In addition to the above, 1971 sq. ft. of sheathing and
2039 sq. ft. of weatherboarding were used. Find the
cost of all of this material at $16.50 per M.
18. The floors of the cottage were as follows: kitchen,
12'Xl3'; dining room, 14'Xl7'6"; living room, 14'xl5';
bed room, 14'X15'; bed room, 14'Xl6'; bath room, 6'x
9'; vestibule, 5'x7'; pantry, 5x5'; front porch, 10 x14'
and 10'xl6'; rear porch, 12 x15'. Add i of the actual
number of sq. ft. to be covered, and estimate the cost of
the material used for flooring at $20 per 1000 sq. ft.
19. The walls of the rooms of this cottage were 10
high. Find the cost of plastering all of the rooms
of the house at $.35 per sq. yd. (no allowances are made
for openings)
20. The cottage mentioned in the preceding problems
has two brick chimneys. The lower part of one chimney
is of the shape of a triangular prism. The base of the
triangle is 6', the altitude, 3*4'. The height of this tri¬
angular prism is 4'. The upper part of this chimney is
162
REVIEW
of the shape of a rectangular prism measuring 2 X4 X
16/4'. In the lower part of this chimney there are two
openings for fire places, each l'x'-X-1? ■ I'1 the upper
part of the chimney there are three openings for flues,
each 9" • 8" * 16l2'. Find the cost of the bricks used to
build this chimney at $7.90 per M, allowing 22 bricks
to the cubic foot.
21. The lower part of the second chimney consists of
two parts: (1) a triangular prism and (2) a rectangular
prism. The base of the triangle is 3' and the altitude,3/2 ;
the height of the triangular prism is 4'. The rectangular
prism measures I^'x4'x4'. The upper part of this
chimney measures 2' x3'X 16/4In the lower part of
this chimney there are two openings for fire places, each
1/Xl^'x2'. In the upper part of the chimney there
are two openings for flues, each 8"x8 "X I6/2'. Find the
cost of the bricks used in the construction of this chimney.
22. The roof of the cottage consists of the following
figures: 2 trapezoids, each with bases 46'9" and 13'6"
and altitude 19'; 2 triangles, each with base 33 and altitude
19 6 "; 2 parallelograms, each with base 21' and altitude 4 ;
2 parallelograms, each with base 13'6" and altitude 4 6 "; 1
trapezoid with bases 22'and 10' and altitude 11'6"; 1 trap¬
ezoid with bases 28 6" and 14'6" and altitude 11'6".
Find the cost of the shingles, for the roof of the cottage
at $4.00 per M, allowing 1000 shingles to the square (100
sq. ft.)
23. Machine rolls cast in the Foundry are I/2" in
diameter and 8" in length. Find the weight of such a
bar, reckoning .26 lb. to the cu. in.
REVIEW
lOJ
24„ A man hole cover cast at the P'oundry was 191;''7
in diameter and -;b" in thickness. What was its weight?
25. Find out (through teacher) the dimensions of the
milk vats at the Creamery and find the number of gallons
of milk held by each.
26. Wh at must be the length of a rod cast at the
Foundry whose diameter is to be 2" and whose weight is
to be 16 pounds?
27. What must be the height of a tank whose diam¬
eter is to be 24" and whose capacity is to be 20 gallons?
28. On a working drawing of a wagon in the Wheel¬
wright Shop, the length of the wagon, which was
7'6" was represented by 55;-/. On the same scale what
represented the width, 3'2"?
29. A spray used on the trees in the Orchard consist¬
ed of 20 pounds of lime, 16 pounds of sulphur, and 10
pounds of salt. Water was added to make 40 gallons.
In 1908, 4,500 trees were sprayed with this mixture, 1 /i
gallons being applied to each tree. The lime cost $.77,'2
per cwt.; the sulphur, $.03/12 per pound; the salt, /4('
per pound. Find the cost of the spray for the 4,500 trees.
30. The feed for chickens at the Poultry Yard is
kept in a bin divided into compartments to hold the vari¬
ous kinds of feeds used. Each compartment is, approxi¬
mately, a prism with a trapezoidal base. The measure¬
ments of the compartments together with the kind of
feed in each follow:
164
REVIEW
measurements of height ok
kinu of fffn
trapezoidal base of prism prism
Corn and oats chops Rases 2'10"and 3'3" ; altitude 4' 1'9"
Prepared chick food " " " .. << 2'3"
;; " " " " " 2'io"
" " 2'
Shorts
Cotton Seed Meal
Bran
5'2" " " 3'
Find the number of bushels of each kind of feed that
the bin can hold, reckoning 2150.42 cu. in. to the bushel.
31. Find the cost at local prices of papering the
walls and ceilings of the Practice Cottage mentioned in
preceding; problems of this exercise. Secure (through
teacher) all necessary information from the House and
Sign Painting Division.
32. ()n may 6, 1910, the Institute received 6 months'
interest on each of the following investments:
30 shares (of stock) of St. Louis and Southwestern
R. R. at V.r.
30 shares (of stock) of St. Louis and Iron Mountain
R. 1\. at V'.
25 shares I of stock) of Alabama and Great Southern
R. R. at 4 Vr.
15 shares (of stock"1 of Missouri and Pacific R. R. at6%.
10 shares 1 of stock) of Norfolk and Southern R. R.
at 5'< .
I'hc value of each share was $1000. The Trust
Company that made the collections charged a commis¬
sion of Vt of total income. Find the net amount re¬
ceived I'M the Institute from these investments.
v;.,.i wji,ir is meant by a share of stock".
POWERS AND ROOTS
When 5 is taken twice as a factor, what product is
obtained ?
When 7 is taken twice as a factor, what product is
obtained?
When 3 is taken three times as a factor, what product
is obtained?
When a number is taken twice as a factor, the resulting
product is called the square or the second power of that
number.
When a number is taken three times as a factor, the
resulting product is called the cube or third power of that
number.
16 is the square of 4, since 16=4X4.
8 is the cube of 2, since 8 = 2X2X2.
4x4 can be written 42, and 2x2x2 can be written 23.
The small figure, called the exponent, placed above and
to the right of a number, indicates the number of times
that it is to be taken as a factor.
Exercise 67
Find the square of the following:
1. 12 5. .3
2. 15 6. .08
3. 70 7. f
4. I 8. 3.02
9. 576
10. .576
11. 2 2
12. 7.002
166
POWERS AND RCO'i f
Find the cube of the following:
13. 11
15. 3.8
17. 5.06
16. I
18. 35
20. 53
21. W 23. (I)3
22. (1.2)® 24. (.009)2
While 36 is called the square! of 6, 6 is called the
square root of 36.
In the same way, while 27 is called the cube of 3, 3 is
called the cube root of 27.
The square root of 36 may be indicated by Using the
radical sign, v • Thus, 1./36 —6
The cube root of 27 may be indicated as follows::
f 27 -3.
Exercise 68
Gi ve the foots indicated.
1. 4.
2. 1/49 5. fW
3. 1/144" 6. ifl25
7. f/iW
8. f/1000
9. V i2]T
10 t/225-
225=3X3X5X5= (3X5) X (3X5)
/ 225 =3X5=15.
11. l/625
14. I 3969 17. i/73375
12. 1/576
15. if 343 18. i/f
POWERS AND ROOTS
167
1 i =1 i ioo =10 i ioooo =100.
We see from the foregoing that the square roots of
numbers between 1 and 100 lie between 1 and 10, and
that the square roots of numbers between 100 and 10,000
lie between 10 and 100, etc. Then, the square root of a
number containing one or two figures is a number of one
figure; the square root of a number containing three or
four figures is a number containing two figures, etc.
In the number 2304, the number of figures in the square
root may be indicated by separating the number into
periods of 2 figures each, beginning at the right as follows:
23 ' 04.
If t represents the tens in a number of two figures and
u, the units, then the number itself is represented by
t + u. The square of this number is represented bv
(t + u)2. But, as is shown in algebra, (t + u)"=t"+2tu
+ u2.
In the number, 57, t = 50 and u = 7. t" =50" =2500;
2tu = 2x50x7 = 700. uz=72--49. (t + u)2 = (50 + 7)2
= 2500+700+49 = 3249.
That 3249 is really the square of 57 can be verified by
finding the square of 57 in the usual way.
Exercise 69
Find the square root of the following
1. 5776
Dividing the number into periods of two figures each,
beginning at the right, we see that the square root con¬
tains two figures.
(a) (b)
t f u
57 76 | 70+6- -76 57 76 76
t2 -702 49 00 49
2 140 8 76 146 I 8 76
2t • u 146 I « 7fi
(j 2tu + u2---6X146 - 8 76
The greatest square in 5700 is 4900. Then t 70. Subtracting
4900 from 5776, we get as remainder 876. This number, 876, must
168
POWERS AND ROOTS
contain 2tu u2. 2t=140. Using 140 as a trial divisor, we di¬
vide 876, obtaining 6 as a trial value for u. 2t 1 u 146.
2tu ; u2 = 6 > 146 = 876. Then, 6 is the value of u required.
Therefore, ( 5775 = 76.
In practice, the shorter form under (b) is to he used.
When the root to he found contains more than 2 figures, the
above process is repeated until all the figures of the required root are
found.
2. 28.5156
The number of roots in this number which contains a decimal is
found by separating it into periods of two figures each, beginning
at the decimal point and marking off periods to the left and to the
right.
28.51 56 | 5.34
25
103 I 3 51
I 3 09
1064 I 4256
1 4256
3. 1379 5. 14161 7. .092416
4. 2601 6. 4.2849 8. .6984
Extract the square root of the following carrying the opera¬
tion to two decimal places.
9. 2 11. 23.7 13. 19
10. 3173 12. 3.1416 14. 53.02
PRACTICAL APPLICATIONS
A triangle containing a right angle
is called a right triangle.
The side opposite the right angle
in a right triangle is called the hypot¬
enuse. Thus, in the figure, AB is
the hypotenuse.
C B It is shown in geometry that
The square on the hypotenuse of a right triangle is equal
to the sum of the squares on the other two sides.
If in the figure, AC = 4, CB=3
AB2 = 32+42 =9+16 = 25
AB = 1/257 or 5.
Exercise 70
1. A hip rafter of the roof of a building was found to
be the hypotenuse of a right triangle whose two sides
were 15' and 35' respectively. Find the length of the hip
rafter. '
2. Another hip rafter of the same building was found
to be the hypotenuse of a right triangle whose two sides
were 20' and 48' respectively. Find the length of this
hip rafter.
3. The gable end of a cottage is of the form of a tri¬
angle two of whose sides are each 24' and whose base is
30'. Find the number of square feet of surface in
this gable. (The altitude of the gable Strikes the 30'
base in the center.)
170
PRACTICAL APPLICATIONS
4. What must be the diameter of an iron rod cast at
the Foundry which is to weigh 16 pounds and to be 6"
long? (.26 lb. to the cu. in.)
5. Ten-pound sash weights for windows are cast at
the Foundry in the form of round bars 20// long. What
is the diameter of these bars?
6. What must be the diameter of the pattern for a
cylindrical rod, which when cast at the Foundry is to
weigh 36 pounds and to be 14" long? In making patterns
%" is to be allowed to every foot for shrinkage.
PYRAMID—CONE—SPHERE
The teacher will exhibit models of (1) pyramid, 2)
frustum of pyramid, (3) cone, (4) frustum of cone, and (5)
sphere.
Point out what is meant by slant height and altitude of
pyramid, cone, frustum of pyramid and frustum of cone.
Students will locate on the Institute grounds and in the
Shops structures like the solids just described.
The volume of a pyramid or a cone is given by one-third the
product of the numbers which express the altitude and area of
the base in corresponding units. See page 144.
The lateral area of a pyramid or a cone is given hy one-
half the product of the numbers which express the slant height
and the perimeter of the base in the same unit.
The perimeter of the base is the distance around the base.
PYRAMID—CONE-SPHERE
171
To find the volume of the frustum of a pyramid or
the frustum of a cone, proceed as follows:
Find the sum of the bases; add to this sum the square root of
the product of the bases; multiply this last result by one-third
the altitude.
By "bases" is meant the number representing the area of the base.
The altitude and bases must be expressed in corresponding units.
The lateral area of the frustum of a cone or the frustum of
a pyramid is found by taking one-half the sum of the perime¬
ters of the two bases and mulitplying the result by the altitude
The volume of a sphere is found by multiplying four-thirds
the cube of the radius by Jy.
The area of the surface of a sphere is found by multiplying
four times the square of the radius by 3\.
Exercise 71
1. Secure (through teacher) the necessary information
and compute the cost of painting the tower of the Insti¬
tute Chapel.
2. A bucket made in the Tin Shop is 9" high. The
diameters of the bottom and top were 8" and ll" re¬
spectively. Find the capacity of the bucket in gallons.
3. The two foundations of the air compressors at the
Institute Water Plant are made of brick. Each founda¬
tion is 12' square at the bottom, 8' square at the top, and
10' high. Find the cost of the bricks used in constructing
these foundations at $7.90 per M. (22 bricks to the cu.
ft.)
172
PRACTICAL APPLICATIONS
4. The brick foundation for a press at the Printing
Office has a top 3'X3/4' and bottom S'xS}^', and is
3'>2' high. Find the cost of the bricks used in the con¬
struction of this foundation.
5. Find the cost of the bricks used in building the 12
columns of Tompkins Hall, each column being 40" in
diameter at the bottom, 30 ' in diameter at the top, and
30' high.
6. Find out (through teacher) the measurements of
the boys' swimming pool and estimate the number of gal¬
lons that it will hold.
7. A piston ring for a dynamo was cast at the Foun¬
dry. This casting was of the form of a frustum of a cone.
The diameter at one end was 15^"; the diameter at the
other end was 13s 8r/. The height was 5-5 s". The cylin¬
drical hole within the casting was 12Y\" in diameter and
5?s" in height. On this casting there were also 4 pro¬
jections, each measuring /4" Xl/4" X3". Find the
weight of the casting.
8. A spherical ball cast at the Foundry was 3iV in
diameter. Find its weight.
9. The spherical ends of a pair of dumb bells cast at
the Foundry were 3/4" in diameter. The handle of each
dumb-bell was 4" long with an average diameter of H".
Find the weight of one of these dumb-bells.
Exercise 72
1. Compute from actual measurements the capacity
of the dipping tank for cattle on the Institute Farm.
Find out the composition of the dipping mixture and es¬
timate the quantity of each ingredient required to make
enough of the mixture to fill the tank. At current prices
what is the cost of the mixture required to fill the tank?
PRACTICAL APPLICATIONS
173
2. Compute from actual measurements the capacity of
one of the silos on the Institute Farm. At the current
price of ensilage, what is the value of the ensilage that
it can hold?
3. Find the n umber of gallons held by the Institute
Reservoir.
4. Find the number of gallons held by the Institute
Water Tank.
Exercise 73
1. Class will visit the Tin Shop and compute (1) the
quantity of material required to make various articles in
the shop and (2) the capacity of various vessels in the
shop.
2. Class will visit Foundry and estimate the weight
and cost of various castings.
Exercise 74
The class will visit the Truck Garden and" find the
number of acres in the plots planted in different crops.
GENERAL REVIEW
Exercise 75
1. The W ashburn-Crosby Co. of Louisville, Ky. sold
the Institute 1 car of flour. This car contained 240
twelve-pound sacks, which sold at $4.65 per barrel (196
lb.), and 80 twenty-four-pound sacks which sold at $4.50
per barrel. The Institute was allowed a reduction for
freight which amounted to $.22 per cwt. Find the
amount paid the firm.
2. The same firm shipped the Institute a car of bran
containing 400 sacks, 100 pounds to the sack. The price
of this bran was $28.00 per ton. A reduction for freight
as in the preceding problem was given. What did the
firm receive for the car of bran?
3. A double window made in the Institute Repair
Shop required the following lumber:
No. of Pieces Size No. of Pieces Size
1
2"x8//—7/8r/
4
1"X6"—6'8"
1
2"x8"—6'
3
1"X6"~ 7'8"
2
2//x6//—6'
2
1"X6"—6'
4
1//X2//—6'
4
V'xV'—V
1
V'x8f,—6'
2
v'xv—y
1
V/2"X21/2"—7'8"
4
j4"x K "—6'
2
%"XVA"—%
Find the cost of this material at $18 per M.
4. Armour and Co. sold the Institute 207 pounds of
sides at $9.68 per cwt., 213 pounds of shoulders at $.13
per pound, 300 pounds of lard at $.09/4 per pound, 1
barrel of soap, 317 pounds, at $.07/^ per pound, 25
pounds of bologna sausage at $.07K per pound. Make
out this bill in proper form.
GENERAL REVIEW
175
5. The Institute bought of the Commercial Electrical
Supply Co. of St. Louis, Mo. 35 cross arms at $27 per
100 less 25%, 15 cross arms at $37 per 100 less 25%, and
100 wood pins, $1.60. How much did the firm receive
for these supplies?
6. The Loeb Hardware Co. of Montgomery sold the
Institute 500 dry spokes at $6.45 per 100 and 100 dry
spokes, $5.00. The trade discount on the above was 10%.
A further discount of 2% was given for payment within
10 days. Find the amount received by the firm.
7. A water cooler made in the Tin Shop consists of
an inner and an outer vessel, each made of galvanized
iron. The faces of the outside vessel made the following
figures (allowances for seams being included, except where
indicated): 4 rectangles, each 12"xl6"; 4 triangles,
each with base 12" and altitude 4 triangles, each
with base 1" and altitude 1 l/z". 2 seams make a strip
5'X 1/^The outside bottom required a piece 13"xll".
The inner vessel has the following faces: 2 rectangles,
each 7/4"x20'/; 2 rectangles, each 7"x20;H>"; the
bottom of the inner vessel required a piece 8' 'X8". The
moulding on the cooler consists of 4 trapezoids, each with
bases 13K" and 14" and altitude 3". The top consisted
of 1 rectangle 8"x8" and 4 triangles each with base 8/2"
and altitude 4 >2". Add for seam a strip /^"x6". I he
iron of which this cooler is made weighs .9062 lb. per sq.
ft. Find the number of sq. ft. of iron in the cooler.
Find the cost of this iron at $4,186 per cwt. (including
freight).
176
GENERAL REVIEW
8. The Macon County Oil Co. sold the Institute
31,900 pounds of cotton seed hulls at $11.50 per ton and
515 pounds of linters at $.04 Vs per pound. Find the
amount paid to settle bill.
9. The Institute bought of J. F. Rilev of Birming¬
ham, Ala. a car of oats containing 56,640 pounds at $.64s
per bushel. A reduction of $162.40 was allowed the In¬
stitute on account of freight charges. Find the amount
paid the firm.
10. The following table gives the per cent of protein,
carbohydrates, and fats in the feed stuffs used at the
Dairy Barn.
Protein
Carbohydrates
F ats
Cotton
Seed Meal
37.2
16.9
12.2
Cotton
Seed Hulls
.3
33.1
1.7
Shorts
12.2
50.
3.8
Wheat
Bran
12,2
39.2
2.7
Rape
1.5
8.1
.2
At the Dairy Barn an effort is made to maintain in the
feed a certain ratio between the protein on the one hand
and the carbohydrates and fats on the other. This ratio
is called the nutritive ratio. This ratio is computed as
follows: (1) Multiply the weight of the fats in the feed
by 2.4. (2) Add this product to the weight of the car¬
bohydrates. (3) Find the ratio of the weight of the pro¬
tein to the sum just found. The nutritive ratio, then,
may be expressed thus,
wt. of protein
2.4X-wt. of fats+ wt. of carbohydrates
GENERAL REVIEW
177
If the nutritive ratio is less than 1 : 6, it is called a
wide ratio; if it is is greater than 1 : 6, it is called a narrow
ratio. At one time the feed for No. 1 cows at the Dairy
Barn was as follows: 5 pounds of cotton seed meal, 30
pounds of cotton seed hulls, 3 pounds of shorts, 2 pounds
of bran, and 50 pounds of rape. Find the nutritive ratio
in this feed. Is it wide or narrow?
11. The daily feed for No. 2 cows was 4 pounds of
cotton seed meal, 30 pounds of cotton seed hulls, 2
pounds of shorts, 1/-2 pounds of bran, and 50 pounds of
rape. Find the nutritive ratio in this feed. Is it wide or
narrow?
12. The daily feed for No. 3 cows was 1% pounds of
cotton seed meal, 30 pounds of cotton seed hulls, 1%
pounds of shorts, Vz pound of bran, and 50 pounds of
rape. Find the nutritive ratio in this feed. Is it wide or
narrow?
13. Secure (through teacher) all information neces¬
sary for computing the nutritive ratios in the rations fed
at the Horse Barn.
14. The Westinghouse Lamp Co. of Bloomfield, N.J.
sold the Institute 48 lamps at $1.35 each and 50 lamps
at $1.00 each. A trade discount of 17)4% was allowed
on the above. An additional discount of 10% was also
allowed to cover possible breakage. Find the amount
paid the firm by the Institute.
15. The Institute bought of J. Loeb Grocery Co. of
Montgomery, Ala. 300 sacks of 'corn weighing 42,000
pounds, at $.6424 per bushel. Find the value of this corn.
178
GENERAL REV' ;W
16. An engine at the Machine Shop had a piston
cylinder 8" in diameter with a 12"stroke. How many
cu. in. of steam did it hold?
17. What must be the length of the stroke of a piston
in a cylinder whose capacity is to be % greater than that
of the cylinder in the preceding problem, and whose di¬
ameter is the same?
18. What must be the diametei of a cylinder the
stroke of whose piston is the same as that in the preced¬
ing problem, but whose capacity is 2/2> as great?
19. The Institute bought of Young and Vann Supply
Co. of Birmingham, Ala. the following: 21 Yi pounds of
packing at $.60 per pound; 24 2" discs at $.18 each; 24
l1/?" discs at $.12 each; 24 1%" discs at $.09 each; 24 1"
discs at $.06 each; 24 3/i" discs at $.05 each; 24 discs
at $.04 each; 24 2"x2" plain nipples at $.18 each; 24
1^"X1^" plain nipples at $.13 each; 24 l/4"x2}4"
plain nipples at $.11 each; 12 }{" air corks at $.45 each;
6 air corks at $.50; 6 72" air corks at $.60 each.
Trade discounts were given as follows: 20% on the pack¬
ing and discs, 80%—5% on the nipples; 75% on the air
corks. Terms: 2%, ten days. The Institute paid the
bill within 10 days. Find the amount sent the firm for
these supplies.
GF JERAL REVIEW 179
20. Wm. Jessop and Sons of New York sold the In¬
stitute the following:
45^ pounds of cast steel 1}&" square;
48/^ pounds of cast steel l/4"xl"',
2434 pounds of cast steel l/VxH";
11/4 pounds of cast steel square;
22yi pounds of cast steel 1Y%" square;
2234 pounds of cast steel 5/8" octagonal;
20}4 pounds of cast steel ¥%" octagonal;
10 pounds of cast steel 1%" round;
21 Y\ pounds of cast steel 1" round;
2SY pounds of cast steel round.
This steel sold at $.15/4 per pound. In addition to the
above, there were sold 10}4 pounds of %" square cast
steel at $.17]4 per pound. A discount of 10% was given
on the order. Find the amount paid the firm for this
steel.
21. H ow long must a 12-pound sash weight for windows
be made at the Foundry, if it is desired to make such
weights 1/i" in diameter? Reckon .26 lb. to the cu. in.
22. The Institute bought from the Pittsburg Plate
Glass Co. of Atlanta, Ga. the following:
Size of Glass Price per Box
lbox 17"xl7" $28.00
1 box 12"xl5" 26.75
lbox 10"X14" 25.50
1 box 12"xl8" 26.75
lbox 12"x22" 26.75
lbox 12"xl6" 26.75
lbox 10"x 14" 25.50
lbox 10"xl2" 25.50
Discounts on the above were 90%—20%. Terms: 2%
ten days. The Institute paid within 10 days of date of
bill. Find the amount received by the firm for the glass.
180
GENERAL REVIEW
23. A box of window glass contains as nearly as pos¬
sible 50 sq. ft. of glass. Find the number of lights meas¬
uring 12' 'X 15" in a box. At the prices given above what
did each such light cost the Institute? Take account of
discounts in your calculation.
24. How many lights 12"xl8" are contained in a
box? Find the amount paid by the Institute for each
light of this size.
25. Find the amount paid by the Institute for each
light measuring 17' 'X 17".
26. A bucket of cylindrical shape made in the Tin
Shop was 11" in diameter and 8" high. Find the num¬
ber of gallons that it holds. Express this result correct¬
ly to the nearest Y pt.
27. The link of an iron chain made at the Blacksmith
Shop may be considered as being composed of four parts:
2 semi-circular ends and two straight pieces connecting
these ends. The chain was made of round iron Y" in
diameter. Each of the straight pieces was lY" long.
The diameter of each of the semi-circular ends was Y\"
(measured from center of stock). Find the length
of iron required for one link, allowing Y" for weld¬
ing. One lineal foot of this iron weighs .6612 pound.
Find the weight of one link of this chain. At $2.55 per
cwt., find the cost of the iron in the chain of 15 links.
How long was this chain?
28. The Institute bought from the National Gum
and Mica Co. of New York llY ounces of mica at $9.50
per pound less 50%. The firm charged the Institute
$.10 for postage. Find the cost of mica.
GENERAL REVIEW
181
29. Blocks of iron 3' long and 2" square at the ends
are cast at the Foundry for use in the Machine Shop.
At the Machine Shop each block is planed down until
it is \y% square at the ends. A V-shaped trough is then
cut the entire length of the block. This V-shaped trough
is 1/4" wide at the top and the point of the V is in the
center of the square ends of the block. Find the weight
of the block when it is received from the Foundry. Find
the weight of the block after the trough has been cut.
Reckon .26 lb to the cu. in.
30. Steiner and Lobman sold the Institute 10 bolts of
cloth containing, respectively, the following number of
yards: 24, 38,48^, 23^, 46^, 41^, 33, 46^, 53^,
42 . This cloth sold at $.22 per yard. 2% was given
as discount for cash within 10 days. Find the amount
received by the firm.
31. In the report of the Principal of the Institute for
the year ending May 31, 1910, the following statement is
found: "The value of our plant, including equipment
and live stock, is now $1,263,249.90, making an addition
of $147,615.09 for the year." Find the per cent of in¬
crease in the value of the plant for the year.
32. The Thread Agency of St. Louis, Mo. sold the In¬
stitute 12 dozen spools of thread at $.58 per dozen less
10%—5%. Find the amount paid the firm.
33. The Institute bought of A. Atzinger and Son of
Louisville, Ky. 10 sides of leather, 192 pounds, at $.40^
per pound. Terms: 2%, 30 days. Find the amount
paid for leather after the discount had been deducted.
182
GENERAL REVIEW
34. The Cudahy Packing Co. sold the Institute 222
pounds of meat at $.07% per pound. Terms: 10
days. The Institute took advantage of the discount.
Find the amount sent the firm for the meat.
35. The Crane Co. of Birmingham, Ala. sold the In¬
stitute 2 valves at $4.00 each less 65%—5% and 3 iron
cocks at $5.25 each less 70%—10%—2)4%. Terms:
2%, 30 days. The Institute paid within 30 days of date
of bill. Find the amount received by the firm for these
supplies.
36. Two end walls were built for a pit at the Institute
Greenhouse. Each wall was 6' 3" long, 9" thick, 2' high
at one end and 2' 6" high at the other end. Counting
22 bricks to the cubic foot, find the cost of the bricks in
this wall at $7.90 per M.
37. A brick cistern near the Institute heating plant
has an inside diameter of 12' and is 7/^' deep. Compute
the capacity of this cistern in gallons.
TABLES
TABLES
LIQUID MEASURE
4 gills = 1 pint
2 pints = 1 quart
4 quarts — 1 gallon
1 gallon contains 231 cu. in.
31/2 gallons make 1 barrel
(in estimating capacity of cisterns, etc.)
DRY MEASURE
2 pints = 1 quart
8 quarts = 1 peck
4 pecks = 1 bushel
1 bushel contains 2150.42
cu. in.
LINEAR MEASURE
12 inches = 1 foot
3 feet = 1 yard
5/4 yards (16/4 ft.) =1 rod
320 rods(5280 feet) =1 mile
SQUARE ]V
144 square inches
9 square feet
30% square yards
160 square rods
640 acres
100 square feet
= 1 square foot
= 1 square yard
= 1 square rod
= 1 acre
= 1 square mile
= 1 square
TABLES
TABLES
CUBIC MEASUR.E
1728 cubic inches =1 cubic feet"
27 cubic feet =1 cubic yarcf
128 cubic feet —1 cord
AVOIRDUPOIS WEIGHT
16 ounces — 1 ft).
100 pounds =1 hundred wei
2000 pounds —1 ton
MISCELLANEOUS
of beans or peas
weighs 60ft)
oats
" 32 ft)
corn (shelled)
" 56 ft)
corn (on ear)
" 70ft>
White potatoes
" 60ft>
Sweet potatoes
" 50 ft)
charcoal
" 22ft>