Robert W. Woodruff
Library
Special Collections
EMORY UNIVERSITY
THE
OR,
732CT8 A9BISVAfn&
CONTAINING THE MOST CONCISE AND ACCURATE RULES FOR PER¬
FORMING OPERATIONS IN
AI1ITIIMETICK
ADAPTED TO THE EASY AND REGULAR INSTRUCTION OF TOUTH,
FOR THE USE OF SCHOOLS,
Third Eilitlon-"EnfargeiI and corrected hy the Anthors>
mis <&
TEACHERS OF ARITHMETICS.
PUBLISHED BY J. F. & A. FOWLER.
THUNTED AT THE "KNOXVILBE REGISTER" OFFICE, BY
RAMSEY & CRAIGHEAD.
1 8 37.
ENTERED according to act of Congress, in the year 18D4.
Br Al.bijah & Josiak FpWLEn,
In the Clerk's office of the District Court of the District of
East Tennessee.
RECOMMENDATIONS.
MESSRS. FOWLERS' ARITHMETICS
This work, which was handed me some time since, for examination,
exhibits a degree of industry and ability highly creditable to the aur
thors. _ The Order of arrangement appears to be judicious, and the il¬
lustrations clear and plain. The circumstance that it is primarily
adapted to our national currency, is, to me, one of its chief recom¬
mendations; and were rto works of an opposite character introduced
into our common schools, we should soon have a currency or mode of
reckoning, simple, uniform, and intelligible to every one. I trust
the gentlemen will meet with such encouragement from the public,
as will more than compensate for the trouble and expense of publica¬
tion. JOSEPH ESTABROOK,
President of Past Tennessee College,
Knoxville, April 29th, 1834.
MESSRS. FOWLERS' ARITHMETIC.
From a hasty examination of this work, 1 would say, its judicious
arrangement, the perspicuity and conciseness of its rules, the clear¬
ness and simplicity of its illustrations, and its adaptation to our nation¬
al currency, render it a desirable companion for the beginner in this
important branch of education. I trust the industry And ability exhib¬
ited by its youthful authors, will meet with liberal encouragement.
ALLEN H. MATHSS,
Late Principal of the Jtlule Academy.
Madisonville, June 14th, 1?34.
THE FEDERAL INSTRUCTOR; oh, YOUTH'S ASSISTANT.
The abovh work, in my opinion, has considerable merit. The rules
appear to me, to be made plain to the understanding of beginners, and
unadvanced learners, in the1 very Useful branch of knowledge on
which it treats. Hope is entertained that Messrs. Fowlers', the au¬
thors of it,' will be liberally rewarded for their undertaking, by the
patronage of a generous public.
HENRY C. SAFFELL,
Principal of the Holston Seminary.
New-Market, June 26th, 1835.
Having carefully examined "Fowlers' Arithmetic," I make no
hesitation in saying that I fully concur with the foregoing gentlemen
iv
in opinion, with respect to the merits of the work, arid cordially unite?
with them in recommending its introduction into our schools and acad¬
emies, as well as particularly into the Tyro's Library.
JQSIAH P. SMITH, Pkilom:
Kingston, Oct., 1836.
messrs. foweeks: »
^ I have carefully examined your Arithmetic, and
must say, after twenty-five years experience as a teacher, that I hav6
not seen a work of the kind that I would prefer before it, especially
fpr young beginners. The shortness, simplicity and plainness of the
rules, asyouhave very justly remarked in your preface, must I think
greatly accelerate the progress of learners. I trust you will meet
with the patronage ofotir fellow-citizens generally.
LANDON DUJSLCAN.
' Giles County, Virginia, Mareh 15th, 1836.
MsssjiN. Fuwpsas.- '
ftentlemen—I have carefully examined your treatise
on Arithmetic, and I think, it superior to any other nqw in U3e to facil¬
itate the progress of the young learner, and is fully adequate for all
line common business of our .country. It Well merits a place in our
schools and Academies, as "well as in our houses.
MICHAEL MORRIS,
Pcdche)'"of the Esiillville Academy*
Estillvilfe, Ya., 13th July, 18S6.
PREFACE.
The design of the authors in bringing this work before the
public is, to teach the science of Arithmetic in a different and
easier manner than lia^been customary. To attain this object,
we have simplified the necessary rules, thus leading the student
out of the darkness of ignorance by a plain path, into the light
of knowledge. The shortness, simplicity and plainness of the
rules, will enable the student to advance with greater ease and
speed than those hitherto promulged.
As calculating in English money is measurably obsolete, the
authors have, with but few exceptions, employed, in this work,
the legal currency of our country, Dollars and Cents. Two
things among us have been but too well fitted to retard the
progress of Arithmetical knowledge; calculations in pounds,
shillings, pence and farthings, a currency unknown among us,
and unstated to the transactions of our common country con¬
cerns; and long, complex rules, difficult to be remembered,
and still more difficult to comprehend. But, make your rules
short, familiar, and easy to be understood, and the student is
encouraged to pursue the shining path of science, thus plainly
pointed out to him, with alacrity and delight.
Tho' this work may appear short, yet there are in it ISOd
questions, or upwards—a sufficiency, we should think, in point
of number; selected so as to be useful, and adapted to the cir¬
cumstances of our country.
Many persons who have ciphered for months, and some who
have gone through tl\e Arithmetick, are at a loSs because they
•do not understand, or have not paid attention to, the rules.-—
This evil will be the more' easily remedied on oursystenq, as
our rules are plain and short, and may, with but little labor, be
committed to memory.
When our Savior came into the world, he was condemned
by the Jews by asking a simple question—can any thing good
come out of Nazareth? If any are disposed, in a similar way,
to denounce our work, we would beg of them to examine care¬
fully and candidly before they decide, and to remember, that,
as the Messiah did come out of Nazareth, so, it is possible for
a good Arithmetick to be made in Tennessee. We are, in¬
deed, devotedly attached to this study, and as we think we have
made improvements in the mode of teaching it, we have risked
■our all to give publicity to the book, to enable others to judge
•of it and to profit by it.
EXPLANATION OF CHARACTERS, SIGNS,
SIGNIFICATIONS.
—Equal, as 100 ets.t=jSl.
-f-More, as 4-f-2=6.
'—Less, as 6—2=4.
X into, with, or multiplied by, as 4X2=8.
4-By, i, e. divided by, as 64-2=3, or 2,16(3
: : ; Proportion, as 2 : 4 : ; 6 : 12. %
2 ^/"Square Root, as 2.^/84=4
3y/CubeRoot, as 3v/04=4.
4v/Poui,th Root, as *V/L6<a=2) Ac.
ARITHMETICK.
Arithmetick is that part of the Mathematics which
teaches the art of imputation by numbers. All oper¬
ations in Arithmetick are performed by means of the
following figures, viz: One 1, two 2, three 3, four 4,
five 5, six 6, seven 1} eight 8, ni le 9, cipher 0.
NEWER ATI ® N.
Numeration teaches the different value of figures by
their different places, and to express any proposed
numbers either by words or characters; or to read and
write any sum or number.
NUMERATION TAELE.
bhgffihhsmc!
p # cs t B"B # s
'(&, w n'p."1 C pjW to
i fi 1 1 o ® t "
«s to f# "*3 JS re
a. j B a
„ cr to
a. _
u g
o 5
« 2
H »
2 a
6
7 6
7 6
7 6
1 One.
2 1 Twenty-one.
3 2 1 Three hundred 21,
4 3 2 1 Four thousand 321.
5 4 3 2 1 54 thousand 321.
5 4 3 2 1 654 thousand 321.
5 4 3 2 1 7 million 654 thousand 321.
5 4 3 2 1 87 million 654 thousand 321.
5 4 3 2 1 987 million 654 thousand 321.
ADDITION".
*
The preceding contains only nine digits, "which ren¬
der it sufficiently large for young students or common
business, although it may be extended much farther,
thus:
Qui"ntiliions.^Quatrillions. ^Trillions! Millions? Millions. Units.
987,654; 327,241; 278,325; 256,148; 212,563; 652,324.
ADDITION.
The use of Addition is to ascertain the amount of
two or more numbers when put together.
RULE.
1st. Set down any one of the numbers and place un¬
der it all the rest in such a manner that units may stand
under units, tens under tens, hundreds under hundreds,
and so on, and draw a line under the last.
2d. Begin at the right hand column and add togeth¬
er all the figures contained in that column. If it
amounts to ten or more, set down the right hand figure
and carry the left hand figure or figures, which add to
the next line, and so proceed till adding the last line.
Then set down the whole amount.
EXAMPLES.
(No. 1.)
d
5.
(2,)
Hd
CD 3
3
(3.)
SCHd
e 2 3.
(4.)
•-5 a H d
P~ e 3.
(5.)
HKHd
Cr C O 3>
ST
n 2"
cL 5° ST
O 3 5. JV
G P. S° »
C tti ™ w
CD I •
2 »; *:
s ft! .
p. 0» „ .
01 •>. •
s » : :
PJ • *
CD • *
2 P.. •
P. w • •
01 • .
4
4
2
2
5 3
4 1
6 9
2 5
2 3 4
12 1
4 6 8
2 2 4
13 4 6
7 2 12
10 3 2
8 1 0 3
2 4 6 8
17 5 5
10 2 0
12 8 0
Ans. 12
18 8
10 4 7
1 7 6 9 3
6 5 2 3
ADDITION.
11
(6.)
C 7.)
(8.)
(9.)
12 3
2 4 6 8
8 7 5 6 1
4 2 14 6
4 2 2
6 2 7 3
1 0 4 2 0
2 3 3 2 3
5 3 1
2
10 3
3 2 6 1 9
1 3 3 5 7
2 4 6
4 3 12
3 14 2 7
2 4 5 5 7
3 2 3
3
10 2
6 14 2 2
1 2 7 8 7
6 4 5
1 8 2 5 8
223449
116 17 0
(10.
)
(11.)
(12.)
2 2
2 5
6 3 12
4 6 2 1
4 10
• 3
0 19 1
2 3 0 0
112 2 4
4 3 0 7
9 6 13 1
2 4 7 9 5
7 7 9
1 2 0 0 1 2
3 6 1
3 5
2 4 0 2
1 2
8 7 2
8 2
1 2
4 8 0 0
9 0 0
00
cn
6 8
4 1
8 7 9 1
2 2 3 9 7 6
13. Add the following numbers, viz: 14,16, 23, 29, 80,
31, and 100, and tell their amount? Ans. 283.
14. What is the amount of 38, 97, 125, 384, 1176.
Ans. 1818.
15. Add 640,79, 80,100, 210, 450, 787, 21, and 2.
Ans. 2369.
16 John gave Joseph 33 apples; Jpmes gave him
91; Peter gave him 56; Joel gave him 107: and David
gave him 95; how many had he? Ans. 382.
17. A'person went to collect money, and received of
one man $542; of another 654; of another 550; of ano¬
ther 787,. and of another 3405. I demand the sum col¬
lected. Ans. $5938.
18. John owes to one man $302; to another 540; to
another 70; to another 2356, and to another 999. How
much does he owe in all? Ans. $4267.
19- John and Charles went to collect nuts; when they
had collected a quantity, set down to count them; when
one had collected 275 and the other 196, what number
did both of them collect? Ans. 471.
20. Desired to purchase a suit of clothes which cost
as follows, viz: a coat $25, a pair of pantaloons 10, a
12
MULTIPLICATION.
waistcoat 6, a shirt 2, ,and a pair of socks 1. What is
the cost of the whole? Ans. $44.
21. A butcher bought of one man 25 head of cattle;
of another 15; of another 40, and of another 9. How
many did he,buy in all? Ans. 89 head.
22. A man in buying cider received of one man 80
gallons; of another 200; of another 300; of another 400,
and of another 500. How many gallons did he buy in
all? A«s. 1490.
23. A gentleman went to purchase brandy, and
bought of one man 125 gallons; of another 160; of an¬
other 190, and of another 210, How much did he buy
in all? • Ans. 685 gallons.
24. A man in buying corn, received of one person
400 bushels; of another 500; pf another 600, and of an¬
other 700. How many bushels did he buy in all?
Alls. 22UQ bushels.
MIJLTIPI^CATIOM.
When the multiplier does noj; exceed 12, work by
HULR I.
Set the multiplier under the right hand figure or fi¬
gures of the multiplicand: then beginning with the
units, multiply all the figures of the multiplicand in suc¬
cession, and set down the several products; but if ei¬
ther of the products be more than 9, set down its right
hand figure only, and add its left hand figure or figures
to the next product. The whole bf the last product
must beset down.
Proof. Diyide the answer by the multiplier, and the
quotient will equal the given sunt.
MULTIPLICATION TABLE,
The learner should commit the following table to
memory before he proceeds further:
MULTIPLICATION.
13
Twice
3 times
4 times
5 times
6
times
7 times
1 make2
1 make 3
1 make4
1 make5
1 make6
1 make7
2 4
2
6
2
8
2
10
2
12
2 14
3 6
3
9
3
12
3
15
3
18
3 21
4 8
4
12
4
16
4
20
4
24
4 28
5 10
5
15
5
20
5
25
5
30
5 35
6 12
6
18
6
24
6
30
6
36
6 42
7 14
7
21
7
28
7
35
7
42
7 49
8 10
8
24
8
32
8
40
8
48
8 56
9 18
9
27
9
36
9
45
9
54
9 63
10 2Q
10
30
10
40
10
50
10
60
10 70
11 22
11
33
11
44
11
55
11
66
11 77
12 24
12
36
12
48
12
60
12
72
12 84
8 times
9
times
10 times
11 times
12 times
1 make 8
1 make 9
ImakelO
lmake 11
1 make
12
2 16
2
18
2
20
2
22
2
24
3 24
3
27
3
30
3
33
3
36
4 32
4
36
4
40
4
44
4
48
5 40
5
45
5
50
. 5
55
5
60
6 48
6
54
6
60
6
66
6
72
7 56
7
63
7
70
7
77
7
84
8 64
8
72
8
80
8
88
8
96
9 72
9
81
9
90
9
99
9
108
10 80
10
90
10
100
10
110
10
120
11 88
11
99
U
110
11
121
U
132
12 96
12
108
12
120
12
132
12
144
(1.) 412 multiplicarid.
2 multiplier.
(2.) 5498
3
(3.) 12347
824 product.
(4.) 12349172
5
61745860
(7.) 64115928
8
512927424
Ans. 16494
(5.) 98754
6
592524
(8.) 21938
9
197442
Ans. 49388
(6.) 12345678910
7
86419752370
[9.] 98765432144
10
987654321440
14
MTJLTIPLICATIOX.
(10.) 5324786
11
,Ans. 58572646
(12.) 1481000763
3
Ans. 4443002289
(14.) 110008191-
4
Ans. . 440032764
(16.) 17853440
5
Ans. 89267200
(18.) 1230721
3
Ans. 3692163
(20.)
(11.) 84532911
12
Ans. 1014394932
(13.) 150000000000
2
Ans, 300000000000
(15.) 987554321
2
Ans, 1975108642
(17.) 1888830000
5
Ans. 9444400000
(19,) 9922446688
4
Ans. 39689786752
L500843211
t, r ' 7
Ans. 420080505902477
21. Multiply 21141 by 2 Answer 42282
22 73211 3 219633
23 87692.... ..4 350768
24 ....95698 5 478490
25 91144 6.... * 546864
26 83456 7 584192
27 21110 8 168880
28 34000 9 306000
29 10056 10 100560
30 ....20000 11 220000
31 800510 12 9606120
MULTIPLICATION.
15
When the multiplier exceeds 12, work by
rule 2.
Multiply by each figure separately. First by the
one at the right hand, then by the next, and so on,
placing their respective products one under another
with the right hand figure of each product, directly
under that figure of the multiplier, by which it is pro¬
duced. Add these products together, and their amount
will be the answer.
examples.
(32.) 120 multiplicand! (33.) 1451
14 multiplier. 16
480 8706
120 1451
Ans. 1680 Ans. 23216
(34.) 124680 (35.) 468
142 72
249360 936
498720 3276
124680
33696
17704560
36. Multiply 4875 by 29. Answer 141375
37 11271 35 394485
38 19004 305 ,.5796220
39 76976 489 37641264
40 84769 . 976 .82734544
41 1978987.. .j 4809 9516948483
Note. When there are ciphers at the right of either the
multiplicand or multiplier, multiply as in the preceding case,
only omitting the ciphers. Then add together the several
products, and place to the right'of the amount as many ci¬
phers as are to the right of both factors-
16
MULTIPLICATION.
examples.
(42.) Multiply 400 by 200 , Answer 80000
200
80000
45 ......... . .8000 400 3200000
44... 3700 200 7400()0
45 4870 2500 12175000
46 876956 990000.......868186440000
Note. "When the multiplier exceeds 12, and is the exact
product of any 2 factors in the multiplication table, the ope¬
ration may be performed thus:—Multiply the given sum by
one of said factors, and that product by the other factor.
examples.
(47.) Multiply 2851 by 15 3 times 5 are 15
3
8553
Ans. 42765
48 Mulfmly 476 by 25 Answer 11900
49 7696 81 623376
50 8976 48 430848
51 87698 72 6314256
52 20784 108 2244672
53 81207 ,...132 10719324
54 47696 144 6868224
55 75687 56 4238472
56 34075 36 1226700
practical examples.
57. A man has 25 stables, and in each stable there are
live horses, how many has he in all? Ans. 125.
58. A man has four chests and in each chest there
are four dollars, how many dollars are there in all?
Ans. 16.
59. Josiah has 30 apples and James has six times
that number, how many has James? Ans, 180.
SUBTRACTION.
IT
60. A man has three tracts of land each containing1
52 acres, how many acres has he in all? Ans. 156.
61. A laborer hired himself for six years at $75 per
year, how much did he receive for the six years' labor?
Ans. $450.
i 62. A certain potato field is 90 hills in length, and
preadth 100, how many hills are there in the field?
Ans. 9000.,
63. A certain cornfield is 98 hills in length and 10 in
breadth, how many hills are there in the field? Ans. 980.
64. A man having built a house, found he had used
18,175 bricks, how many bricks will be necessary to>
build 14 houses Of the same size? Ans. 254450.
SUBTRACTION.
Subtraction is used to know the difference between a
larger and smaller number.
rule.
Set down the larger number first, and under it with
units under units, tens under tens, the smaller. Then
begin at the right hand or unit's place, and take the
lower figure from the one above it if the upper figure
be more than the lower, and set down the remainder.
But if the upper figure be less than the lower, add 10
to the upper figure, take the lower figure from the
amount, set down the remainder and carry one to the
next lower figure.
Proof. Add the lower number and the answer to¬
gether, and their amount will equal the upper.
examples.
(1.) From 964 (2.) 841
Take 333 579
Ans. 631
Ans. 262
3.
From 487
Take 96 Ans. 391
4.
875
302 573
5.
967
351 616
6.
1001
487 514
7.
9765
1307 8458
IS
SUBTRACTION.
8. From 87696 Take 10091 Ans. 77605
9. 455692 300120 155572
10. 1000000 1 999999
11. 10000 9 9991
12. James has 44 apples, and John 24. How many
more has James than John? Ans. 20.
13. Henry has 25 marbles and Charles 8. How ma¬
ny more has Henry than Charles? Ans. 17.
14. William holds Jesse's note for $99. He has now
paid $37. How much does he still owe? Ans. $62.
15. A merchant had $1000, but has lent 105. How
much has he left? Ans. $895.
16. I owe $560. After I pay $69, how much will I
still owe? Ans. $491.
17. A merchant had 180 yards of cloth, but sold 75.
How many had he left? Ans. 105 yds.
18. A farmer had 999 acres of land, but has given his
son 500. How much has he left? Ans. 499 acres.
19. There are two piles of bricks. In the greater pile
there are 7896, ftnd in the less 4389. How many more
are there in the greater pile than in the less? Ans. 3507.
20. A merchant bought 4875 bushels of wheat, out of
which he sold 2976 bushels. How ipany bushels had
he left? Ans. 1899 bushels.
21. I deposited in bank $1240. I have since taken
out $1082. How much remains? Ans. $158.
22. A farmer had 5487 acres of land. He sold to A
325, to B750, and to C 1000 acres. How many had he
left? Ans. 3412 acres.
23. I had 1200 pounds of pork, and sold to one man
400, to another 350, and to another 125. How much
was left? Ans. 325.
24. In a certain milk house there were 44 crocks of
milk, but it so happened an unruly cat broke in and de¬
stroyed 19. How many were left? Ans. 25.
25. In a certain barrel are 94 gallons of wine. If 20
be drawn out, how many will be left? Ans. 74.
26. A ship's crew consisted of 75 men, 21 of whom
died at sea. How many arrived safe in port? Ans. 54.
27. A tree had 647 apples on it, but 158 of them fell
SHORT DIVISION.
19
off. How many were there then remaining on the tree?
Ans. 489.
28. I saw 15 ladies; 8 returned back. How many
passed on? Ans. 7.
29. A general had an army of 43250 men; 15342 of
them deserted. How many remained? Ans. 27908.
30. A man starting a journey of 950 miles. When
he may have gone 348 miles, how far has he still to go?
Ans. 602 miles.
31. A trader had 655 hogs; 99 of them were stolen;
24 died of sickness; he then sold 400. How many had
he left? Ans. 132.
SMORT ©IVISIOjV.
By Division we ascertain how often one number is
contained in another. The number to be divided is
called the dividend. The number to divide by is call¬
ed the divisqr. The number of times the dividend con¬
tains the divisor is called the quotient. If on dividing
there be a remainder it is called the overplus.
RDLE.
Place the divisor to the left of the number you wish
to divide. Consider how many times the number by
which you wish to divide is contained in the first figure
or figures of the number to be divided, and set down
the result, noting whether there be any remainder. If
there be no remainder consider how often the divisor
is contained in the next figure or figures; but if there
be a remainder conceive it to be placed to the left of
the next figure; into which divide as before, and set
down the reshlt.
Proof. Multiply the quotient by the divisor; add in
the remainder, if any. The product will equal the di¬
vidend.
EXAMPLES.
(1.) Divide 336 by 3 (2.) Divide 448 by 2
3)336 2)448
Ans. 112 Ans. 224
20
LONG DIVISION.
(3.) 2)4681278
2340639
(5.) 4)1896431
4741074-3
(4.) 3)65912963
21304321
(6.) 5)863200
172640
(7.) 6)9654630
(8.)
7)1269503450
1609105
1813576354-5
9.
Divide 8767
by
5
Answer
17534-2
10.
— 9698
6
—
16164-2
11:
— 97899
—
7
—
139854-4
12.
— 80409
—
8
—
100514-1
13.
— 981021
9
—
109002-f3
14.
— 897697
_
10
—
89769-f7
15.
— 9876978
—
11
—
8979074-1
16
— 4967844
—
12
—
413987
17. Divide 336 pounds of sugar equally among 3
boys. Ans. 112.
18. Divide 1284 pounds of cotton equally among 4
girls? Ans. 321.
19. Divide 8654 acres of land equally between 2
heirs? Ans. 4327.
20. Bought 6 horses for 318 dollars. How much
did each cost? Ans. 53 dollars.
. 21. John would divide 120 ears of corn among ten
horses. What was the share of each? Ans. 12.
22. Divide 1260 pounds of Coffee among 12 women?
Ans. 105.
23. I would divide 8880 apples among 8 boys. What
was the share of each? Ans. 1110.
LONG DIVISION.
Dong Division is used when the divisor exceeds 12.
RULE.
Place the divisor to the left of the dividend, as in
LONG DIVISION.
21
short division. Consider how often the divisor is con¬
tained in the least number of figures into which it can
be divided, and set down the result to the right of the
dividend. Multiply the figure set at the right of the
dividend by the divisor, and set the product under the
figure in which you considered how often the divisor
was contained. Subtract the product from the line
above it, and set down what remains, which must al¬
ways be less than the divisor. Bring down the next
figure to the right of the remainder, and proceed as
before, till all the figures of the dividend are brought
down. When there are ciphers at the right of both
factors the operation may be shortened by cutting ofT
an equal number of ciphers from each.
EXAMPLES.
(1.) divisor 24)480 dividend. Ans. 20
48
0
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
(2.)
Divide 456
361
958
12350
1475
4277
25757
256976
997816
4697680424
9924000
74000000
80906000
555555555
3875642
by
25)450
Ans. 18
25
200
200
r 21
Ans. 21
Remainder 15
19
19
18
53
4
15
823
5
28
52
19
31
137
30
37
696
5
41
6267
29
59
16912
8
125
37581443
49
64000
183
42
3700
20000
180
449477
14
55555
10000
5555
7898
. 490
5622
LONG DIVISION.
18. divide 98765432 by 1234 Ans. 80036 Remainder 1008
19. 12486240 87654 142 39372
20. 57289761 7569 7569
21. 99607765 27000 3689 4765
22. 15463420 1600 9664 1020
PRACTICAL EXAMPLES.
23. If 1860 pounds of beef be divided equally among
60 men, what will be the share of each?
Ans. 31 pounds.
24. 4556 pounds of salt are to be equally divided
among ato army of 44 men. What will be the share ot"
each man? Ans. 103-}-24.
25. 4006 pounds of malt are to be divided equally
among an army of 84 men. What will be the share of
each man? Ans 47-}-
26. 1600 bushels of corn are to be divided equally
among 40 men, how much is that a piece? Ans. 40
27. A regiment consisting of 500 men are allowed
1000 pounds of pork per day. How much is each
man's part? Ans. 2 lb.
28. If a field of 32 acres produce 1920 bushels of
corn, how much is that per acre? Ans. 60 bushels.
29. A prize of $25526 is to be equally divided among
100 men. What will be each man's part?
Ans. $255-f-
30. How many horses, at $30 per head, may be
bought for $38040? Atis. 1268
31. If a field containing 25 acres produces 375
bushels of wheat, how much does one acre produce?
Ans-15 bushels.
32: 96 persons are to have 480 pounds of beef di¬
vided equally among them. What is the share of
each? Ans. 5 pounds.
33. 144 men are to pay equal shares of a debt which
amounts to $14400. How much must each man ad¬
vance to make up the sum? Ans. $100.
34. If $2400 be equally divided among 16 persons,
what will be the share of each? Ans. $150.
LONG DIVISION.
23
85. A man gave 35 reapers $385, each to have an
equal part. How much did each man receive?
Ans. $11.
36. A man travelled 560 miles in 40 days. How far
was that in one day? Ans. 14 miles.
37. A boy hired 60 days, for which he was to receive
$120. How much was one day's labor worth?
Ans. $2.
38. When I have labored 60 days for the sum of
$180, how much is one day's labor worth at that rate?
Ans. $3.
kxampi.es to try the student in order that he mat
understand the fokegoing rules, viz: additiom, mul¬
tiplication. subtraction and division.
39. John had 40 apples. He gave his brother 10;
kept 10; and divided the rest equally between his two
sisters. How many had each sister? Ans. 10.
40. John owes James $50. Peter owes him $80.
David owes him $105. Samuel $91. Eli $7. And Jo¬
seph $40. After James collects the above debts and
pays $99, which he owes, how much will he have?
Ans. $274.
41. A Farmer has three tracts of land, each con¬
taining 20 acres; buys an adjoining one of 90 acres.
If he sell 40 acres, and divide the rest equally between
his two sons, what will be the share of each?
Ans. 55.
42. A person has 50 sheep; buys from his neighbor
50 more; he then sells 25 to the butcher. How many
has he left? Ans. 75.
43. A gentleman dying left $2500, to be divided as
foil jws: To his son 1500 dollars, and the rest equally
between his two daughters. How much did each
daughter receive? Ans. 500 dollars.
44. A person went to collect money, and received of
one man 800 dollars; of another 50; of another 18; of
another 440; and of another 25. After which, by
gambling, he lost 103 dollars. How much had he left?
Ans. 1230 dollars.
24 TABLES OP WEIGHTS AND MEASURES.
45. Suppose a certain field be 140 hills in length,
and 124 in breadth. Admit there be two stalks in every
■hill, and on each stalk an ear of corn, how many bush¬
els are there in the field, suppose 100 years to make a
bushel? Ans. 347 bushels-t-
46. Bought 25 yards of fine cloth for 250 dollars.
How much was it per yard? Ans. 10 dollars.
47. Bought 16 loads of hay at 4 dollars per load.
What did it amount to? . Ans. 64 dollars.
48. How many yards of cloth, at 6 dollars per yard,
can I have for 90 dollars? Ans. 15 yards.
49. How many pair of gloves, at 1 dollar per pair,
-can I have for 4 dollars? Ans. 4.
TABLES
OF MONEY, WEIGHTS & MEASURES.
FEDERAL MONEY.
The denominations are,
10 Mills (marked m.) make 1 Cent, ct.
10 Cents - 1 Dime, d.
10 Dimes (or 100 cts.) - - 1 Dollar, D. or $
10 Dollars 1 Eagle, E.
AVOIRDUPOIS WEIGHT.
The denominations are,
16 Drams (marked dr.) make 1 Ounce, oz.
16 Ounces 1 Pound, lb.
128 Pounds 1 Quarter, qr.
4 Quarters (or 112 lbs.) 1 Hundred weight, cwt.
■20 Hundred weight - 1 Ton. T.
TROY WEIGHT.
The denominations are,
24 Grains make 1 Pennyweight, dwt.
20 Pennyweights 1 Ounce, oz.
12 Ounces 1 Pound, lb.
TABLES OF WEIGHTS AND MEASURES. 25
APOTHECARIES WEIGHT.
The denominations are,
20 Grains (g.*) make 1 Scruple,
3 Scruples 1 Dram,
S Drams r - * 1 Ounce,
12 Ounces 1 Pound,
i>.
o.
e.
Note.— By Avoirdupois Weight are weighed all things of a
•coarse, drossy nature; and all metals, but gold or silver, by
Troy Weight. Jewels, gold, silver and liquors, are weighed
by Apothecaries Weight. Apothecaries mix their medicine;
but buy and sell by Avoirdupois Weight.
LONG MEASURE.
The denominations are,
12 Inches (in.) make 1 Foot, ti.
3 Feet - 1 Yard, yd.
Yards (or 16£ feet) 1 Rod, pole or perch, If.
40 Poles (or 220 yds.) 1 Furlong, fur.
8 Furlongs (or 1760 yds.) 1 Mile, M.
3 3Iiles 1 League, L.
60 Geographic, or ? ., , n d
69J Statute $ s 1 "eSree> ae"-
360 Degrees the circumference of the Earth.
LAND OR SQUARE MEASURE.
The denominations are,
144 Square inches (in.) make 1 Square loot, fi.
9 Square feet 1 Square yard, yd.
30£ Square Yards - 1 Rod, pole or perch, P.
40 Square Perches - 1 Rood, R.
4 Roods 1 Acre, A.
640 Acres 1 Square Mile, M.
•For want of the proper marks in Apothecaries weight, a
small capital g. is used for grains—s. for scruple—». for
dram—o. for ounce—p. for pound.
C
26 TABLES OF WEIGHTS AND MEASURES.
CLOTH MEASURE.
The denominations are,
2i Inches (in.) make 1 Nail, na.
4 Naiis - - - 1 Quarter of a yard, qr.
4 Quarters - 1 Yard, yd.
3 Quarters - 1 EU Flemish, E. Fl.
5 Quarters - 1 Ell English, E. E,
6 Quarters - - 1 EU Freneh, E. F.
LIQUID MEASURE.
The denominations are,
4 Gills (gi.) make 1 Pint, pt.
3 Pints - 1 Quart, qt.
4 Quarts - - - > 1 Gallon, g^il.
3Q Gallons - 1 Barrel, bar.
63 Gallons • 1 Hogshead. hhd.
2 Hogsheads - 1 Pipe or butt, P. or B.
2 Pipes(252gal.or4hhds)l Ton, T.
DRY MEASURE.
The denomination^ are,
2 Pints (pt.) make 1 Quart, qt.
8 Quarts - - - 1 Peck, pe.
4 Pecks - - - 1 Bushel, bu.
.Vote.—Long Measure is used for measuring lengths, dis'-
tances, &c. Land or Square Measure is used for measuring
lands, &c. Cloth Measure is used for measuring eloth, tape,
&c. Liquid Measure is used for measuring vinegar, rum, bran¬
dy, wine, cider, perry, oil, 8tc. And Dry Measure is used for
measuring grain, fruit, salt, &c.
TIME.
The denominations are,
til) Seconds (sec.) make 1 Minute, min.
60 Minutes - - 1 Hour, hr
24 Hours - 1 Hay, da
7 Days - 1 Week, w.
52 Weeks, 1 day & 6 hours, or }
365 Days and 6 hours, ' \ 1 1 ear' ^
12 Calender months - 1 Year, y.
13 Lunar months - 1 Year, y
COMPOUND ADDITION.
27
The following is a statement of the number of days in
each of the twelve calender months:
Thirty days hath September,
April, June and November;
All the rest have thirty-one,
Except the second month alone,
Which has but twenty-eight in fine,
Till leap year gives it twenty-nine.
COMPOUND ADDITION
Compound Addition consists of several denomina¬
tions.
rule.
Set the nuttibers of like denomination under each
other, leaving a space between. Then begin at the
right hand column, and add, as in Simple Addition.
Divide the amount by as many as will make one of the
next greater. If there be any remainder set it down
under the column added. If no remainder, set down
a cipher. Carry the quotient produced by dividing, to
the next higher denomination, and so proceed.
Proof.—As in Simple Addition.
Note.—In adding Fractions, count \ one, £ two, | three,
because four fourths make a whole one. Or if thirds count
3 one, § two; because three thirds make a whole one.
examples.
(1.) D. cts. (2.) D. cts, (3.) D. cts.
10 30 110 50
5 14 12 25
2 62 9 20
1 75 112 18
Ans. 17 15 Ans. 19 81 Ans.244 13
28
COMPOUND ADDITION.
(4.J D.
cts.
(5.) D.
cts.
(6.) D. cts.
125
50
120
18|
910 31$
812
30
56
25
16 18
560
12
130
12$
122 12$
12
10
25
25
90 09
6
00
72
56$
999 99
330
01
1
09
125 06$
Ans. 1846
03
Ans. 405
46$
Ans, 2263 76
(7.) D.
cts.
(8.) D.
cts.
(9.) D. cts.
500
00
24
m
40 00
200
00
19
&7$
6 00
150
00
22
50
2 00
140
00
17
55
2 00
130
00
10
37$
2 00
120
62$
1
06$
3 75
2
12$
1 124-
Ans. 1240
62$
-T-
1 37$
Ans. 97 671
Ans. 58 25
10. Laid out in market for cloth 12 dollars 50 cents;
for tobacco 20 dollars 75 cents; for salt 13 dollars 50
cents, for calico 40 dollars, for cinnamon 18 dollars
29$ cents; and for sugar 90 dollars 22 cents, Ijow
much did the whole amount to?
Ans. 195 dollars 26$ cents.
11. I have bought 4 yards of lace for 5 dollars; a
veil for 13 dollars 50 cents; 9 yards of silk for 8 dollars
S7$ cents, 12 yds. of i;ibbon for 1 dollar 18$ cents; 19
yds. of linen for 14 dollars 50 cents; 2 pair of gloves for
87$ cents; 3 pieces of domestic for 5 dollars 37$ cents;
9 yds. of lace for 7 dollars 87$ cents, and 6 yds. of cam-
brick for 20 dollars. What did the whole amount to?
Ans. 82 dollars 18$ cents.
12. Bought of Buckner Willingham, cloth for a coat,
for 25 dollars; a pair of pantaloons for 12 dollars 51)
cents: a vest for 6 dollars 12$ cents; a hat for 8 dol¬
lars 50 cents; a shirt for 2 dollars; a cravat for 1 dollar;
COMPOUNi) ADDITION
29
a pair of socks for 1 dollar 50 cents; a pair of boots for
7 dollars 56$ cents; a pair of slips for 1 dollar 25 cents;
a pair of suspenders for 75 cents; a pair of gloves for
1 dollar; a handkerchief for 1 dollar; and a great coat
for 35 dollars. What did the whole suit cost?
Ans. 103 dollars 18£ cents.
13. A gentleman in building a fine house, finds his
plank costs 950 dollars; his workmen will have 1000
dollars; the stone will cost 260 dollars; the window
glass 40 dollars, boarding his hands 600 dollars. What
is t^cost of the whole? /, l~. Ans. 2950 dollars.
14. My agent has bought in market a turkey for 1
dollar 87$ cents; a, pair of shoes fori dollar 68$ cents;
a ham of pork for 43$ cents; a quarter of venison for
1 dollar 37$ cents; a piece of beef for 93$ cents; a hog
for 56$ cents; a quart of strawberries for 37$ cents; some
lard for 31$ cents; and a peck of potatoes for 12$ cents.
What did the whole amount to?
Ans. 7 dollars 6SJ cents.
15. A man desirous to set up a store, laid out monies
as follows, viz: for cloth 650 dollars 91 cents; for iron
220 dollars; for calicoes &c. 1200 dollars 5 cents; sugar
90 dollars 40$ cents; coffee 559 dollars 99$ cents; nails
80 dollars; books 1000 dollars; ink-stands 40 dollars;
slates 60 dollars; leather 100 dollars; tobacco 96 dol¬
lars; blankets 205 dollars 1 cqnt; cinnamon 13 dollars
51 cents; oil 29 dollars 19 cents; steel 30 dollars 33$
cents; molasses 16 dollars; hats 10p dollars 4$ cents;
castings 400 dollars 55 cents; thread 75 dollars 71$
cents: and for rum 227 dollars 37$ cents. What is the
cost of the whole? Ans. 5204 dollars 8$ cents.
AVOIRDUPOIS WEIGHT.
(16.; T.
cwt.
qr.
lb.
117.) T.
cwt.
qr.
lb.
oz.
2
14
1
5
3
2
1
5
6
4
U
3
7
4
12
3
7
8
5
6
2
19
5
6
2
0
2
1
3
1
6
4
19
0
27
15
Ans. 13
16
0
9
Ahs. 18
0
3
12
15
30
COMPOUND ADDITION*
18. Add 12t. 16cwt. lqr. 191b. 15oz. 114t. lOcwt 2qr.
271b. 4oz. I3dr. 72t. 4cwt. 2qr. 241h. 14oz. 3di\ 176t.
15cwt. 3qr. 41b. 15oz. lldr.
Ans. 376t. 7cwt. 2qr.211b. loz lldr.
19. Add 139t. 19cwt. 3qr. 181b. 13oz. iOdr. 17541.
lOcwt. 2qr. 111b. 2oz. 14dr. 27t. 3owt. 141b. lloz. 13cwt.
13oz. Ans. 1922t. 6cwt. 2qr. 171b. 8oz. 8dr.
20. Add 20t. 2cwt. 2qr. 12t. 15t. 2qr. and 2t.
Ans. 49t. 3cwt.
TROY WEIGHT.
lb.
oz.
dwt.
lb.
oz.
dwt.
gp.
(21.) 4
5
6
(22.) 185
2
19
20
8
9
13
56
9
15
6
1
4
7
1472
11
2
17
5
8
11
3S5
0
8
5
1
3
2
10
8
7
12
21
6
19
2110
8
13
12
23. Add 71b. 9oz. lldwt. 22gT. 161b. 4oz. lSdwt. 6gr-
1631b. 7oz. 12dwt. 18gr. 171b. 13dwt-
Ans. 2041b. lOoz. 15dwt. 22gr.
24. Add 101b. 5oz. 2dwt. lOgr. 51b. lOoz. lOdwt. 2gr.
221b- 9oz. 15dwt. lgr. Soz lOgr. 31b. 4oz. 2dvvt. lgr
Ans. 431b. loz. lOdwt.
25. Add 121b. lOoz. 2dwt. 3gr. 41b. Soz. 8dwt.
19gr. 131b. 7oz. lldwt.
Ans. 301b. lloz. ldwt. 22gr.
APOTHECARIES' WEIGHT.
(26.) p. o. d. s. (27.) p. o. d. s. (28.) p. o. d. s. g.
6321 3213 10 9426
12 817 6432 19 164 4
112 635 10 024 75232
40 4 1 0 108 6 1 0 126 8 1 1 3
2621 19 432 1122 2 3 8 1
174 4 5 2 147 5 5 2 1286 3 6 0 16
29. Add 16p. lo. In. 2s. 12e. 175p. IOo. 5d. 10g. 320p.
3o. Id. 2s. 15g. llo. 2n. 3s. Ans. 513p. 2o. 3d. 2s. 17g
COMPOUND ADDITION. HI
30. Add l9t. llo. 7d. Is. 19g. 126p. 7o. 5d. 2s. 15g.
1)6p. Id. 3g. Ans. 241p. 7o. 6d. Is. 17c.
LONG MEASURE.
(31.) L.
M.
fur.
P.
(32.) yd.
ft.
in
2
4
7
10
o
1
4
4
6
5
1
5
2
7
1
O
2
20
6
0
11
75
9
8
25
9
3
5
156
0
1
16
1
1
1
Ans. 246
1
0
32
26
0
4
33. Add 500E. 1M. 2fur. 20P. ly^I. 2ft. 4in. J4P. lyd.
3in. 1J>1. 2fur. 29P. lOin. 4fur. 2fur. lOin. lyd. 2ft. 3in.
Ans. 501L. OM. 3fur. 23P. 5yd. Oft. tfin.
34 Add 462L. 1M. 7fur. 29P. lyd. 1ft. lOin. IIP. 1ft.
lOii 4E. lAI. 2fut\ 2SP. lyd. 2ft. 9in. 13P.
Ans. 467L.3fur. IP, 4yd. 5in.
CLOTH MEASURE.
(35.) yd. qr. na. (36.) yd. qr. na. (37.) E.E. qr. na.
2 3 4 111 19 3 2
513 222 42 3
76 21 333 27 31
21 1 2 5 4 2 14 1 4
106 1 2 14 0 0 66 1 2
38. Add 19yd. 2qr. 3na, 14yd. 2qr. 32yd. 2na. 3qr. lna.
142yd. 3qr. 2na. Ans. 210vds.
39. Add 20E.F. 2qr. 3na. 401E.F. 3qr. 2na. 120E F.
5qr. lna. 782E.F. Ans. 1330E.F. 5qr. 2na,
40. Add 2E.F1. lqr. 3na. 1E.F1. lqr. lna.3qr.
Ans. 5E.F1.
LAND OR SQUARE MEASURE.
(41.) A. R. P. (42.) A. R. P. (43.) A. R.
21 0 27 39 2 37 ' 51 0
19 2 12 62 1 17 17 3
80 3 13 68 0 38 13 3
110 1 29 129 3 12 21 1
224 2 10 532 1 18 1 1
Ans. 456 2 11
S32 2 2
32
COMPOUND ADDITION,.
44. Add 620A. 2R. 20P. 908A. 1R. 39P. 173A. 3R.
27P. 1000A. 1R. 17P. Ans. 2703A. 1R. 23F.
45. Add 999A. 3R. 33P, l$2lA. 14P. 25A. 3R. 19P.
150A. 2R. IIP. and 2000A. Ans. 4997A. 1R. 37P.
LIQUID MEASURE.
(46.) T.
hhd.
gal.
(47.) hhd.
gal.
qt.
pt.
gi-
4
1
3
2
19
0
0
1
45
3
49
0
0
1
1
• 0
75
1
2
3
17
2
0
2
91
2
58
0
&
0
1
0
87
3
5
Q,
0
0
0
1
304
3
54
5
58
0
1
0
43. Add 24bar. lgal. lqt. lpt. lgi-13gal. 2qt. Opt 3gi.
Ibar. 2gal. 3qt. 2pt. Ogi. lgal. 2qt. lpt. Ogi. 6bar.
Ans. 31bar. 19gal. 2qt. lpt. Ogi,
49. Add 3S5hhd. 42gal. 3qt. lpt. 27hhd. 36gal. 2qt.
J32hhd. 17gal. 163hhd> 47gal. 2qtlpt.2gi.
Ans. 709hhd. 18gal, Oqt. Opt. 2gi!
DRV MEASURE,
(50.) bu. pe. qt. (51.) bu. pe. tyt. pt. (52.) bu. pe. qt. pt.
37 2 1 50 2 7 1 85 1 5 1
1,52 3 2 65 3 £ 2 96 3 4 0
423 1 0 185 1 2 0 191 2 3 1
162 r> 1 173, 2 11 ,201 1 7 0
357 0 2 90 3 4 0 909 3 5 1
1163 1 6 566 1 ' 5 0 1485 111
53. Add 144bu. 3pe. 2qt.lpt Ipe. 2qt. 3qt. lpt.462bu.
3pe. lpt. 72bu. 5qt. lpt. Ans. 680bu. Ope. 6qt. Opt.
54. Add 6(>bu. Ipe. lqt. lpt. 41bu. 3pe. 4qt. Opt. 500
bu. 2pe. 7qt. lpt. 183bu. Ope, 5qt. Opt.
Ans. 7S6hu. Ope. 2qt. Opt,
COMPOUND ADDITION.
33
TIME.
(55.) Y. M. (56.) w. da. br. min. (57.) da. hp. min. sec.
80 5 S 2 9 20 4 23 45 30
12 3 1 5 10 30 1 12 14 16
15 7 2 1 9 25 3 19 17 22
20 8 3 3 15 57 2 00 00 10
Ans. 128 11 10 5 21 12 12 7 17 18
58. Add 25y. 7m. 12y. 3m. 96y. 10m. 26y. 9m. lly.
7m. and9y. Ans. 182y. Om.
APPLICATION.
59. Bought potatoes to the amount of $37 50 cts;
corn to the amount of $19 21$ cts; wheat to the amount
of $81 37$ els. What is the cost of the whole?
Ans. 138 08$ cents.
60. Bought pepper to the amount of $358 75 cents;
oil to the amount of $105 06$ cents; molasses to the
amount of $4 48$ cts. What did the whole amount to?
Ans. $468 25 cts.
61. Bought 6 pieces of linen; the first contains
57yds. 2qr.; the second 29yds. 3qr, 2na.; the third
45yds. lqr; the fourth 32yds. 3qr. lna. and the other
two each 38yds. 2qr. What number of yards are
therein the whole? Ans. 242yds. lqr. 3na.
62. There are 4 bags of corn; the first contains 2bu.
2pe., the second 3bu. 3pe. 5qt. the third 3bu. lpe.
lqt., the fourth 2bu. and 4qt. How much is in the
four bags? Ans. llbu.Spe. 2qt.
63. A man has three farms; the first contains 142a.
2r., the second 32a. 3r, 12p.; the third 108a. 3r. 18p.
How many acres are there in all? Ans. 284a. Or. 30p.
64. There are 3 pieces of tape; 'the first measures
15yds. 3qr., the second 18yds. lqr. 2na., the third
25yds. 3qr. 2na. How many yards are there in the
three pieces? Ans, 60yds.
65. If a man on a journey, travel the first day 43m.
Sfur., the second 29m. 34p., the third 57m. 2fur. 32p.,
and the fourth 12m. 3fur. I8p., how many miles did
he travel in the four ddys? Ans. 142m. 2fur. 4p.
34
COMPOUND MULTIPLICATION.
66. Suppose a man to have, in one barrel 40bu.3pe.
lqt. of wheat; in another 50bu. 6qt. lpt.; in another
4Lbu. 2pe., in another 64bu. 5qt. in another 6bn. Ipe.;
in another 19bu. Ipe. 2qt. lpt.; and in another 65bu.
6qt. 2pt. how many bushels are there in the whole?
Ans.287bu. Ipe. 6qt. Opt.
67. Suppose a man has in one trunk 4871b. IOoZ.
18dwt. 22gr; in another 5001b. 8oz. lldwt. 10gr., in
another 2341b. lloz. lOdwt. 16gr.; how much has he
in all? Ans. 12231b. 7oz. ldwt. Ogr.
68. A physician received from Baltimore three
boxes of medicine, which cost him as follows, viz: the
first box $21 32J cts., the second $19 37i cts., the
third $40 17| cts. What did the whole cost.
Ans. $80 87$ cts.
COMPOUND MULTIPLICATION.
When the , multiplier does not exceed 12, work by
Pule 1.
Set down the number to be multiplied, and place the
multiplier under its right hand denomination; and in
multiplying observe the same rules for carrying from
one denomination to another, as in Compound Ad¬
dition.
Note.—If there be £ in the sum, divide the multiplier by 4;
a J by 2; | by 2 and4j a £ by 3; or if there be a fraction in the
multiplier, divide the sum in like manner, and add tbeir amount
to the sum produced by the whole number.
examples.
FEDERAL MONEY.
(1.) $ cts. (2.) $ cts. (3.) $ cts.
2 SO 12 56i 22 12J
2 4 6
Ans. 5 00 Ans. 50 25 Ans. 132 75
COMPOUND MULTIPLICATION. 35
(4.) $ cts. (5.) $ cts, (6.) $ cts.
26 18$ 58 78$ 125 06£
3 5 7
Ans. 78 56$ Ans. 293 93f Ans. 875 43f
$ cts.
7. multiply 58 06}
8. 25 37}
9. 565 62}
10. 112 lof
11. 222 22|
$ cts.
by 4 Answer 232 26
8 203 00
12 6787 50
10 1121 05
11 2444 47£
avoirdupois weight.
(12.) T. cwt. qr. Ib. (13.) T. cwt. qr. lb. oz. dr. (14.) qr. lb. oz. dr.
861 16 6 14 2752 3 14 64
3 4 8
Ans. 24 19 0 20 26 18 1 1 4 8 28 3 4 0
15. Bought eight bags of sugar,' each weighing 2cwt. lqr.
41b. What is the weight of the whole? Ans. 18cwt; lqr. 4lb.„
16. Multiply 4cwt. 3qr. 17lb. by 11. Ans. 53cWt. 3qr. 191b.
troy Weight.
(17.) lb. oz. dwt. (18.) lb. oz.dwt.gr. (19.) lb. oz. dwt.gr.
56 4 14 47 2 0 8 112 8 2 20
2 3 5
112 9 8 141 6 1 0 563 4 14 4
20. Multiply 961b. 9oz. lldwt. lOgr. by 8.
Ans. 7741b. 4oz. lldwt. 8gr.
APOTHECARIES WEIGHT.
(21.) p. o. b. s. (22.) o. Bj s. G. (23.) p. 0. n. s. g.
4821 47 212 12 12 3420
5 7 12
Ans. 23 5 3 2 33Q 3 5 0 4 147 7 0 0 0
36 COMPOUND MULTIPLICATION.
24. Multiply 67p. 60. 3d. 2s. by 7. Ans. 472p. 9o. 1b. 2s.
25. There are 9 parcels, each weighing 109p. 7o. 6d. 2s. 2g.
what is their weight? Ans. 986p. 10o.4u.0s. 18g.
LONG MEASURE.
(26.) . M. Fur. P. (27.) L. M. Fur. P.
1 3 36- 3 2 1 28
12 7
17 6 32 26 0 3 36
28. Multiply 14M. 5Fur. 39P. by 11. Ans. 162M. lFur. 29P.
29. Multiply 1L. 2M. 3Fur. IP. 1yd. 1ft. 2in. by 2.
Ans. 3L. 1M. 6Fur. 2P. 2yd. 2ft. 4in.
CLOTH MEASURE.
(30.) yd. qr. na. (31.) E.E. qr. na. (32.)E.F. qr. na.
12 3 2 22 2 3 16 2 1
4 6 8
Ans. 51 2 0 *135 1 2 131 0 0
33. IF 20yd. 2qr. Sna. be multiplied by 7, what number of
yards will there be? Ans. 144yd. 3qr. Ina.
LAND OR SQUARE MEASURE.
(34.) A. R. P. (35.) A. R. P. (36.) A. R. P.
38 3 13 47 2 10 20 3 30
2 5 9-
77 2 26 237 3 10 188 1 30
37. Multiply 40A. 1R. 19p, by 12. Ans. 484A. 1R. 28P.
38. How many acres will 7 teams plough in one day, allow¬
ing them 1A. 3R. 39P.'each? Ans. 13A. 3R. 33P.
LIQUID MEASURE.
(39.) hhd. gal. qt. (40.) T. hbd. gal. qt. pt. (41.) hhd. gal. qt. pt.
2 13 3 2 1 12 2 1 6 43 2 1
4 8 7
8 55 0 18 1 38 0 Ot 46 53 1 I
COMPOUND MULTIPLICATION. 37
42. Multiply 2T. lp. 40gal. 3qt. lpt. by 6.
Ans. I5T. lp. lhhd. 56gal. Iqt.
43. Multiply 4T. lhhd. lOgal. lpt. by 10.
Ans. 42T. Shhd. 38gal. Iqt.
DRY MEASURE.
(44.) bu. pe. qt. pt. (45.) bu. pe. qt. pt.
180 5 2 1 12 2 7 1
8 3
1450 2 4 0 38 0 6 1
46. Multiply 120bu. 3pe. Oqt. 2pti by 4.
Ans.483bu. Ope. 4qt. Opt.
47. Multiply 189bu. 3pe. 7qt. by 7. Ans. 1329bu. 3pe. Iqt.
48. Multiply 98bu. Ope. 5qt. lpt. by 9.
Ans. 883bu. 2pe. Iqt. lpt.
TIME.
(49.) Y. M. (50.) Y. M. (51.) Y. W. D.
3 11 8 4 12 19 5
11 9 50 0 24 39 3
52. Multiply 49Y. 9M. by 7. Ans. 348Y. 3M.
53. Multiply 19Y. 29Da. by 9. Ans. 171Y. 261Da.
When the multiplier is more than twelve, and is the
exact product of two factors in the multiplication ta¬
ble, work by rule 2. Multiply the given sum by one
of the factors; then multiply that product by the other
factor.
EXAMFI.ES.
$ cts. m. $ cts.
(54.) Multiply 66 37 5 by 36 (55.) 5 09 by 16
6 2
398 25 0 10 18
6 8
Ans. 2389 50 0 81 44
38
COMPOUND MULTIPLICATION.
$
cts.
m.
$
cts.
m.
57.
66
37*
by 36
Ana. 2389
50
0
58.
44
25
3
56
2478
16
8
59.
12
1S|
96
1170
00
0
60.
22
12
5
42
929
25
0
61.
26
18
7
48
1256
97
6
62.
75
24
9
81
6095
16
9
63.
20
08*
108
2169
00
0
64.
10
12*
144
1458
00
0
A.
R.
P.
A.
R.
P.
65.
47
3
20 by 54
2585
1
66.
25
2
8 30
766
2
00
M.
F.
P.
M.
F.
p.
67.
48
7
25 by
88
4307
7
0
p.
0.
n.
p.
0.
s.
68.
56
9
6 by
00
4772
3
0
When the multiplier is not the exact product of any
two factors in the multiplication table, work by rule 3.
Use the two factors whose product comes nearest the
multiplier; then multiply the given sum by the number
which supplies the deficiency, and add its product to
the sum produced by the two factors.
EXAMPLES.
$ cts. m.
69. Multiply 2 25 4><2*. by 52
10
22 54 0
5
112 70 0
4 50 &
117 20 8
*Ten times 5 make 50, and 2 supplies the deficiency
COMPOUND MULTIPLICATION.
39
$
cts.
m.
$
cts.
4
75
8 by 29
Ans. 137
98
7
8 7i
47
370
12}
28
68}
68
1950
75
49
75
87
4328
25
94
18#
31
2919
81}
42
31}
58
2454
12}
71.
72.
73.
74.
75.
76. 7cwt. 3qr. 221b. by 51 Ans. 405cwt. lqr. 21b.
77. 121b. 5oz. 8dwt. 39 4851b. 6oz. 12dwt.
78. 4m. 6far. 21p. 87 418m. 7fur. 27p,
79. 50a. 2r. 5p. 34 1718a. Or. lOp.
80. 60bu. 2pe. 5qt. 43 2608biw Ope. 7qt.
81. 2hhd. 41gal. 2qt. lpt. 17 45bhd.14gal.2qt.lpt'.
When the multiplier is greater than the product of
any two factors in the multiplication table work by
rule 4.
Multiply continually by as many tens, less one, as
there are figures in the multiplier. Then multiply the
product of the last ten by the Jefl hand figure of the
multiplier. If greaterthan I, again multiply the given
sum by the units figure of the multiplier;, the product
of the first ten by "the tens figure? the product of the
second ten if any, by the hundreds figure, &c. Then
add the products of these several figures together for
the answer.
$ cts. $ cts. m.
(82.) Multiply 2 02A)<2 by 222 (83.) I 11 2X1 by 511
10 10
20
25X2
11
12
0X1
10
10
202
50
111
20
0
2 left hand figure.
5
405
00
556
00
0
4
05
1
11
2
40
50
11
12
0
449
55
568
23
2
40 COMPOUND MULTIPLICATION.
$
cts.
$
cts.
84. Multiply
5
18# by 325
Answer—1685
93#
85.
1
56#
456
713
64
86.
2
8 7i
576
1656
00
87.
4
31#
679
2928
18#
88.
18
93#
457
8654
43#
89.
25
43#
879
22359
56#
yd.
ft. in.
. yd. ft.
in.
90.
5
1 2
504
2716 0
0
M.
Fur. P.
M. Fur.
P.
91.
25
3 18
1265
32170 4
10
^d<
qr. na.
yd; qr.
r
na.
92.
22
2 1
3204
72290 1
0
APPLICATION.
93. Sold 125 bushels of wheat at 22cts. per bushel.
What did it amount to? Ans. §27 50 cents.
94. Sold 60 bushels of apples at 15 cents per bushel.
What did they amount to? Ans. $9.
95. If I buy 13 yards of cloth at 10 cents per yard,
what must I pay? Ans. §130 cents.
96. When one cord of wood cost $2 10 cents, what
will be the price of nine cords at the same rate?
Ans. $18 90 cents.
97. Sold 5owt. of tobacco at $12 50 cts. per cwt.
what did the whole amount to? Ans. $62 50 cts.
EXAMPLES.
$ CtS. $ CtS.
(98.) Multiply 10 62#by 4 (99.) Multiply 5 12* by 8
4 8
42 48 40 96
2 2
Ans. 42 50
40 98
COMPOUND SUBTRACTION
4i
100. Bought 24 bushels of wheat at SI 12$ cents
per bushel. What did the whole amount to?
Ans. 827.
101. Bought 44bu. of corn at 37$ cents per bushel.
What did the whole cost? Ans. $16 50 cents.
102. A merchant bought two pieces of linen, the one
contained 38 yards and the other 26 yards* What
did the two pieces cost at $3 87$ cents per yard?
Ans. £248.
103. What cost a box of sugar weighing 100 lbs.,
at 15$ cents per pound? Ans. $16 16$ cts.
104. What will 13$ gallons of molasses come to at
40 cents per gallon? Ans. 85 40.
105. How much will 25 bushels of oats come to at
15 cents per bushel? Ans. 83 75 cents.
COMPOUND SUBTRACTION.
RULE.
Place the numbers under each other which ure of
the same denomination: the less always being under
the greater. Begin at the right hand figure, and if it
be larger than the one above it, consider the upper one
as having as many added to it as make one of the next
greater denomination. Subtract the lower from the
upper figure thus increased, and set down the remain
der, observing to Ifarry one to be added to the next
higher denomination, and so proceed.
Proof as in Simple Subtraction.
EXAMPLES.
FEDERAL MONEY.
8 cts. tn. $ cts. m. $ cts. m.
(1.) 5 54 7 (2.) 1 50 2 (3.) 19 84 4
2 10 5 28 4 10 18 9
■mm*
Ans. 3 44 2 1 21 8 9 65 5
D
42
COMPOUND SUBTRACTION.
$ cts. $ cts. $ pts.
(4.) 64 87$ (5.) 10 37$ (6.) 100 00
25 12$ 5 06$ 55 62$
39 75 5 31$ 44 37$
•SB Cts. SB cts. SB cts.
(7.) 45 64$ (8.) 30 30 (9.) 150 93$
5 99$ 1 12$ 90 10
39 65$ 2y 17$ 60 83$
10. I owed $559 22$ cents, but have paid $148 50 cts.
How much remains unpaid? Ans. $410 72$ cents.
11. Lent a man $400; he now returns $211 12$ cents.
How much does he still owe? Ans. $188 87$ cents.
12. A merchant had in his desk $500 87$ cents, but
drew out $120 93 cts. to pay a debt. How much had
he left in the desk? Ans. 379 dollars 94$ cents.
13. I had 303 dollars 6$ cents, but lent 9 dollars 91$
cts. How much had I left? Ans. 293 dollars 15 cts.
14. From $1000 take 1 mill, Ans. $999 99cts. 9m.
AVOIRDUPOIS WEIGHT,
cwt. qr. lb. T. , cwt. qr. lb.
(15.) 6 3 25 (16.) 28 3 1 27
4 2 12 13 1 0 19
Ans. 2 1 13 15 2 1 08
17. From 14t. lOcwt, 2qr. 161b. take 111b.
Ans. 14t. 10cwt. 2qr. 51b.
18. Bought 400cwt. of sugar, but have since sold
2cwt. 3qr. 141b. What quantity remains?
Ans. 397cwt. Oqr, 141b.
TROY WEIGHT,
lb. oz. dwt. gr. lb. oz. dwt. gr.
(19.) 24 6 19 13 (20.) 13 9 5 22
19 5 18 23 8 11 16 10
Ans. 0 1 0 14 4 9 9 12
COMPOUND SUBTKACTION.
43
21. Prom 271b. 9oz. 16dwt. take 19dwt.
Ans. 271b. 8oz. 17dwt.
22. Subtract lib. Ooz, 17dwt. 15gr. from 151b. 9oz.
18dwt. 8gr. Ans. 141b. 9oz. Odwt. 17gr.
APOTHECARIES' WEIGHT.
p.
0.
». p.
0.
i).
s.
p.
• 0.
n.
s.
(23.)
186
7
5 (24.) 96
4
0
2 (25.)
100
9
8
2
67
8
4 75
4
2
1
99
8
3
2
Ans.
118
11
1 20
11
6
1
1
1
6
0
CLOTH MEASURE,
yds. qr. na. yds. qr. na. yds. qr. na.
(26.) 160 3 3 (27.) 969 2* 1 (28.) 14 0 3
37 1 2 786 1 2 9 3 2
Ans. 123 ^ 1 183 0 3 4 1 1
29. Bought 27 yards of domestic, but have since sold 9 yds,
3qr. How much remains? Ans. 17yds. lqr.
EE. qr. na. E.Fr. qr. na. E.Fr. qr. na.
(30.) 44 3 2 (31.) 62 2 3 (32.) 27 5 2
23 3 1 43 3 2 19 3 3
AOs. 21 0 1 18 5 1 8 13
4 LONG MEASURE.
L. M. fur. p. yd. ft, in. L. M. fur. p. yd. ft. In.
(33.) 6 2 5 9 4 2.6 (34.) 9 1 7 18 5 1 11
4328137 725 19 12 9
Ans. 12 3 12 1 11 • 121 39 32 2
35. Two men travelling the same road; one travels at the
rate of 27m. 2fur. 39p.; the other at the rate of 19m, lfur. 17p,
At night how far are they distant? Ans. 8m. lfur. 22p.
44 COMPOUND SUBTRACTION,
LAND OR SQUARE MEASURE-
A. R. P. A. R. P. A. R. P. A. R. P.
(36.) 96 2 16 (37.) 640 3 12 (38 ) 96 0 18 (39.) 50 3 19
87 3 18 114 4 3 74 2 4 13 1 6
Ans. 8 2 38 525 3 9 21 ^ 14 37 2 14
40. A Fattier dying left his son Joseph 200a. 2r. 20p.,a'nd to
James 180a. 3r. 39p. What is the difference in their shares?
Ans. 19a. 2r. 21 p.
LIQUID MEASURE.
T.
hhd.
gal. qt.
pt. T.
hhd. gal.
qt.
(41.) 8
2
42 2
1 (42.) 188
3 9
1
3
2
14 . 3
0 98
2 8
2
Ans. 5
0
27 8
1 90
1 0
3
43. A person boilght 4hhd. 25gal. of cider;—he has since
sold 2hhd. 15gal. 3qt. Ipl. How much has he 'remaining?
Ans. 2hhd. 9gal. Oqt. lpt.
44. If 5hhd. lgal. lqt. lpt. of oil be drawn from 6hhd.
2gal. 2qt. lpt. how much will remain?
Ans. lhhd. lgal. lqt. Opt
DRY MEASURE,
bu. pe. qt, pt. bu. pe. qt. pt. buj pe. qt. pt.
(45A 44 2 1 1 (46.) 80 3 7 -1 (47.) 789 0 5 0
32 3 2 1 15 1 1 1 578 3 6 1
Ans. 11 2 7 0 65 2 6 0 210 0 6 1
48. From 719bu. 3pe. 6qt. take 533bu. 2pe. 6qt.
Ans. 186bu. Ope. 7qt.
49. Raised 189bu. Ipe. 7qt. lpt. of corn; have since sold
167bu. 2pe. lqt.; what quantity have I remaining?
Ans. 21bu. 3pe. 6qt, lpt.
TIME.
Y.
M.
Y.
M.
hr.
min.
sec.
(50.)
12
11
(51.) 7
1 (52.)
18
45
59
7
5
3
10
2
51
28
Ans.
5
6
3
3
15
54
31
COMPOUND SUBTRACTION.
43
63. Subtract 125y. 9m. from 450y. 11m.
Ana. 325y. 3m.
34. Take 36da. I4hr. 30min. and 25sec. from 44da. lbr.
iSmin. and53sec. Ans. 7da. llhr. 18min. 33sec.
Note.—The interval or 9pace of time between two given
dates is thus found; Set down the greater date, and under it
the less: Begin with the days. If the upper number of days
be greater than the lower, subtract the lower from it, and set
down the remainder. But if the lower number be greater,
add as many days to the upper as make a month of the lower,
and subtract the lower therefrom; then carry one to the months
•f the less date, and subtract as before, and so proceed.
EXAMPLR9.
35. Abijah was born on the 15th of November, 1807, and
Josiahonthe 10th of July, 1811. What is the difference in
their ages*
Y. M. da.
1811 7* 16
1807 11 15
Ans. 3 8 1
•Note.—July is the seventh month, and November the elev¬
enth.
58. Charles was born on the 18th day of June, 1821.
How old will he be on the 13th duy of August, 1840?
Ans. 19y. lm. 25da.
57. William was born on the lltli day of August,
1813, and John on the 5th day of July, 1827. How-
much older is William than John? Ans. 13y. 10m. 25da.
58. A man gave his note on the 10th day of May,
1824, and lifted it on the 8th day of December, 1829.
For what time did he pay interest? Ans. 5y. 6m. 29da.
APPLICATION.
59. Bought 2 pair of stockings, at75cts. per pair;
16yd. of linen, at 87£ cts. per yard; 28yd. of domestic,
46
COMPOUND DIVISION.
at22cts. per yard; and 5 pair of gloves, at 31J cts.
per pair; and to him from whom I bought those arti¬
cles, I deliver $50 00, out of which he is to take the
sum due him. How much change will there be com¬
ing to me? AnS. $26 77fcts.
60. If I buy 660yd- of muslin for $90 60 cts., and sell
the same again for $100 04 cts., how much do I gain
by the sale? Ans. $9 44 cts.
61. Bought 50yd. of superfine cloth, at $8 75 cts. per
yard; 30 podnds of coffee, at 2*2| cts. per pound; and
44 bushels of salt, at $2 per bushel. What sum must
I pay for the whole? Ans. $532 25 cts.
62. I haVe several tracts of land; one of them con¬
tains 690a. 2r. 16p.; another 400a.; and two others,
each 63a. 3r. 24p. If I sell 200 acres what number re¬
mains? Ans. 1018a. lr. 24p.
63. Bought 400bu. 3pe. of wheat; 160bu. of rye;
l50bu. 2pe. of oats. I have since sold 22-5bu. lpe. of
wheat; 37bu. 2pe. of rye; ?8bu. 3pe. of oats. How
many bushels of each have I remaining?
f I75bu. 2pe. wheat.
Ans. < 122bu. 2pe. rye.
( 71bu. 3pe. oats.
COMPOUND DIVISION.
Compound Division teaches to divide any sum or
quantity which consists of several denominations.
BULK.
Begin at the highest denomination, and divide the
several denominations of the given sum or quantity one
after another, and set their respective quotients Under¬
neath. When a remainder occurs reduce it to the next
lower denomination by multiplying it by as many of
the next denomination as make one of that denomin¬
ation from which the remainder is derived, and add
COMPOUND DIVISION.
4%
the next denomination to the product; then divide as
before, and so proceed.
Note..—If the dividend be not large erfough to contain the
divisor, reduce it till it will be, and proceed aS before.
EXAMPI.ES.
(1.) D., cts. (2.) D. cts. m. (3.) D. cts.
2)12 61 3)187 91 4 4)168 99
Ans. 6 '304 Ans. 62 63 8 Ans. 42 24$
$
cts.
4.
Divide 366
18$
5.
496
75
6.
384
871
7.
587
68$
8.
976
43$
9.
1979
331
yd. qr. na,
10. Divide 44 '1 2
11. 56 3 3
M. fur. p.
12. Divide 105 5 22
13. 45 7 18
bu. pe. qt.
14. Divide 48 2 0
15. 86 3 7
$ cts.
by 3
Ans. 122 06$
8
62 091+
6
64 14:4-
9
65 29|4-
11
88 76.',4-
12
164 94^4-
yd. qr. na.
by 7
Ans. 6 1 14-
11
5 0 34-
M. fur. p.
by 12
Ans. 8 6 1H4-
6
7 5 9-j-
bu. pC. qt. pt.
v 4
Ans. 12 0 4 0
3
28 3 7 14-
Note.—-When the divisor is more than 12, work by Long
Division. Divide the highest denomination of the giren sum
by the divisor, and reduce the remainder, if any, to the next
lower denomination, adding to it when reduced the number
there is of that denomination in the given sum or quantity.—
Then divide as before, and so proceed.
48
COMPOUND DIVISION.
EXAMPLES.
$ cts. m. ( $ cts.
(16.) Divide 88 45 6 by 19 (17.) Divide 250 50 by 25
$ eta. m. $ cts.
19)88 45 6. {Ans. 4 65 5- 25)250 50 (Ans. 10 OS
76 25
124 0 50
114 50
105 00
95
106
95
11 Remainder.
D. eta. m. D. cts. m.
18. Divide 88 77 8 by 44 Ans. 2 24 4+
19. 45 66 5 36 1 26 6+
20. 77 87 5 96 0 81 1-f
21. 288 68| 0 108 2 67* -f
22. 496 37* 0 132 3 76 0+
23. 47 68 7 45 1 05 9-f-
24. 196 75 0 78 2 52 2+
25. 496 87* 0 97 5 12 2-f
26. 376 61* 0 123 3 06 3-f
27. A laborer received for thirty days $900. How
much did he receive per day? Ans. $30.
28. If a boy receive $60 for twelve months work,
how much is that for one month? Ans. $5.
29. How many bushels of corn maybe bought for
$100 at $2 per bushel? Ans. 200 bushels.
30. When 72 bushels of corn cost $56 25 cents,
what is the price of one bushel? Ans. 78cts. 1 m.-f-
31. Suppose $1875 81* cents to be equally divided
among 125 men, what will be the share of each man?
Ans. $15 00* cent-f-
32. 89 men agree to equally divide 150 gals. 2qts,
lpt. of brandy among them, how much will be the
shareof each? Ans. lgal. 2qt. lpt.4-48
REDUCTION DESCENDING.
49
REDUCTION DESCENDING.
Reduction Descending- teaches to change any sum
or quantity to a lower denomination, but retaining the
same value.
RULES.
Multiply the highest denomination of the given sum
or quantity by as many of the next lower denomina¬
tion as make one of the higher, adding to the product
the number there is of that denomination in the given
sum or quantity.
Note.—To reduce dollars to cents, annex two ciphers to
the dollars.
EXAMPLES.
FEDERAL MONEY.
(1.) Reduce $18 50 cts. to cts. (2.) Bring $75 to cents.
100 100
Ans. 1850
S. Bring $100 to ce its.
4. Reduce 20 dollars to cents.
5. Bring 25 dollars to cents.
6. Reduce 45 dollars to cents.
7500
Ans. 10000 cents.
Ans. 2000 cents.
Ans. 2500 cents.
Ans. 4500 cents.
Note.—-To reduce dollars to halves, quarters or thirds of a
cent, bring them first into cents, and then bring the cents intq
halves, quarters or thirds, as required.
(7.) Bring $50 into half cts. (8.) Bring $40 into thirds of act.
100 100
5000 4000
2 3
Ana. 10000 halves.
12000 thirds.
50
REDUCTION DESCENDING.
(9.) Reduce 25 cts. to fourths. (10.) Beduce 12 cts. to thirds,
4 3
— T—
Ans. 100 fourths. Ans. 36 thirds.
11. Reduce ten dollars to dimes. Ans. 100 dimes.
12. Reduce 220 dollars to mills. Ans. 220,000 mills.
13. Reduce $426 88$ cts. to halves of a cent.
Ans. 85377 halves.
14. Bring $487 44f cents to fourths of a cent.
Ans. 194979 fourths.
15. Bring $17 18| cents to fourths of acent.
Ans. 6875 fourths.
AVOIRDUPOIS WEIGHT.
16. Bring 2 tops to cwt. (17.) Reduce 260 to quarters.
20 4
Ans. 40 cwt., Ans. 1040 qr.
18. Reduce 36qr. to pounds. Ans. lt)081b.
19. Bring 17 pounds to ounces. Ans. 272oz.
SO. Bring 2qr. 251b. lOoz. to drams. Ans. 2G896dr.
TROY WEIGHT.
21. Reduce 20 pennyweights to grains.
24
80
40
Ans; 480 grains.
22. Reduce 5 ounces to grains. Ans. 2400gi\
23. Bring 40 pounds to pennyweights. Ans. 9600dwt.
24. How many grains are there in 191b. lloz. 14dwt.
21gr. Ans. 115077gr.
APOTHECARIES WEIGHT.
25. Reduce 40 pounds to ounces. Ans. 480oz.
12
480
REDUCTION DESCENDING.
51
26. Bring1 72o. to drams.
27. Beduce 15p. 9o.4d. 2s. 17g. to grains.
Ans. 576b.
Ans. 91017a.
LONG MEASURE.
28. Reduce 10 Ft. to inches.
12
Ans. 120in.
120
29. Bring 40 yd. to feet. Ans. 120ft.
30. Reduce 120 yd. 1ft. 4in. to inches. Ans. 4336in.
31. Reduce 20 miles to yards. Ans. 35200yd.
32. Reduce 450m. 6fur. 32p. to poles. Ans. 144272p.
33. In 21. lm.3fur. 16p. 3yd. 2ft. lOin. how many inches?
Ans. 470590in.
Ans. SSna.
Ans. 144qr.
Ans. lOOqr.
^4ns. 120qr,
Aps. 33qr.
Ans. 313na.
CLOTH MEASURE.
34. Reduce 22 quarters to nails.
4
88
35. Bring 36yd. to qr.
36. Bring 20 English Ells to quarters.
37. Bring 20 French Ells to quarters.
38. Bring 8vd. lqr. to-qr.
39. In 19$t^2qr. ln^. how many nails?
LAND OR SQUARE MEASURE.
40. Bring 2 roods to perches. Ans. 80 perches.
40
80
41. Reduce 140 acres to perches. Ans. 22400 perches.
42. Bring 54 acres, 3 roods. 23 poles, to poles.
* Ans. 87S3p.
43. Bring 6 square feet to square inches. Ans. 864in.
44. Bring 120 square yards to squareinches.
Ans. 155520in.
45. Bring 29 square yards, 2 square feet, 102 square
inches to square inches. Ans. 37974 square inches.
52
REDUCTION DESCENDING.
LIQUID MEASURE.
45. Reduce 31 quarts to pints. Ans. 62pt.
2
62
AT. Bring 28 gal. to quarts. Ans. 112qt.
48. Reduce 5hhd. to gallons. Ans. 315gal.
49. In 6 tons, how many pints? Ans. 12096pt.
50. Reduce 4hhd. 3qt. to pints. Ans. 2022pt.
51. Bring 5 tons lhhd. 15gal. lqt.lpt. to pints.
Ans. 10707pt.
DRY MEASURE.
52. Reduce 16 qt. to pints.
2
32
63. Bring32pe. to quarts.
64. Reduce 7bu.to pecks.
55. Reduce 12bu. to pints.
66. Bring 24bu. lpe. 2qt. lpt. to pints.
TIME.
Ans. 32pts.
Ans. 256qt.
Ans. 28pe.
Ans. 768pts.
Ans. 1557pt.
67. Bring 40 minutes to seconds.
60-
2400
Ans. 2400 sec.
68. Bring 20 hours to seconds. Ans. 72000seo.
59. Reduce 12 years to months. Ans. 144m.
60. Bring 45 years to days. Ans. 16425da.
61. Reduce 3 days, 5hr.29min. to minutes.
Ans. 4649mln.
62. Reduce 7y. 8w»4da. 20hr.20min. and 20see. to se¬
conds. Ans. 222380420seo.
SEDUCTION ASCENDING.
53
REDUCTION ASCENDING.
Reduction Ascending teaches to change any sum or
quantity to a higher denomination.
rule.
Divide the given sum or quantity in the lowest de¬
nomination by as many of that denomination as make
one of the next higher, and soon,uiftii you have brought
it into that denomination which your question requires.
Notb.—Mills may be brought to dollars, cents and
mills, by cutting off one figure on the right for mills,
two more for cents; the rest will be dollars. Or to
bring cents to dollars and cents, cut off two figures on
the right for cents.
examples.
FEDERAL MONEY.
1. Bring 2900 cents to dollars. Ans. $28.
28100
2. Bring 11222 mills to dollars, cents and mills.
11122(2 Ans. $11 22cts. 2m.
3. Bring 4444 cents to dollars and cents.
Ans. $44 44cts.
4. Bring 854 halves of a cent to whole cents.
Ans. 432ets.
5. In 963 thirds how many cents? Ans.821cts.
6. In 591 fourths how many cente? Ans. 147jcts.
7. Bring 630 thirds to cents. Ans. SlOcts.
AVOIRDUPOIS WEIGHT.
8. Bring 118 lb. to quarters.
28)118( Ans. 4qr. 61b.
112
6
54
REDUCTION ASCENDING.
9. Bring1 90qr. to cwt. Ans, 22cwt. 3qr,
10. Bring 1781 lb. to cwt, Ans. 15cwt.3qr. 171b.
11. In 1872dr. how many ppunds? Ans. 71b. 5oz.
12. Bring 75cwt. to tons. Ans. 3t. 15cwt.
13. Bring 98561b. to cwt. Ans. 88cwt.
troy weight.
14. Bring 186oz. to pounds. Ans. 151b. 6oz.
12)186
151b. 6oz.
15. In 544dwt. how rqany pounds'? Ans, 2Ib.3oz. 4dwt.
16. Bring 960dwt. to pounds. Ans. 41b.
17. Bring 9624gr. to pounds. Ans. lib. 8oz. ldwt.
apothecaries'Veight.
18. Bring 240 grains to scruples. Ans. 12s.
210)2410
12
19. Bring 2720s. to ounces. Ans. 113o. 2d. |2s.
*20. Bring 12660g, to pounds. Ans. 2p. 2o. 3d.
21. In 155520g. how many pounds? AnB. 27p.
long measure.
22. Bring 120 miles to leagues.
3)120
40
23. Bring 1280 poles to fur.
24. Bring 2880 poles to leagues.
25. Bring 5760 poles to leagues.
cloth measure.
26. In 60 quarters how many yards?
4)60
15
27. Bring 4000 nails to yards.
Ans. 401.
Ans- 32fur.
Ans. 31.
Ans. 61.
Ans. 15yds.
Ans. 250yds.
REDUCTION ASCENDING. 55
28. Bring 1260 quarters to E. F. Ans. 210 E. F.
29. Bring 1818 nails to yards. Ans. 113yds. 2qr.2na.
LAND OR SQUARE MEASURE.
30. In 2400 perches how many R'sT Ans. 60R.
4|0;240j0
60
31. Bring 2040 perches to A. Ans. 12A. 8R.
32. Bring 190b020 perches to A. Ans. 11925A. OR. 20F.
33. In 1728square inches how many square feet?
Ans. 12 feet.
LIQUID MEASURE.
34. In 480 gills how many pints? Ans. 120 pts.
4)480
120
35. Bring 1840 pts. to gals. Ans. 2.30 gals.
36. Bring 1890 gal. to hhds. Ans. 30 hhds.
37. In 504 gallons how many bar. Ans. 16 bar.
DRY MEASURE.
3S. In 800 pints how many qts.? Ans. 400qts.
2)800
400
39. Bring 240 pints to pe. Ans. 15 pe.
40. Bring 8888 pecks to bu. Ans. 2222 bu.
41. In 12840 pts. how many bu.? Ans. 200bu. 2pe.4qt.
TIME.
42. Bring 2400 seconds to minutes. Ans. 40 min.
610)240(0
40
56
REDUCTION ASCENDING.
43. In 7200 seconds how many hours? Ans. 2 hours.
44. Bring1144 months to years. Ans. 12 years.
45. In 4849 minutes how many days?
Ans. 3da. 5hr. 29m.
PROMISCUOUS EXAMPLES.
1. In 20 dollars how many cents? Ans. 2000 cents.
2. In 63 roods how many perches? Ans. 2520 per.
3. How many miles are there in 98 fur.
Ans. 12m. 2ftar.
4. In 175 pecks how many bushels? Ans. 43bu. 3pe.
5. How many min. are there in 720 sec.? Ans.l2min.
6. In 103 pints how many quarts? Ans. 5lqts. lpt.
7« In 1821 cents how many dollars?
Ans. $18 24 cents.
8. In 8t. 15cwt. how many hundred weight?
Ans. 175 cwt,
9. How many English Ells are there in one hundred
quarters of a yard? Ans. 20 E.EIle.
10. How many scruples are there in 9n. Ans. 27 scru.
11. In 203 days how many weeks? Ans. 29w.
12. In 108 dwt. how many ounces? Ans. 5oz. 8dwt.
13. How many cwt. are there in 20 tons? Ans. 400cwt.
14. In 202 cents how many qrs. of a cent? Ans. 808qrs.
15. How many dollars are there in 8762 cents?
Ans. $87 62cts.
16. How many fur. are there in 3m. lfur.? Ans. 25fur.
17. In 13 lb. avoirdupois how many drams?
Ans. 3328dr.
IS. In 21 gallons 3 qts. lpt., how many pints?
Ans. 175 pints.
19. How many Ells F. are there in 60 qrs.? Ans. 10E.F.
20. How many lbs. are there in 2461 dwt.
Ans. 101b. 3oz. ldwt.
21. How many dr. are there in 725 lb. 6oz. av.
Ans. 185696dr.
22. In 12yds. 2qrs. lna. how many nails? Ans. 201na.
M- How many cwt. are therein 27552 lb.? Ans. 246c wt.
BULE OP GAUGING.
57
24. In 584621 gallons how many tons?
Ans. 231&t. 3hhd. 44gal.
25. How many min. are there in 3da.? Ans. 4329min.
26. In 7hhd. 3gal. how many gallons'? Ans. 444gal.
27. In 763 dayshow many weeks.' Ans. 109 weeks.
28. How many bu. are there in 1357pts.
Ans. 21bu. Ope. 6qt. Ipt.
MULE OF GAUftlNG.
The length, depth and breadth being given in feet
m the clear, to find how many bushels of corn in a crib.
rule.
Multiply the length by the depth, and that product
by1 the breadth; divide the last product by 2, the quo¬
tient will be the answer in bushels.
Note.—2 cubic feet of corn in the ears make a bushel ol
shelled. If the crib tapers allowance must be made.
Note.—Complete accuracy is not to be expected in every
respect, from a rule to gauge a crib which contains corn in the
ears, there being so much difference in the quality of corn.
Though from experience we think the above as correct us can
be given.
examples.
1. Suppose a crib be 20 feet long, 10 feet deep, and
C feet wide, how many bushels of corn will it hold?
20 length.
10 depth.
200
6 breadth.
Cubic feet 2)1200
Ans 600 bushels.
£
58
RULE or GAUGING.
2. Suppose another crib be 18 feet long:, 7} feet high,
and 8 feet wide, how many bushels of corn will it
bold?
18 length.
7i depth.
136
9
135
8 breadth.
2)l0s0
Ans. 540 bushels.
3. A crib 18 feet long, 12 feet deep, and 5 feet wide*
how many bushels therein? Ans. 540 bu.
4. How many bushels in a crib 24} feet long, 8 feet
wide, and 10} deep? Ans. 1004J bu.
5. How many bushels are there in a crib 13} feet
long, 4} feet wide, and 7} feet deep? Ans. 220 bu.-f-
The length, depth andbreadth being given in feet, in the clear,
to find how many busk'Is of coal, wheat, rye, oats, shelled
earn, fruit, salt, tj'-c.; in a house, box, <fic.
RUL fe.
Multiply the length by the depth, and that product
by the breadth. To this last product annex two ci¬
phers. Then divide that product by 124. The quo¬
tient will be the answer in bushels.
Note.—If the length, depth and breadth in inches, had been
multiplied together, and the last product divided by 2150 2-5,
the number of solid inches in a bushel, the quotient would be
about the same answer as dividing in the above rule by 124.
EXAMPLES.
1. Shippoee a house he 12 feet long, 10} feet deep,
and 6 feet wide. How many bushels of coal will it
contain? Ans. 600 bu.
UTILE OP GAUGING.
59
12 long.
10g deep.
120
4
124
6 wide.
124)74400(600
744
00
2. Suppose a box be 14 feet long, 3i feet deep, and
3£ feet wide. How many bushels of apples will it con¬
tain? ' Ans. 12Sbu.+
3. Suppose a box be 8 feel long, 5 feet deep, and 6
feet wide. How many bushels of salt will it contain?
Ans. 193 bu.-f-
4. Suppose a box be 5 feet deep, 4 feet wide, and
6 feet long; how many bushels of oats will it contain?
Ans. 96bu.-f-
5. Suppose a wagon bed be 10 feet long, 3£ feet wide,
and 2 feet deep; how many bushels of shelled corn will
it contain? Ans. 56bu.+
6. Suppose a house be 20 feet long. 8 feet deep, and
16 feet wideuiluvv many busl|els of coal will it con¬
tain? Ans. 2064 bu.-4-
7. A little boy said he had collected chesnuts until
he had filled a box full, which was 4 feet long, 1£ feet
deep, and 2 feet wic(p. How many bushels had he?
Ans. 9 bu.-f-
Tofind the number of Gallons contained in a Cask.
RULE.
Find the length in inches from the bung to the under
edge of the head in the clear, which length multiply by
itself) and that product by an equivalent number. Di¬
vide the last product by 370; the quotient will be the
answer in gallons.
60
RULE OP GAUGING.
Notb.—If the bung be not in the middle, measure from the
bung each way, add their lengths together, and half of their
sum use as before.
Note.—Complete accuracy is not to be expected in every
respect, from any rule to gauge casks. Though by the above
rule they may be measured with sufficient exactness; there be¬
ing so much difference in the bend of staves or bulges of casks.
"When any unusual curve or bulge presents itself in a cask, al¬
lowance should be made for such irregularity.
examples.
1. Suppose a cask measure 23 inches from the "bung
to the under edge of the head; how many gallons will
it hold?
23
23
69
46
529
23 equivalent number.
1587
1058
370)12167 (Ans. 32gal. 3qt, lpt.+
1110 4 '
1067
740
327
4
1308 (3qt,
1110
198
2
396 (lpt.
370
26
btjxe op gauging.
61
2, Suppose a cask measure from the bung to the un¬
der edge of the head 20 inches, how many gallons does
it contain?
20
20
400
20
370)8000 (Ans. 21gal. 2qt. Opt. 3gi.-f
740
600
370
230
4
920 (2qt.
740
180
2
360 (Opt.
4
1440 (3gi.
1110
330
3. A cask measures 25 inches from the bung to the under
edge of the head. How many gallons does it contain'
Ans. 42gal, Oqt. lpt -f-
4. When a cask measures 10 inches from the bung to the
under edge of the heads how many gallons does it contain?
Ans. 2gal. 2qt. lpt.-}-
5. Suppose a cask measure 22 inches from the bung to the
under edge of the head; how many gallons will it contain?
' Ans. 28gal. 3qt.0pt.-f.
6. A cask measures from the bung to the under edge of the
head 20 inches. How many gallons does it contain?
Ans. 72gal. 3qt. lpt.-}-
62
RULE OF GAUGING.
7. A cask measures from the bung to the under edgo
of the head, one way 42 inches, and the other way 4(h
How many gallons does it contain?
42
40
Thus 2)82
41
41
41
164
1681
41
1681
6724
370)68921 (186gal. lqt. Opt. Ogi.-j-:
370
3192
2960
2321
2220
101
4
404
370
34
68
4
272
RULE OP TWO.
63
RULE OF TWO.
The Rule of Two is that in which two terms are
given to find a third, which is the answer.
To find the whole cost of any number of articles at
any price per article,
RULE.
Multiply the articles by the given price of one article;
the product will be the answer.
EXAMPLES.
1. What will eleven oranges come to at 12$ cents
each?
2, How much will 60 bu. of apples come to at 8$ cts.
per bu.?
11 60
12$ the given pr. of one article. 8$
132 480
5$ the half of 11 is 5$. 15 the fourth of 60 is 15
Ans.$l 37$ Ans. $4 95
3. Row much will 105 pounds of sugar come to at
12$ cts. per pound? Ans. $13 12$ cents.
4. What will 60 apples come to at 2$ cents each?
Ans. $1 35 cents.
5. What will 87$ pounds of beef come to at three
cents per pound? Ans. $2 (12$ ets.
6. Bought 40 pounds of cofiee at 31$ cents per pound;
what did it amount to? Ans. $12 30 cts.
7. Purchased ninety gallons of molasses at 50$ cents
per gallon; what did it amount to? Ans. $50 02$cts.
8. What will nineteen pounds of bacon come to at
hj cents per pound? Ans. $1 5^J cents.
0. What is the cost of 400 pounds of chee«e at 8}
cents per pound? Ans. $33 33$ cents.
10. Bought 101 bushels of wheat at $1 04 cents per
bushel: what did it amount to? Ans. $105 04cts.
64
RULE OP TWO.
11. What will 62$ gallons of whiskey come to at 62J
cents per gallon? Ans. $39 06$ cents.
12. What will 25 bushels of oats come to at 25 cents
per bushel? Ans. $6 25 cents.
13. How much will eleven pounds of butter borne to
at 8j cents per pound? Ans. 91$ cents.
14. What wilf 84 pounds of lard come to at ten cents
per pound? Ans. $8 40 cents.
1.5. How much will two thousand books come to at
20 cents per book? Ans. $400.
16. What cost 789 pounds of iron at 4$ cents per lb.?
Ans. $35 50$ cents.
17. What cost 40 bushels of rye, at 20 cts. per bush¬
el? Ans. $8.
18. What will 6 pounds of soap come to at ten cents
per pound? Ans. 60 cents.
When it is required to know how many articles may
be bought with any sum of money.
RULE.
Divide the sum by the price of one article; have the
dividend and divisor of one denomination. The quo¬
tient will be the number of articles.
EXAMPLES.
1. How many pounds of butter may be bought with
$1 60 cents, at 8 cents per pound?
2. How many pounds of iron can I buy with $7 00
cents, at 3$ cents per pound?
price of 1 article. 8)1 60 3$ 7 00
—— 2 2
Ans. 20 lbs.
halves. 7) 14 00 halves.
Ans. 200 pounds.
3. When one pound of sugar costs 12$ cents, how
many pounds may be had for 30 dollars.
Ans. 240 pounds.
4. A gentleman gave his son 60 dollars, which he
hule of two.
65
was to lay out for tea at 37£ cents per pound. How
many pounds did he buy? Ans. 160 pounds.
5. How mahy bushels of corn can I buy for 400 dol¬
lars, if I give113 cents per bushel?
Ans. 3076bu. 3pe. 5qt. lpt.-f-
6. When I can buy one poutid of tobacco for 25
cents, how many pounds can I buy for $75?
Ans. 1800 pounds.
7. How many pounds of iron may be bought with
87 dollars at 4 cents per pound? Ans. 925 pounds.
8. Having $378 10 cents, and wishing to purchase
feathers, what quantity can I purchase at 33£ cents per
pound? Ans. 1134i pound+.
9. If sixty dollars be the price of an acre of land,
how many acres can I have for $192 60 cts?
Ans. 3a. Or. 33p-f.
10. Suppose a man has $1900 06£ cents, and is desi¬
rous to purchase salt. How many bushels can he buy
at 1 dollar 62^ cents? Ans. 11691 bu.-f-.
11. How many pounds of coffee at 22 cents per
pound can I have for 22 dollars? Ans, 100 pounds.
12. HoW mapy pounds of pork at three cents per
pound can I have for 960 dollars 60 cents?
Ans. 32020 pounds.
13. How many yards of cloth at 15 cents per yard
can I have for 450 dollars 45 cts? Ans. 3003 yards.
14. IIow many fowls at 6} cents each can I buy fpr
ninety dollars? Ans. 1440 fowls.
When a number of articles cost any sum of money,
and the price of one article is required at the same rate.
bulb.
Divide the whole cost by the number of articles; the
quotient will be the price of one article.
note.—If the dividend be not large enough to contain the
divisor, reduce it till it will be.
66
BULK Off TWO.
EXAMPLES.
1. 100 bushels of corn cost 12 dollars 50 cents,
what is the price of one bushel at the same rate?
2. If 4£ pounds of pepper cost $2 00 cents, what cost
one pound at the same rate?
The articles. 10|0 12 5|0 4| 2 00
2 2
Ans. 12i cts.
9) 4 00
Ansi 44cts. 4m-f-
3. If 6 fish cost 50 cts. what will one cost?
Ans. 8§ cents.
4. If I buy 40 bushels of flax seed for 40 dollars 40
cents, how much do I give per bushel?
Ans. SI 01 cent.
5. A man travelled 420 miles in twelve days. How
far did he travel each day? Ans. 35 miles.
6. Bought 120 pair of shoes for 400 dollars 60 cents.
What was the cost of one pair? Ans. $3 33| cts.
7. Bought 6000 gallons of whiskey for nine hundred
dollars. What was the price of one gallon?
Ans. 15 eents.
8. If I buy 1517$ acres of land for 7500 dollars 37 i
eents, how much does it cost me per acre?
Ans. $4 94iets.+.
9. A merchant bought 1950 pen-knives for 960 dol¬
lars 441 cents. What did one cost. Ans. 49£cts.-K
10. If I buy 22i yards of cloth with 7 dollars 50
oents, what cost one yard? Ans. 33£ cents.
11. I was offered 2000 books for $500 00 cents. Tell
me what one book would cost at that rate?
Ans. 25 cents.
12. I was offered 2000 books for $380 50 cents. How
much was that for one book? Ans. 19 cents.-f-
13. When a man's yearly income is $474 50 cents,
how much is it per day? Ans. $1 30 cents.
RULE OE THREE
67
14, If seven months' work bring* $25 00 cents, how
much will one month bring? Ans. $3 57 cents.-f-
15. Suppose the President of the United States re¬
ceive $25000 00 cents a year, how much is,that per
day? Ans. $68 49 cts. 3m.-f-
PROFORTIOX; or RULE OF THREE.
The Rule of Three is that in which three terms are
given to find a fourth or answer.
rule.
Set that term in the third place which is the same
kind of the answer. Consider from the nature of the
question whether the answer ought to be greater or
less than this third term. If it is to be greater, set the
greater of the two remaining terms in the middle for
the second, and the less for the first; but if it is to be
less, ^et the less of those two terms in the middle for
the second term, and the other for the first. Then have
the first and second terms of one denomination. If
the third term consist of several denominations, re¬
duce it to the lowest denomination in it; then multiply
the second and third terms together, and divide the
product by the first term. The answer will be of the
same denomination as the third term.
Note.—The operation may frequently ba performed, thus:
If the first term will divide the second by the quotient, multi¬
ply the third; or if the second will divide the first by the quo¬
tient, divide the third term.
examples.
1, If four bushels of corn cost 80 cents, how* much will 8
bushels cost?
2. If three yards of cloth cost fifty cents, how much will tea
yards cost?
68
RULE OP THREE.
ba; bu. cts.
4 : : 8 : 80
2
Ans. $1 60
vd. yd. cts.
"3 : 10 : : 50
' 10
3 | 500
^vAns. $1 66f
3. If four yards of muslin cost six cents, what will eight
cost? Ans. 12 cents.
4. If six yards of cloth cost 17 cents, what will seven yards
come to at the same rate? Ans. 19 cents 8m.-j-
5. If five bushels of potatoes cost 80 cents; what Cost 14
bushels at the same rate? Ans. $2 24 cents.
6. If four bushels of corn cost $2 00 cents, how much will
12 bushels cost at the same rate? Ans. $6 00 cents.
7. If eight yards of silk cost 40 cents, how much will 16
yards cost? Ans. 80 cents.
8. If three pounds of cheese cost 10 cents, what will 80
pounds come to at the same rate? Ans. $2 66-fcts.
9. If 6 pounds of coffee cost 55 cents, what will 75 pounds
come to at the same rate? Ans. $6 87^ cts.
10. If 2$ bushels of salt cost $4 08 cents, how much will 15£
bushels come to at the same rate' Ans. $24 88| cts.
11. Bought 24 pounds of beef for $1 62£ cents, how1 much
is 90^ pounds worth at that rate? Ans. $6 12£ cts. 4-
12. What are 60 bushels of apples worth, when 13 bushels
cost 45 cents' Ans, 2 dollars 07$ cts.-f-
13. If 8 bushels of potatoes cost 3 dollars 94 cts. what will
105 bushels cost' Ans. 51 dollars rivets.
14. If 45 cents buy 11 pounds of tobacco, how much will
91$ cents buy at that rate? Ans. 22£lb.-f-
15. What will 22 books come to, if 60 cost 20 dollars 51cts?
Ans. 7 dollars 52 cts.-f-
16. If 1 yard 2 quarters of cloth cost 56£ cents, what will
17 yards 1 quarter cost? Ans. 6 dollars 46| cts.-f-
17. If 4 dollars will pay for 16 days work, how' many days
work may be had for 98 dollars? Ans. 392 days.
18. If 23 bushels of salt cost 2 dollars 62£ cents, how many
bushels may be had for 556 dollars 18J cents? Ans. 529fbu.-f-
19- If 7 pounds of coffee cost 87^ cents, what must I pay
for 244 pounds? Ans. 30 dollars 50 Qts.
RULE Of THREE.
69
20. If 450 barrels of flour cost 1350 dollars, what will 8 bar.
rels cost? Ans. 24 dollars.
21. If 750 men require 22500 rations of bread for a month,
what will a garrison of 1200 require? Ans. 36000 rations.
22. If 12 men can do a piece of work in 20 days, in what
time will 18 men do it? Ans. 13£ days,
23. What will be the cost of 17 tons of lead, if 5 tons cost
500 dollars? Ans. 1700 dollars.
24. If a pasture be sufficient for 3000 horses 18 days, "how
long will it be sufficient for 2000? Ans. 27 days.
25. If 8 men can build a tower in 12 days, in what time can
12 do it? Ans. 8 days.
26. How much carpeting that is 1£ yards in breadth, will
cover a floor that is 1\ yards in length, and 5 yards in breadth?
Ans. 25yd.
27* How many yards of matting, feet broad, will cover a
floor that is 27 feet long and 20 feet broad? Ans, 72yd.
28. What must bethelength ofa board that is 9 inches in width,
to make a surface of 144 inches or a square foot? Ans. 16in„
29. If 5 yards of cloth cost 1 dollar 12£ cents, what is the
value of 4 pieces, each containing 8 yards and 1 quarter?
Ans. 7 dollars 42£ cts.
30. If 1§ ounces of spice cost 13 cents, what cost 16 \ ounc¬
es? Ans. .1 dollar 40£ cts.-f-
31. If 100 skeins of silk fcost 25 dollars 21 cts. how many
may be bought for 1800 dollars 50 cts? Ans. 7141 skeins.-f-
32. If 2 dollars 50 cts. pay for 2 weeks boarding, how long
can I board for 40 dollars 40 cents? Ans. 32w. 2da.-|-
33. Suppose A -hired to B 12 months for 60 dollars, after
working 7 months B agreed to pay A at that rate, what must
he pay? Ans. 35 dollars.
34. If lcwt. of sugar cost 11 dollars 3 7\ cts., what will 18cwt,
3qr. 191b. cost? Ans. 215 dollars 21 cts.-J-lOJ
35. How many men will it require to repair a piece of work
in 50 days, when 14 men can do it in 100 days? Ans. 28 men.
36. In what time will 600 dollars gain the interest which SO
dollars would gain in 15 years? Ans. 2 years.
37. If 2 yards of tape cost 50 cents, what will 54 English
ells 3qr. cost at the same rate? Ans. 1J dollars ets.
38. If the price of 1 acre of land be 5 dollars 25 cts. what
Will 350 acres 1 rood 18 perches come to at that rate?
Ans. 1839 dollars 40 cts. 3m .-f.
70 RULE OP THREE.
Note.—In all cases wherein labor Is required to be perform¬
ed, the day must be reckoned at 12 hours.
39. Suppose 20 days be required for 12 men to build a house,
ia what time can 18 men do the same? Ans. 13da- 4hr.
40. In what time will 48 men make a fence which 12 men
can do in 24 days? Ans. 6da.
41. If 6 men can do a piece of work in 18 days, how long
will it require 12 men to do it? Ans. 9da.
42. If 8 men can mow a piece of meadow in 24 days, how
many men can do it in 4 days? Ans. 48 men.
43. If a traveller perform a, journey in 5 days when the days
are 11 hours long, how long will he require to do it when the
days are 15 hours long? Ans. 3da. 8hr.
44. How many yards of paper 2$ feet wide will be required
'to cover a wall which is 12 feet long and 9 feet high?
Ans. 14yd. 1ft. 2in.-j^
45. What quantity oflinen that is 3 quarters of a yard wide,
will line 7$ yards of cloth that is 1$ yards wide? Ans. 15yds.
46. A ship's crew consisting of 45 men are provided with
4500 pounds of bread, of which each man eats one pound per
day; how many weeks will it last them? Ans. 14w. 2da.
PROMISCUOUS EXAMPLES,
IN THE RULE OF TWO AND THREE.
47. If 7 oxen be worth 10 cows, how many cows will
21 oxen be worth? Ans. 30 rows.
48. If board for one year amount to 182 dollars,
what will 39 weeks come to? Ans. $136 50cts.
49. If 30 bushels of rye be bought for 120 bushels of
potatoes, how many bushels of rye can be bought for
600 bushels of potatoes? Ans. 150bu. rye.
50. A farmer made 146 barrels of cider, which he
afterwards sold at 3 dollars 12$ cts. a barrel; what was
the amount of the whole? Ans. 456 dollars 25cts.
■ 51. A lady purchased a set of silver weighing 51b.
6oz. 5dwt. at 1 dollar 50cts. an ounce; what was the cost
of the whole? Ans. $99 37$ cts,
52. A lady intending to make a bed-quilt containing
6 square yards, desired her daughter to inform her how
RULE OF THREE.
71
much domestic, & quarters of a yard wide, would be
required to line the same. How many did it take?
Ans. 8yd.
53. A pipe will drain off* a cistern of water in 13
hours. How many pipes of the same size will empty
it in 30 minutes? Ans. 24 pipes.
54. A gentleman bought a bag of coffee for his own
use, weighing 1271b., for which he gave 15 dollars 25
eents. What was it a pound? Ans. 12cts.-4~
55. If a man spend 4 dollars62^ cents each day, how
much will that amount to in a year?
Ans. $1688 12£cts.
56. I lent my friend 359 dollars for five months, he
promising to do me the same favor, but when request¬
ed he could spare only 125 dollars. How long ought I
to keep it to balance the favor?
Ans. 14 months.
57. If a person's income be 10C0 dollars a year, how
much can he save provided he spends $1 50 cents each
day? Ans. 452 dollars 50 cts.
58. If the third of six be three, what may one fourth
of twenty be? As 2 : 5 : : 3 Ans. 7£.
59. If 30 days tuition cost 3 dollars 50 cents, how
much is one day worth at that rate? Ans. llfets.
60. How many planks 6 inches wide and 12 feet long
will it require to lay a floor that is 18 feet wide and 24
feet long? Ans. 72 planks.
61. A certain boat is 80 feet long and 18 feet wide. I
demand the number of planks required to fioo^ it, 13
feet long andi foot 3 inches wide? Ans. *S8H-
Notb.—The diameter of a circle given to find the circum¬
ference. State if 7 give 22 what will the diameter give. Or
the circumference given to find the diameter. As 22: is to 7,
so is the circumference.
62. If a wheel be 20 feet in diameter, what is its cir¬
cumference? 7 : 20 : : 22 (Ans. 624
63. If a wheel be 60 feet in circumference what is its
diameter? 22 : 60 : : 7 (Ans. 19-f-
7 2
DOUBLE RULE OF THREE.
ROUBLE RUEE OF THREE.
Double Rule of Three is that in which five terms are
given to find the sixth or answer.
RULE.
That which is the principal cause of gain, loss or
action, is the first term. Space of time or distance of
place the second. The gain, loss or the action, the
third. Then place the other two terms under those of
the same name. If the blank fall under the third term,
multiply the first and second terms together for a di¬
visor; the other three for a dividend. But if the blank
fall under the first or second terms, multiply the third
and fourth terms together for a divisor; the other three
for a dividend. The answer will be of the same de¬
nomination as the blank term.
Xotb.—If the blank Fall under the third term, it is direct
proportion.—If under the first or second, inverse proportion.
EXAMPLES.
1. If f> men in 10 days mow 60 acres of grass, hotfr
long will it take 5 men to mow 80 acres.
2. If 7men can reap 84 acres of wheat in 12 days,
how many men can reap 100 acres in 5 days? *
men
300
men. da.
7 : 12
5
84
5
.A
: 84
100
12
1200
7
3|00)48|00
Ans. 16 days.
42|0) 840)0( Ans. 20men,
84
DOUBLE RULE OP THREE.
73
3. If 4 men in 8 days eat 51b. of bread, bow much
will 12 men eat in 20 days? Ans, 37^1b.
4. Suppose 4 men mow 48 acres in 12 days, how
many acres can 8 men mow in 16 days? Ans. 128a.
5. If $100 gain $6 in twelve months, what will $400
gain in 9 months? Ans. 18 dollars.
6. If 8 men in 16 days can earn 96dollars, how much
can 12 men earn in 26 days? Ans. 234 dollars.
7. If ten men in 18 days can earn 56 dollars, how
many dollars can 20 men earn in 35 dgys?
Ans. $217 77cts, 7m.+
8. Suppose 8 men can make 120 pair of shoes in 30
days, how many can 12 men make in 90 days?
Ans. 540 pair.
9. If 56 dollars 31i cts. be the wages of 20 men for
5 days, what will 48 men earn in 32 days?
Ans. $828 92 cts.
10. If 100 dollars in a year give 6 dollars interest,
what will 335 dollars give in 3 years?
Ans. 60 dollars 30 cts.
11. When 10 oxen in 18 days eat 2 acres of grass,
how many acres will serve 20 oxen 27 days?
Ans. 6 acres.
12. Suppose the wages of 6 persons for 2t weeks
be 288 dollars, what must 14 persons receive for 46
weeks? Ans. 1472 dollars.
13. If 371b. of beef be sufficient for 12 persons 4
days, how many pounds will suffice 38 men 16 days?
Ans. 468 lb. IO^oe.
14. If 30 horses in 4 days eat 40 bushels of corn, how
many bushels will suffice 100 horses 20 days?
Ans. 666$bu.
15. If the carriage of 9cwt. 45 miles, cost 54 dollars
51 cents, how far may 36cwt. be carried for 98 dollars
72 cts? Ans. 20m. 2fur 36p.-f-
16. If 100 dollars in 12 months gain 6 dollars inter¬
est, what will be the interest of 400 dollars for 14
months? Ans. 28 dollars.
r
74
DOUBLE RULE OF THREE".
17. If 100 dollars in 12 months gain 8 dollars inter¬
est, what sum will gain 50 dollars in 24 months?
Ans. 312 dollars 50 cts.
18. If 100 dollars in 365 days gain 6 dollars interest,
what will be the interest of 1000 dollars for 27 days?
Ans. 4 dollars 44 els. nearly.
19. If 100 dollars in 52 weeks gain 10 dollars inter¬
est, what will be the interest of 75 dollars for 7 weeks?
Ans. 1 dollar COJct.
20. If 12 bushels of oats be sufficient for 20 horses
22 days, how many bushels will serve 62 horses 36 days?
Ans. 60bu. 3pe. 3qt. lpt.-f-
21. When 4 boys in 20 days, collect 1500 bushels of
apples, how many days will it require 25 persons to
eollect4000 bushqls? Ans. 8days.+
22. What is the interest of 563 dollars for 4| years,
at 6 per cent per annum? Ans. 152 dollars Olct.
23. What will be the interest of 80 dollars for 10
months at 10 per cent? Ans 6 dollars 66f cts.
24. If 100 dollars in 12 months gain 33 dollars 33j cts
what will be the interest ol*64" dollars for 84 months?
Ans. 13 dollars 11 cts.-f
25. If 100 dollars in one year gain 7 dollars 50 cents
interest, what sum will gain 9 dollars in 4 months?
Ans. 360 dollars.
20. What is the interest of 19 dollars for 5} months,
at6 percent? Ans. 49J cts.-j-
27. What sum at 6 per cent will produce 500 dollars
interest in one year? Ans. 8333j dollars.
28. A gentleman said the money he had on interest
at6 percent, produced one dollar per day. What sum
had he on interest? Ans. 6083£ dollars.
29. With how many dollars could I gain 6 dollars in
one year, if with 560 dollars I gain 56 dollars In one
year and 8 months? Ans. 100 dollars.
30. A wall which is to be built to the height of 40
feet has been raised 20 feet in 10 days by 16 men, how
many men must be employed to finish the work in 5
days? Ans. 33 men.
PRACTICE.
practice;
Practice is a short method of ascertaining the value
of any number of articles at? any given price per arti¬
cle.
TABLE OF ALIQUOT PARTS.
qr. ' lb. cwt.
2 or 56 =
28
i
~5
16
1
T
o
14
X
"8
SO
* a
8
1
1 4
3
1
1
l s
*
Case 1.
When the price is i, j, j, -§, or £ of a cent per arti¬
cle, pound, yard, acre, bushel, &c,
Rule.
Divide (h^ gi ven sum or quantity by the aliquot parte
of a cent for the answer in cents.
EXAMPLES.
1; What is the value of 124 apples at i of a cent
each?
76 PRACTICE.
2. What is the value of 1260 peaches at i cent each?
i | * J 124 } | i | 1260
Ans. 31 cts. Ans. $6 30 cts.
3. What i& the value of 192 plums at | of a cent
each? Ans. #1 44 cts.
4. What is the value of 24 quills at g of a cent each?
Ans. Scents.
5. What is the value of 12 cherries at § of a cent?
Ans. 8 cents.
6. How much will 29 come to at £ of a cent each?
Ans. 7£ cents.
7. How much will 11 come to at | of a cent each?
Ans. Si cents.
8. What is the value of 19 at $ cent each?
Ans. 9£ cents.
9. What is the value of 20 at 2 mills each?
Ans. 4 cents.
10. What is the value of 40 at 5 mills each?
Ans. 20 cents.
11. What is the value of 30 at 1 mill each?
Ans. 3 cents.
Case 2.
When the given price is cents:
rule.
Divide the given sum by the aliquot parts of a dollar
for the answer in dollars.
examples.
1. What is the value of 3216 at 6i cents?
2. What is the value of SG20 at 10 cents?
6*
3216(Ans. $201. 10 I | 8620
Ans.
16
16
PRACTICE.
77
*
cts.
m.
3.
What is the value of 4260
at 20 cts.
Ans. 852
00
0
4.
8264
20
1652
80
0
5.
4264
12^
533
00
0
6.
5876
50
2938
00
0
7.
386
25
96
50
0
8.
18626
55.
10244
30
0
9.
3542
45
1593
90
0
10.
1724
374
646
50
0
n.
31925
80
25540
00
0
12.
3654
18f
685
12
5
IS.
13854
564
7792
87
5
C^SE 3.
When the given price is dollars and cents.
Rule.
Multiply the given sum by the dollars, and take parts
for the cents, and add the products together for the an¬
swer in dollars.
examples.
1. What is the value of 420 bushels of wheat at 1
dollar 20 cents per bushel?
20
A I 420
1
420
84
| 504 dollars.
$
cts.
$
cts.
m.
2. What is the value of 2412 a
.t 2
064 Ans.
4974
75
0
3. 1224
3
m
3825
00
0
4. 870
1
18£
1033
12
5
5. 197
4
20
827
40
0
6. 162
2
25
364
50
0
7, 217
5
3 7i
1166
37
5
8. 1228
7,
62*
9.363
50
0
7 8
PRACTICE.
Case 4.
When the given sum consists of several denomina¬
tions, such as yd. qr. na. &c.
Rule.
Set down the given price of one of the highest de¬
nomination, and multiply it by the whole of the highest
denomination given; then take aliquot parts of the
next lowest denomination, continually, and add the
products together for the answer.
examples.
1. What is the value of lOcwt. 2qr. 71b. at $10 25
•ents per cwt.
qr.
2
lb.
7
$ cts.
10 25
10 cwt.
102 50
5 12i
64
Ans. $108 26£cts.-f-
2. Whatisthe value of5cwt.lqr. 141b. at2 dollars
50 cts. per cwt? Ans. $13 43£ cents.
3. What is the value of 7cwt. 3qr. 191b. at 4 dollars
15 cts. per cwt? Ans. $32 86£ cents.
4. What is the value of 7S0bu. 3pe. 2qt. at 1 dollar
17cts. per bushel? Ans. $913 55 cents .+
5. What is the value of 129cwt. lqr. 10 lb. at 1 dollar
5 cents per cwt? Ans. $135 80 6m.-|-
6. What is the value of25cwt. lqr. 9 lb. at 1 dollar
75 cents per cwt? Ans. $44 32cts.-f-
7. What is the value of 2qr. 14 lb. at $27 lOcts. per
cwt? Ans. $16 93|cts.
8. What is the value of 12cwt. 3qr. at $40 20 cents
per cwt? Ans. $512 55 cents.
interest-.
79
9. What is the value of J9bu. lpe. of corn at Oocts-
per bushel? Ans. 6 dollars 73^! cents.
10. What is the value of 816 ounces 13d wt. 12gr. at
12J cents per ounce? Ans. 162 dollars 84 cents.
11. What is the value of 27yds. 3qr. at $9 65cts. per
yard? Ans. 267 dollars 7Scts. 7m.
12. What is the value of 860yds lqr. at 84 cents per
yard? Ans. 723 dollars 61 cents.
13. What is the value of 126yds. 2qr. 2na. at 4 dol¬
lars 75 cents per yard? Ans. 601 dollars 46cts. 8m.-f-
14. What is the value of 17hhd. logal. 3qt, at 64
dollars 75 cents per hhd?
Ans. 1116 dollars 93 cents 7m.
IUTTJEEEST.
Interest is a consideration allowed for the use of mo¬
ney, relative to which are 4 particulars, via: Princi¬
pal, Time, Kate per Cent and Amount. The princi¬
pal is the money for which interest is to be received;
the rate per cent per annum is the interest of 100 dol¬
lars for one year; the time is the number ofyears or
months, &,c. for which interest is to be calculated; the
amount is the principal and interest added together.
Case 1.
To find the interest for any, number of years, or
years and months.
rui-e.
Multiply the principal, consisting of dollars, by the
rate per cent, and that product by the number of years;
or if there be months, take aliquot parts of a year,
cut off two figures on the right ofthe product for cents;
or if there be cents in the principal, cut off one figure
on the right as a remainder; one more for mills; two
more for cents; those on the left will be dollars.
80
INTEREST.
Case 2.
To find the interestfor any number of months.
rule.
Find the interest at 6 per cent by multiplying the
principal by half the number of months; or at any
other per cent, find the interest at 6; then state if 6
give that interest, what will the per cent you wish to
calculate give, and cut off" figures in the product for
cents, as in Case 1st.
Case 3.
To find the interest for any number of days.
rule.
Multiply the principal by the number of days; divide
the product by 6, the quotient will be the interest in
mills at 6 per cent. If the principal consist of dollars
and cents, destroy 2 figures on the right of the product;
the balance will be the interest as before. If any other
per cent is required, take aliquot parts and add or sub¬
tract, according as the per centis more or less than 6.
Note.—Case 3rd is estimating 360 days in a year, which will
make the interest rather large? it may be more accurately
found by multiplying the principal by the number of days, and
dividing the product by a proper divisor in the following table,
which divisors are found by the following stating:
per cent. $ da. per cent $ da.
Thus: 4 ; 100 ; : 365 Again, thus: 5 : 100 : : 365
per cent. Divisors. Rate per cent. Divisors.
14
9125
I7
5214
h*
8111
1 n
4866
?
7300
8
4562
5i
6636
8i
4294
6
6083
9
4055
5615
n
3842
0
0000
10
3650
INTEREST.
81
A divisor may also be found for weeks or months,
by using 52 weeks or 12 months in room of365 days.
Case 1.
examples.
1. What is the interest of $500 fori year, at 6 per
eent per annum?
2. What is the interest of 40 dollars 50 cents for on©
year and six months, at six per cent per annum?
500
6
Ans. $30|00cts.
months.
6
$ cts,
40 50
6
243 00
1
243 00
121 50
Ans. 83 64cls. 5m.
3. What is the interest of 400 dollars for one year at
six per eent? Ans. 24 dollars.
4. What is the interest of 600 dollars for one year at
six per cent per annbm? Ans. 36 dollars.
5. What is the interest of250 dollars for one year at
five per cent? Ans. 12 dollars 50 cents.
6. What is the interest of 51 dollars for one year at
six per cent? Ans. 3 dollars 6 cents.
7. What is the interest of44 dollars for two years at
•even per cent per annum? Ans. 6 dollars I6cts.
8. What is the interest of 90 dollars for three years
at five per cent? Ans. 13 dollars 50 cents.
9. What is the interest of 68 dollars for four years
at four per cent? Ans. 10 dollars 88 cents.
10. What is the interest of 1000 dollars for four
years at eight per cent? Ans. 320 dollars.
11. What is the interest of 50 dollars for five years
at five per cent? Ans. 12 dollars 50 cents.
INTEREST.
12. What is the interest of 19 dollars for two years
at four per cent? Ans. 1 dollar 52 cents.
13. What will be the interest of 1772 dollars for two
years at six per cent? Ans. 212 dollars 64 cents.
14. How much interest will 75 dollars draw in five
years at4} percent? Ans. 16 dollars 87^ cents.
15. What is the interest of 100 dollars for two years
and six months at 6'per cent per annum?
Ans. 15 dollars.
16. What will be the interest of 350 dollars for three
years and four months at 6 per cent per annum?
Ans. 70 dollars.
17. What will be the interest of 48 dollars for four
years and one month at 5 per cent per annum?
Ans. 9 dollars 80 cents.
18. What is the interest of 64 dollars for one year
and seven months at 7 per cent per annum?
Ans. 7 dollars 9§ cents.
19. What is the interest of 14 dollars for four years
and 11 months at 7 per cent? Ans. 4 dollars 81£ cts.
Cash 2.
examples.
1. What is the interest of 40 dollars for four months
at 6 per cent per ahnum? Ans. 80 cents.
2. What is the interest of 60 dollars for 6 months at
eight per cent per annum? Ans, 2 dollars 40 cts.
dt>
tjp qp
40
60
2
3
SO cents.
6:8:
: 180
8
6;l440
$2 40
IUTEREStf.
89
-3. What is the interest of 18 dollars for six month®
at six per cent per annum? Ans. $0 54 cents.
4. What is the interest of 50 dollars for eight month®
at seven per cent per annum? Ans. $2 33$ cts.
5. What is the interest of $900 for five months at five
per cent per annum? Ans. 18 dollars 75 cents.
6. What is the interest of 91 dollars 50 cents for four
months at 4 per cent? Ans. 1 dollar 22 cents.
7. What is the interest of,|80 dollars for five months
at seven per cent? Ans. 2 dollars 33$ cents.
Note.—When the amount is required add the interest to the
principal.
8. What is the jamount of $62 50 cents for thirteen
months at 6 per cent per annum? Ans. $66 56bts. 2m.
9. What is the interest of $75 for fourteen months at
six percent? Ans. 5 dollars 25 cents.
10. What is the interest of 5 dollars 50 cents for 5$-
months at"six percent? , Ans. 15 cents.-j-
Note.—In this case after finding-the interest a* six per cent
if any other rate per cent be required, take aliquot parts and
add or subtract, according as the rate per cent is more or less
than six.
11. What is the interest of 80 dollars for eight months
at five per cent?
19. What is the interest of 60 dollars for four months
at eight per cent?
6 per.
$ per.
Ans.
80
4
320 int. at 6 perct,
534
2 U
60
.2
20 int. at 6 per ct.
40
$1 60 cents.
84
INTEREST,
13. What is the interest of 120 dollars 60 cents for
fifteen months at 6 per cent? Ans. 9 dollars 4 cts. 5 m.
14. What"is the interest of 5420 dollars for 17 months
at 4 per cent per annum? Ans.'307 dollars 13? cts.
15. What is the interest of7200 dollars for 14 months
at6 per cent per annum? Ans. 504 dollars.
16. What is the interest of 8050 dollars 87^ cents for
47 months at 6 percent per annum?
Ans. 1891 dollars 95 cts. 5m.
17. What is the interest of 948 dollars 62^ cents for
eight months at 8 per cent per annum?
Ans. 50 dollars 59 cents.-f-
18. What is the interest of 36 dollars for one month
at 8 per cent per annum? Ans. 24 cents.
19. What is the interest of 1000 dollars for 40 months
at 6 per> cent per annum? Ans. 200 dollars.
20. What is the interest of 328 dollars for 12 months
at 6 per cent? - Ans. 19 dollars 68 cents.
When there is si fraction in the rate per cent, as 5|, 6£, or
6|, multiply and add i or $, (as the ease maybe,') of the prin¬
cipal to the product, and proceed as before.
21. What will be the interest of 540 dollars for 24;
months at 5 per cent per annum? Ans. 54 dollars
22. What would be the interest of 482 dollars for 84
months at 6 dollars per cent per annum?
Ans. 202 dollars 44 cts.
23. What is the interest of 325 dollars for 50 months-
at 4 per cent per annum? Ans. $54 16 cents 6m.
24. What is the interest of 840 dollars for 63 months
at 4 per cent per annum? Ans. $176 40 cents.
25. What is the interest of 840 dollars for 64 months
at 7 per cent per annum? Ans. $313 60 cents.
26. What is the interest of 560 dollars for 4 months
at six per cent per annum? Ans. $11.20 cents.
27. What is the interest and amount of 100 dollars
for ten months at ten per cent per annnm?
Answer 5 ® 8 ^ interest.
Answer, j ^1Q3 33,
INTEREST.
85
28. What is the amount of 76 dollars 25 cents for
25 months at 6 per cent jier annum?
Ans. $85 78cts.
CASE 8.
Xotb.—Multiply any principal by the rate per cent, and
that product by the number of days it bas been on interest,
and diride the last product by 365. The quotient will be the
intereat
EXAMPLES.
1. What is the interest of 1000 dollars for five days
at 6 per cent per annum? Ans. 83 cents 3m.-f-
2. What is the interest of 500 dollars for 60 days at
8 per cent per annum? Ans. $6 66cts. 6m.+
6)5000 6)30000
83|3i 2 I i 5000
I 1666|
6|66|6f
8. What is the interest of 400 dollars for 40 days at
8 per cent per annum? Ans. $2 66cts. 6m.-(-
4. What is the interest of 900 dollars for fourteen
days at 6 per cent? Ans. $2 10 cents.
5. What is the interest of 1000 dollars for 4 days at
8 per cent? Ans. 66f cents.
6. What is the interest of 500 dollars for one day at
6 per cent? Ans. 8 cents 3m.+
7. What is the interest of 16 dollars 33| cents for 24
days at 6 per cent? Ans. 6 cents 5m.+
8. What is the interest of 64 dollars 64 cents for 18
days at 6 per cent per annum? Ans. 19 cents 3m.
S6
INTEREST.
9. What is the interest of 45 dollars for 22 days at
per cent per annum? Ans. 15 cents.-+-
10. What is the interest of 90 dollars for 51 days at
8 per cent per annum? Ans. 1 dollar 2 cents.
Note.—When the time is years, months and days, proceed
•with die years and months as in Case 1st, and for the days
take aliquot parts of 30.
11. What is the interest of 50 dollars for 1 year, 2
months, and 5 days, at 6 per cent per annum?
Ans. S3 54 cents.
12. What is the interest of 100 dollars for one year,
7 months and 11 dpys, at 6 per cent?
Ans. $9 68 cents.-jr
13. What is the interest of 21 dollars for 4 years, 4
months, and 4 days, at 5 per cent?
Ans. $1 56 cents.-f-
14. What is the interest of 5 dollars for 10 years, 3
months and 19 days, at 6 per cfent?
Ans. $3 09 cents.-f-
15. WThat is the interest of 5 dollars 87$ cents for 9
months and 24 days, at 6 per pent per annum?'
Ans. 28 cents. 7m.4-
Case 4.
The amount, time and rate per cent given to find, the
principal.
atrhKv
Find the amount of 100 dollars at the rate per cent
and time given, which amount is the first term; the
given sum the 2d; 100 dollars the 3d; proceed by the
rule of three; the quotient will be the principal required.
examples.
1. What principal at interest for 8 years at 5 pec
cent will amount to 840 dollars?.
INTEREST.
87
100
5
$
14Q : 840 : : 100
100
500
14|0)8400|0(Ans.f600.
84
8
00
Interest. 40|00
100
Amount. 140
2. What principal at interestfor5yearS atdpereent
per annum will amount to 650dollars? Ans. $500
8. What principal at interest for 5 years at 6 percent
pea- annum will amouqtto 3470 dollars? Ans. $1900
Case 5.
■To fine1! the rate per cent when the amount, time and
principal are given.
Subtract the principal from the amount; then state
if the principal give the interest or remainder, what
will 100 dollars give. Divide the answer by the num¬
ber of years; the quotient will be the rate per cent.
1. At what rate per cent per annum will $500 amount
to $850 in five years!
rule.
$
$
$
Amount. 650
Principal. 500
500. 100 :': 150.
150
150 interest.. 5000
100
5|00)150|00>
Years. 5)30
Ana* 6 per cent..
88
IXTERKST.
S. At what rate per cent will 600 dollars amount to
$744 in four years? Ans. 6 per cent.
3. If 834 dollars at interest 2 years and 6 months
amount to §927 82£cts. what was the rate per cent per
annum.7 Ans. 4$ per cent.
Case 6.
To find the time when the principal amount and rate
per cent are given.
rule.
Divide the whole interest by the interest of the prin¬
cipal for one year. The quotient will be the time re¬
quired.
1. In what time will 400 dollars amount to 520 dol¬
lars at 5 per cent per annum?
400 520
5 400
20|00 2|0)12|0
Ans. 6 years.
8. In what time'will 600 dollars amount to 798 at
6 per cent per annum? Ans. 5£ years.
3. Suppose 1000 dollars at 4$ per cent per annum
amount to 1281 dollars 25 cts., how long was it at inter¬
est? Ans. 6 years 3 months.
promiscuous examples.
1. What is the interest of500 dollars for one year and
2 months at 6 per cent? Ans 35 dollar*.
2. What is the interest of450 dollars for 2 years and
6 months at 5 per cent per annum?
Ans. 56 dollars 25 ct*.
8. What is the interest of 65 dollars 87Jr cts. for 9
months at 6 per eent? Ans. 2 dollars 96£ cts.
4. What is the interest of 800 dollars for four years,
Insurance, commission and brokerage. 89
5 months and 19 days, at 6 per cent per annum?
Ans. 214 dollars 53 cts. 3m.+
5. What is the interest of 18 dollars 75 cts. for 1 year,
U months and 7 days, at 6 per cent per annum?
Ans. 1 dollar 33£ cents.
6. What is the interest of 90 dollars for 8 months at
9 per cent? Ans. 5 dollars 40 cts.
7. What is the interest of 6 dollars for 6 days at 6
percent? Ans. 6 mills.
8. What is the amount of* 1000 dollars 25 cts. for 4
years, 4 months and 5 days at 7£ per cent per annum?
' Ans. 1326 dollars 37 cts. 3m.+
9. In what time will 1000 dollars amount to 1500 dol¬
lars, at 8 per cent per annum? Ans. 6 years 3 months.
10. What is the interest of 25 cts. for 25 years at 6
per cent per annum? Ans..37£cts.
11. What is the interest of 87£ cents for 1 year and
6 months at 6 per cent per annum? Aris. 7 cts. 8 m.-f-
12. At what rate percent per annum will 1200 dol¬
lars amount.to 1800 dollars in 5 years? Ans. 10 per ct.
INSURANCE, COMMISSION AM®
BROKERAGE.
Brokerage is an allowance to insure factors and
brokers at a stipulated rate per cent, agreed on by the
parties concerned.
RULE.
Multiply the sum by the rate per cent. If the rate
be less than one per cent take aliquot parts.
EXAMPLES.
1. What is the commission on 500 dollars at 5 per
cent?
2. What is the commission on 400 dollars at £ dollars
per cent?
g
90
DISCOUNT.
500 J i 400
5
} i 200
Ans. $25 00 100
Ans. $3 00
3. What is the insurance of 60 dollars at 3 percent?
Ans, 1 dollar 80 cents.
4* What is the commission on 1351 dollars 50 cents
at 5£ per cent? Ans. 74 dollars 33 cents.-f-
5. The sales of certain goods amount to 1680 dol¬
lars, what sum is to be received for them, allowing 2£
per cent for commission? Ans. 1633 dollars 80 cents.
6. What is the commission on 3450 dollars at 4£ per
cent? Ans. 155 dollars 25 cents.
7. When a broker sells goods to the amount of 081
dollars 50 cents, what is his commission, at 1£ per cent?
Ans. 12 dollars30 cents 6m.+
8. What is the insurance of 1250 dollars at 7^ per
cent? Ans. 93 dollars 75 cents.
9. If a broker buys goods for me, amounting to 1650
dollars 75 cents, what sum must I pay him, allowing
1| per cent? Ans. 24 dollars 76 cents lm.-b
10. What is the commission on a sale of goods a-
mounting to 1184 dollars, at 5 per cent?
Ans. 59 dollars 20 cents.
11. What is the commission on a sale of goods a-
mounting to 4320 dollars, at 4£ per cent?
Ans. 216 dollars 90 cents.
DISCOUNT.
Discount is an allowance made for the payment of a
sum of money before it becomes due, and is the differ-
encejbetween that sum due sometime hence and its pre¬
sent worth.
DISCOUNT.
SI
RULE.
Find the interest of 100 dollars at the per cent and
time given; to this interest add 100 dollars, which h-
nount is the first term; the given sum the second;
100 dollars the third. Proceed by the Rule ot Three.
The answer will be the present worth. Subtract the
answer from the given sum, and the remainder will be
the discount.
examples.
1. What is the discount of 500 dollars for 4 years,
discount at 5 per cent per annum?
$
100
5
500
4
20|00
100
120 : 500 : : 100
100
12|0)5000|0
present worth. 416 6Gf
$ cts.
.500 00
416 66f
Discount. $83 33%
2. What is the present worth of 600 dollars due in
2 years, discount at 6 per cent per annum?
Ans. §535 71 cents 4m.+
3. What is the discount of 590 dollars for 2 years,
discount at 6 per cent per annum? Ans. $63 21£ cts.
92
DISCOUNT.
4. What is the present worth of 480 dollars due ill
4 years, at 4 per cent discount?
Ans, 413 dollars 79$ cents.+
5. What is the discount of 645 dollars for 9 months,
at 6 per cent per annum? Ans. $27 77 cents 6m.
6. What is the present worth of 580 dollars due in 8
months, discount at 6 per cent per annum?
Ans. $557 69 ccnts.-f-
7. What is the present worth of 775 dollars 50 cents,
due in 4 years, at 5 per cent per annum?
Ans. $646 25 cents.
8. Bought goods amounting to 615 dollar^ 75 cents,
at 6 months credit, how much ready money must be
paid if a discount of 4$ per cent be allowed?
Ans. $602 20 cents.
9. Bought goods amounting to 900 dollars, at 4 years
credit, how much ready money must be paid if a dis¬
count of 6 per cent be allowed?
Ans. $725 80$ cents.-|-
10. What is the discount of 90 dollars for 1 year and
6 months, at 6 per cent per annum? Ans. $7 43$ cents.
11. What is the discount of 205 dollars due in 15
months, at 7 per cent per annum? Ans. $16 49$ cts.-f-
12. A. owes B. 100 dollars due in one year, but B. a-
grees to allow A. a discount of 25 percent per annum,
for present payment. What sum will discharge the
debt? Ans. 80 dollars.
13. What is the discount of 100 dollars due in 12
months, at 25 per cent per annum? Ans. 20 dollars.
Note.—When discount is made without regard to time, it is
found precisely like the interest for one year.
14. What is the discount of 800 dollars at 6 per cent ?
15. What is the discount of 99 dollars at 5 per cent?
$ $
800
99
6
5
Ans. $48 00 discount. Ans. $4 95
TARJJ AND TRET.
93
16. What is the discount of 476 dollars, at'3 per
cent? Ans. 14 dollars 28 cents.
TARE AND TRET.
Tare and Tret are certain allowances made by mer¬
chants in selling their goods by weight. Tare is an al¬
lowance made for the Weight of the barrel, box, &c.,
that contains the commodity bought. Tret is an al¬
lowance of 4 lb. in every 104 lb. for waste, dust, &c.
Gross weight is the goods, together with the barrel,
box, or whatever contains them. When the tare is
deducted from the gross, what remains is called suttle.
Neat weight is the weight of articles after all allowan¬
ces are deducted.
RULE.
1st. Subtract the whole tare from the whole gross;
the remainder will be neat. 2nd. When the tare i^ so
much per barrel, box, &c., multiply the tare per bar¬
rel, box, &c., by the number of barrels, boxes, &c.—
The product will be the whole tare.' Subtract the
whole tare from the whole gross, and the remainder
will be neat. 3d. When the tare is so much per cwt.
run aliquot part, or parts of a cwt. through the whole
gross. Subtract the quotient therefrom, and the re¬
mainder will be neat. 4th. When tret is allowed
with tare, subtract the tare from the gross as before.
The remainder will be suttle. Divide the suttle by 26.
The quotient will be tret. Subtract the tret from the
suttle, and the remainder will be neat.
EXAMPLES.
1. What is the neat weight of a hogshead of tobac¬
co weighing 2cwt. 3qr. 251b. gross, tare in all lewt.
2qr. 12 lb.?
cwt. qr. lb.
2 3 25 gross.
1 2 12 tare.
Ans. 1 1 13 neat-
94
TARE AND TRET.
2. What is the neat weight of a hogshead of tobacco
weighing 5cwt. 2qr. 15 lb. gross, when the tare is 3qr.
71b.? Ans-4cwt. 3qr. 81b.
3. What is the neat weight of 369cwt. 2qrs. 21 lb.
gross, tare in the whole 10cwtf lqr, 12 lb.?
Ans. 359 cwt. lqr.91b.
4. What is the neat weight of 6 hogsheads of sugar,
each weighing 4dwt. lqr. 41b. gross, tare in the whole
13cwt. 3qr. 191b.?
cwt. qr. lb.
4 14
6
25 2 24 whole gross weight.
•13 3 19 whole tare.
11 3 5 neat.
5. How much is the neat weight of 7 casks of indi¬
go, each weighing 3c wt.2qr. 121b. gross, tare 25 lb. per
cask?
cwt. qr. lb. cwt. qr. 1b-
3 2 12 0 0 25
7 7
25 1 0 gross. 1 2 7 tare in all.
12 7
Ans. 23 2 21 neat.
6. What is the neat weight of 6 casks of raisins,
each weighing 3cwt. 2qr. 10 lb. gross, tare 201b. per
cask? Ans. 20cwt. lqr. 24 lb.
7. What is the neat weight of 35 kegs of figs, gross
Weight37cwt. lqr. 201b., tare per cwt. 141b.?
cwt. qr. lb.
lb. | i | 37 1 20
14 j j 4 2 20 quotient.
Ans. 32 3 00 neat.
TARE AND TRET.
95
8. What is the neat weight of 6 hogsheads of sugar,
each weighing 7cwt. 3qr. 141b. gross, tare 201b. per
cwt.? Ans.38cwt. 3qr. 71b.
9. What is the neat weight and value of 12 bags of
coffee, each 2cwt. lqr. 10 lbs. gross, tare 18 Ibi per cwt.,
tret 4 lb. per 104 lb. at 19 dollars 60 cents per cwt?
. „ $ 22evvt. 2qr. 18 lb. neat,
nswe , ^ dollars 15cts. value.
10. What is the cost of 24 casks of prunes, each
cask weighing lcwt. lqr. 23 lb. gross, tare 18 lb. per
cask, at 5 dollars 17$ cents per cwt?
A ns. $160 79cts. 4m.
11. What is the neat weight of 5 hogsheads of su¬
gar, each lOcwt. lqr. 20 lb. gross, tare 3qr. 25 lb. per
hogshead, tret 4 lb. per 104 lb.
cwt. qr. lb cwt. qr. lb.
10 1 20 0 3 25
5 5
52 0 16 gross. 4 3 13 tare.
4 3 13 tare.
Divide by 26)47 1 3 suttle.
13 7 tret quotient.
Ans. 45 1 24 neat.
To find the neat weight of Pork, established by cus¬
tom, when the gross is given.
rxtle.
Place each hundred seperately. Then subtract £ or
25from the first hundred: £ or 12$ from the second
hundred. The remainders will be neat. All over the
second hundred is neat. Add the remainders and all
over the second hundred together for the neat.
Note—£ must be taken from any number of pounds grois,
under 100 including:—£ from all over 100 pounds and under
200 including.
96 EQUATION.
EXAMPLES.
1. What is the neat of a hog weighing 181 pounds
gross?
2. What is the neat of a hog weighing 212 pounds
gross?
25 I £ I 100 12$ |$| 84 25 I $ I 100 12$ I | 1 100 12
| I 25 | | 10$ J J 25 J I 12^
75 73$ 75 87$»
73$ 87$
12
Ans. 148$ Neat.
Ans. 174$ Neat;
3. What is the neat of a hog weighing 305 pounds
gross? Ans. 267$ lb. neat.
4. What is the neat of 3 hogs weighing gross as fol¬
lows, viz: no. 1,191 lb.; no. 2, 76 lb.; no. 3, 201 lb.?
Ans. 375$ lb. neat.
5. What is the neat of 2 hogs weighing gross as fol¬
lows, viz: no. 1,219 lb.; no. 2,1X3 lb.?
Ans. 268 lbs. neat.
EQUATION.
Equation is used to find the mean time of several
payments due at different times.
RULE.
Multiply each payment by its time- Add up the sev¬
eral products, and divide the sum by the whole debt.
EXAMPLES.
1. A. owes B. 60 dollars, of which 40 dollars is to be
paid at 6 months, and 20 dollars at 3 months, but they
agree that the whole shall be paid at one time. When
must it be paid.
EQUATION*
97
$
40x6=240
20x3= 60
6|0)30|0
Ans. 5 months..
2. C. owesD. 380 dollars, of whichlOO dollars is to-
be paid at 6 months, 120 dollars at 7 months, and 160
dollars at 10 months, but they agree that the whole
shall be paid at one time. When must it be paid?
Ans. 8 months.
3. A merchant has owing to him 300 dollars, to be
paid as follows, viz: 100 dollars at 2 monlhs; 100 dol¬
lars at 4 months; 100 dollars at 6 months; but they a-
gree that the whole shall be paid at one time. When
must it be paid? Ans. 4 months.
4. A merchant has purchased goods to the amount
of 2000 dollars, of which sum 400 dollars are to be-
paid at present, 800 dollars at 6 months, and the rest
at 9 months; but it is agreed to make one payment of
the whole. When must it be paid. Ans. 6 months..
5. A. owes J. 500 dollars, which will be due four
months hence. It is agreed that 100 dollars shall be
paid now, and that the rest remain unpaid a longer
time than four months. When must it be paid?
Ans. 5 months.
6. A. owes B. 100 dollars, of which 75 dollars is to
be paid at 4 months, and 25 dollars at 2 months; but
they agree that the whole shall be paid at one time.—
When must it be paid? Ans. 3J months.
7. C. is indebted to a merchant to the amount of 2500
dollars, of which 1000 dollars is payable at the end of
4 months, 800 dollars in 8 months, and 700 dollars in
12 months; when ought payment to be made if all are
paid together? Ans, 7=2 months.-}-
6s
SARTEH.
BARTER.
Barter is the exchanging- of one commodity for an¬
other according to a certain price or value agreed on
by the parties concerned. Questions in Barter may
be solved by the Rule of Three.
When any articles at a given price per article, is to
be bartered for any other articles at a given price per
article.
RULE.
Find the value of the articles whose quantity is giv¬
en. Then find how many of the other articles may be
bought with that money.
EXAMPLES.
1. A. has 400 yards of cloth at 20 cents per yard,
for which B. is to give him books at 50 cents each.
How many books must A receive?
2. C, has 100 bushels of wheat at 75 cents per bushel,
for which D. is to give him rye at 37$ cents per bushel.
How many bushels of rye ought C. to receive?
cts. cts. yd. cts. cfs. bu.
50 : 20 : : 400 37$ : 75 : : 100
400 2 2
5|0)800|0 75 150
100
Ans. 160 Books.
75)15000(Ans. 200 bu.
150
00
3. j>I. has 500 barrels of flour at 6 dollars per bar¬
rel, for which R. is to give him salt at 1 dollar 25 cents
per bushel. How many bushels of salt ought M. to
receive? Ans. 2400 bu.
4. A.'has 20 pounds of sugar at 12$ cents per pound,
for which J. is to give him fowls at 10 cents a piece.
How many fowls ought A. to receive? Ans. 25 fowls.
BARTER.
99
5. HoW many bushels of rye at 40 cents .per bushel,
are equal to 90 bushels of wheat at 50 cts. per bushel?
Ans. 112$bu.
6. G. has 160 yards of stuff at 14 cents per yard, for
which N. agrees to give him oats at 20 cents per bush¬
el. XIow many bushels of oats ought G. to receive?
AnS. 112 bu.
7. P. sold 108 yards of calico at 10 cents per yard,
for which E. gave him 6 dollars in money and the rest
in flax-seed at 8 cents per bushel. How many bushels
of flax-seed did P, receive? Ans. 60 bu.
8. How many pounds of tea at 30 cents per pound
must be given in barter for 25 pounds of coffee at 22$
cents per pound? Ans 18f pounds.
9. A merchant has'1000 yard^ of canvass at 20 cents
per yat-d, which he is to barter for serge at 22$ cents
per yard. How many yards of serge should he receive?
Ans. 888 ±g. yards.
10. A. has sugar at 12$ cents per pound, for a quan¬
tity of which C. is to give him 450 pounds oftea, at 1
dollar per pound. How much sugar must C. receive?
Ans. 3600 pounds.
11. H. has 1000 bushels of salt atl dollar 10 cents-
per bushel; for which W. is to give him 80 gallons of
brandy at 87$ cents per gallon, and the rest in cotton
at 15 cents per pound. How many pounds of cotton
must H. recei ve? Ans. 6866$ pounds.
12. What quantity of candles at $9 50 cents per*
owt. must be given for 15cwt. Oqr. 27 lb. of tobacco at
20 cents per pound? Ans. 35cwt. 3qr. 20 Ib.-f-
13. Two persons barter—A. has 17cwt of iron, at
13$ cts. per lb.—B. has 1200 lb. of cheese at 14 dollars
per cwt.—which of them must receive money, and
how much? Ans.—A. 107 dollars 4 cents.
14. E. has 2108 lb. of bacon at 10 cents per pound,
and 31 bushels of apples at 11$ cents per bushel, which
he barters with F. thus: E. to have 135 dollars 25 cents
in money, and the rest in pork at 1 dollar 58 cents per
barrel. How many barrels is he to receive?
Ans. 50 barrels.-f-
100
LOSS AND GAIN.
15. K. bought of Y. 102 lb. of lard at 8| cents per
pound, and is to pay him as follows, viz: in cash 1 dol¬
lar I dent, 20 lb. of leather at 20 cents per pound, and
40 pounds of beef at 2£ cents per pound, and the rest
in butter at6£ cents per pound. How many pounds of
butter must Y. receive? Ans. 39pounds.
LOSS AIVD CrAUV-
Loss and gain is used to show how much is gained
or lost in dealing.
RULE.
1st. Subtract the cost from the sale; the remainder
will be the gain. Or, if the cost be more than the sale,
subtract the sale from the cost, and the remainder will
be the loss. 2d. When you wish to sell any commod¬
ity at a certain gain per cent, and wish to know what
sum it must be sold for, say if 100 give 10Q with the
per cent added, what will the first cost give. 3rd.
When the amount is given at a certain rate gain per
cent, to find the first cost—say if 100, with the rate
per cent added, give 100, what will the amount give.
4th. When any commodity is sold at a certain rate per
cent loss, to find the sum received, say if 100 give 100
less the per cent lost, what will the first cost give.
EXAMPLES.
1. What will a merchant gain by buying 95 bushels
of salt at 1 dollar 20 cents per bushel, and selling, it
again at 1 dollar 50 cts. per bushel?
1 50' 95 bushels.
1 20 30
Gain on one bushel 30 Ans. $28 50 cents.
XOSS AND GAIN.
101
2. TBought 55 yards of cloth at 13 cents per yard,
and sold the same again for 15 cents per yard. How
much was gained by the transaction? Ans. $1 lOcts.
3. If I buy 50 yards of cloth at 25 cents per' yard,
and sell the same again for 30 cents per yard, how
much do I gain? Ans. 2 dollars 50 cts.
4. If I buy 100 yards of tape at 20 cents per yard,
and sell it folr|18 cents per yard, how much do I lose in
the transaction? Ans. 2 dollars.
5. If I buy 40 saddles at 11 dollars 50 cents each,
and sell them again at 10 dollars 99 cents each; how
much do I lose by the sale? Ans. 20 dollars 40cts.
6. Bought 12 bushels of corn at 22\ cents per bushel,
and soldi it again at 22 cent^ per .bushel. How much did
I lose by the transaction? Ans. 6 cents.
7. A man bought flour at $5 per barrel, and sold it at
$5 25 cents per barrel. How much did he gain on 363
barrels? " Ans. 90 dollars 75 cts.
8. If I lay out 500 dollars in cloth at 5 cents per
yard, and sell the same again at 12£ cents per yard,
how much do I gain? Ans, 750 dollars.
9. If I buy a horse for 60 dollars, at RAw much must
I sell him to gain 20 per cent?
If100 : 60 : : 120. Ans. $72.
10. If I buy 100 yards of cloth for $50, at how much
must I sell it per yard to gain 20 per cent by the whole?
Ans. 60 cents.
11. If I buy 54 yards of muslin for 29 dollars 84 cents,
and sell the same again at 60 cents per yard, how
much do I gain? Ans. 2 dollars 56 cents.
12. If I buy 90 horses for 1800 dollars, at how much
must I sell each horse to gain 180 dollars in the whole?
Ans. 22 dollars.
13. A merchant sold 40 ya^ds . of cloth at 20 cents
per yard, and by so doing gained 10 per cent. What
"was the first cost of each yard? Ans, 18 cents.4*
102
LOSS AND SAIN.
40
20
110 : *800 : : 100
100
11|0)8000|0
Yards 4I0;72|7*
1S+
14. Bought a quantity of tea for $250, and sold it for
275 dollars. What is the gain, and gain per bent?
Ans. 25 dollars gained, 10 per cent.
15. Bought 490 bushels of corn for 326 dollars, and
sold the same for 370 dollars 10 cents. What was the
profit on each bushel? f Ahs. 9 cents.
16. Bought a parcel of goods for60 dollars, and sold
the same immediately for 90 dollars with 6 months
credit. Ho^jtmuch per cent per annum was gained?
Ans. 100 per cent.
17. When a broker receives ip exchange 5 cents per
dollar profit, how much is the gain per cent? Ans. $5
18. A man purchased .7pieces.of cloth at $13 75 cts.
per piece; but finding it somewnat damaged, he paid
$3 12^ cts. per piece for dying it. At how much must
each piece be sold to gain 12 per cent on the whole?
Ans. $18 90 cts.
19. ,A trader bought 250 barrels of flour at $4 50 cts.
a barrel. How must he sell each barrel to gain 100
dollars by the bargain? Ans. $4 90 cts.
20. If I purchase 16 pieces of cloth at 14 dollars per
piece, and sell 5 pieces at 17 dollars per piece, and 6 at
15 dollars per piece, what must I sell the rest at per
piece to gain 12 per cent on the whole?
17cts. 6m
PARTNERSHIP.
103
PARTNERSHIP,
Partnership is a joint interest or property, the union
of tvro or more persons in the same trade, by which
rule persons in company trading together, are enabled
to make a just division of the gain or loss, in propor¬
tion to each man's stock.
When the respective stocks have no time—
Add the several shares tjogether, vfchich amount is
the first term, either persons share the 2nd., the whole
gain or loss the 3rd. Proceed by the Rule of Three.
2nd. When the respective stocks have time, multipjjy
each man's stock by its time. Adci the several pro¬
ducts together, which amount is the first term, either
particular product the 2nd, the whole gain or loss the
3rd. Proceed as before. *
Proof.—Add together all the shares of gain or loss.
SKAMplIS?
1. A, B and C matle a stock. A put in $?0, B $30, C
{540,and by trading, they gained 36 dollars'# What
was each man's share ofthe gain?
Proof. $36
2. A and B purchased goods worth 80 dollars; of
which A pays 30 dollars and B 50 dollars. They gained
21) dollars!; what is the gain of each]
Ans. A $7 50 cts. B $12 50cts.
3. Thre|e merchants trading together gained $500.
rule.
A 20
B 30
C 40
Ambunt. 90 : 20 : : 36.
90 : 30 : : 36.
90 : 40 ; : 36.
Ans. A's share $8
Ans. B's share $12
Ans. C's share $46
104
PARTNERSHIP.
A's stock was $800; B's stock $700; C's stock $500.
What was each man's share of the grain?
Ana. A's share $200; B's $175; C's,$125.
4. A merchant being1 deceased, worth 1800 dollars,
is found to owe the following sums:—To A $1200; to
B $500; to C. 700. How much is each to have in pro¬
portion to the debt? Ans. A $900; B $375; and C $525.
5. B, C and D, made a stock, by which they gained
800 dollars; whereof B's stock was 400 dollars; C's
50Q dollars; and D's 600 dollars. 1 demand each man's
share of the gain. Ans>B's $213§; C's $266$; D's $320.
6. Three drovers pay among them $60 for1 pasture,
into which they put 200 cattle; of which A had 50; B
80; C 70. I would know how much each hacl to pay?
Ans. A $15; B $24; C $21.
7. Four men formed a capital of3200 dollars^ They
gained in a certain time 6560 dollars. A's stock was
560 dollars; B's 1040 dollars; Cf s 1200 dollars, end D's
400 dollars. What did each gain?
Ans. A's $1148; B's 2132; C's 2460, and D>$820.
8. B, C and D traded together, B put in 50 dollars
for four months; C 100 dollars for 6 months, and D150
dollars for 8 months. They gained 1S6 dollars 80 cts;
what is each man's share of the gain?
$ m."
B 50*4=200
C 100x6 600
D 150x 8 1200
'■ $ cts. $ cts.
2000 ; 200 : : 126 80 C 12 68 B
2000 : 600 : : 126 80 Ans. < 3^ 04 C
2000:1200 i : 126 80 ( 76 08 D
9. O, P and R, traded together; O put in 100 dollars
for 2 months, P 200 dollars for four months, and R.400
dollars for 5 months, and by trading together they
gained 600 dollars 50 cents. How much is each man's
gain in proportion to his stock?
C O 40 dollars 3$ cents.
^lUS. < P 160 dollars 13$ cts.
(R 400 dollars33$ cts.
EXCHANGE.
105
10. A. and W. made a stock: A. put in 500 dollars
tor 6 months, and YV. 2000 dollars for 8 months; and
by trading they gained 2600 dollars. I demand each
man's share of the gain?
• 5 A. 410 dollars 52 cents 5m.+
I W. 2189 dollars 47 cents 3m.4*
11. S. G. and W. made a stock for 12 months. S,
put in at first 500 dollars, and two months after he
put in 40 dollars more; G. put in at first 805 dollars
50 cents, and at the end of ten months he took out
300 dollars; W. pUtin at first 000 dollars 25 cents, and
4 months after, he put in 100 dollars, and 6 months
after that, he put in 50 dollars 50 cents mbre. At
the exprration of 12 mpnth^ theirfrjgain is 1800 dollars
50 cents; what is each man's share of the gain?
( S. $488 89 cents 2m.
Ans. < G» $892 51 cents 7m.
( W. $619 06 cents. 0m.
EXCHANGE.
TABLES OF MONEY.
ENGLISH MONEY.
The denominations are,
4 farthings (marked qr.) make 1 penny, d.
12 pence 1 shillings, s.
20 shillings 1 pound. £.
H
106
feXCHAKGE.
SHEWING- THE VALUE Ofr EV«UISK JlplNE* IN FEIJEHAI. MOJTKT.
New York and
North Carolina.
South "Carolina
and Georgia.
Kew Jersey,
Pennsylvania,
Delaware and
Maryland. |
N, |lampshue,
Massachusetts,
Khode Island,
Connecticut^
Virginia, Ken¬
tucky & Ten¬
nessee.
s.
d.
$
£ts.
s.
d.
$
cist.
s.
i.
«
CIS- s.
d.
$
cts
2
2
34
2
2
2
2#
3
3
3
5|
3
34
3
4
4
4
4#
1
4
4
54
H
4#
6
9 .
8
t
44
5
44
6#
6 •
9
64
9a
f
10#
16
6
9
6#
10
j
84
124
1
0
124
1
0
21#
1
0
134
1
0
16#
1
6
m
1
>
32
1
6
20
1
s
25
2
0
25
2
t)
421
48
2
0
26#
2
0
^34
2
3
23
2
3
2
3
* 30
2
3
374
2
6
314
2
6
534
2
6
2
6
41#
2
9
34#
2
9 ■
$8J
i g
9
3£#
2
9
45#--
3
0 .
574
» 3
4
644
3
0
40 .
3
1)
50
3
9
46#
3
9
804
3
9
50
3
9
624
66#
4
,0
o<y
4
0
85#
4
P
53#
4
0
4
6
56#r
4
6
964
4
6
60
4
6
75
5
0
624
5
0
J
7"
5
0
66S
5
0
834
6
0
75
6
0
284
6
0
So
6.
0
1
00
6
9
844
6
9
1
444
6
9
90
6!
9
1
124
7
6
934 ,
7
6 .
1
60#
7
6
1
00
7
5
1 1
25
10
6
1
31i|10
6
2 J
25 J
10
6 H j
40
1016 '
1 1
75
Note.—In calculating the above table, remainders are not
marked, being less than J, &c.
£1 of New York and North Carolina, is $2 50
£1 of South Carolina and Georgia, is $4 2844-
£1 of New Jersey, Pennsylvania, Delaw; re
and Maryland, is $2 66#
JEI ofN. Hampshire, Massachusetts, Hho^le
Island, Connecticut, Virginia, Kentucky,
and Tennessee, is
$3 331
A TABLE OF COINS, avi HI 'i HEIR STERLING AND FEDERAL VALUE.
Names of Coins.
Standard
Weight.
Sterling Mo-
ney of Great
-Britain.
Nevv Ham-
shire, Mas¬
sachusetts R.
Island, Con-
heeticut, Vir¬
ginia, Ken¬
tucky" k Ten¬
nessee.
(New Jer-
lsey,Penn-
'1. York sylvania,
St NorthiDeiaware,
Carolina. Ik Mary
j land.
S. Caroli¬
na k Geor¬
gia-
Federal
■value.
GOLD.
dwt. gr
£ d.
' £ s. d.
£ s. d.
£ s. d.
£ s. d
$ cts.m.
A' Johannag.
18 0
3 12 0
[4160
6 8 0
6 0 0
4 0 0
It 00 0
A half Johannas.
9 0
1 16 0
'2 8 0 -
3 4 0"
3 0 0
2 0 0
8 0') 0
A Doubloon.
16 21
3 6 0
4 3 0
5 16 0
5 12 6
3 10 0
14 9- 3
A Moidore.
6 18
17 0
1 16 0
2 8 0
2 5 0
1 8 V
6 GO 0
An English Guinea.
5 6
110
ISO
1 17 0
1 15 0
119
4 66 7
A French Guinea.
5 5
110
17 6
1 16 0
1 14 6
115
4 60 O
A Spanish Pistole.
4 6
0 IS 0
12 0
19 0
18 0
0 18 0
3 77 3
A French Pistols.
4 4
0 16 0
12 0
18 0
17 6
0 17 6
j 65 7
SILVER. *"
1 10 0
An Englioh or Fren. Crown.
18 0
5 00 0
0 6 8
0 8 9
0 8 3
0 5 0
The dollar of Spain, \
17 6
0 4 6
0 6 0
0 po
0 7 6
0 4 8
1 00 0
Sweden or Denmark. $
.
\n Ei isIi Shilling.
3 14
0 10
0 14
0 19
0 18
0 11
0 22 2
A Pistareen. I
3 11
0 0 10|
0 1 2
0 17
0 16
0 0 11
0 20 0
(Xj*All other £old coins of equal fineness at 86 cts. per dwt. and silver at ill cts. per oz.
108
exchange:
A TABLE OF OTHER FOREIGN COINS, &o,
WITH THEIR VALUE IN FEDERAL MONET.
$ cts. m.
Pound Sterling, 4 44 4
Pound of Ireland, 4 10 0
Pagoda of India, 1 94 0
Tale of China, 1 48 0
Millrea of Portugal, 1 24 0
Ruble of Russia, 0 66 0
Rupee of Bengal, 55 5
§ cts. m.
The Guilder of the ^ ([)
United Netherlands 5
Mark Banco of ? 33 *
Hamburg, 3
Livre Turnois of 7 5
Fran'ce, 3
Real Plate of Spain, 10 0
Note.—Some persons to try others' skill in numbers, may give
them the multiplying of pounds, shillings, pence, &c. by the same;
or the multiplying of cents by the same, &c. The following will be
sufficient, thus:—Pounds multiplied by pounds, give pounds. Pounds
multiplied by shillings, give shillings. Shillings multiplied by shil¬
lings, give the 20th part of a shilling. Shillings multiplied by pence,
give the 20th part of a penny. Pence multiplied by pence, give the
240thpart of a penny, bcc.; and cents multiplied by cents, give the
100th part of a cent, &.<;■
EXCHANGE.
Exchange teaches to change a sum of one kind of
money to a given denomination of another kind; to re¬
duce the currency of each of the United States(to dol¬
lars and cents, or Federal Money.
RULBt
Reduce the sum to pence; to the pence annex two
ciphers; then divide by the number of pence which
make a dollar in that state or country. The quotient
will be cents; which reduce to dollars.
Notb.—This rule applies to the currency of any state or
country, if its currency be in pounds, shillings, pence, &e.
EXAMPLES.
I. In90 pounds New England, Virginia, Kentucky
and Tennessee currency, how many dollars and cents,
a dollar being 72 pence.
EXCHANGE4
109
£
90
20
1800
12
72)2160000(3300 00
216
0000
2. Bring 12 pounds 3 shillings and 9 pence to dol¬
lars and cents, same currency. Ans. $40 62£ cts.
3. Reduce 19 shillings and 10 pence to dollars and
cents, same currency? Arts. "S3 30cts. 5m.
4. In 763 pounds how many dollars, cents and mills,
same currency? Ans. 32543 33cts, 3m,
5. Reduce 30£ and 3s., to dollars and cents, same
currency? Ans13100 50 cents.
6. In 27£ 2s., how many dollars and cents, JNfrtw
York and North Carolina currency, pne dollar being
98 pence? Ans. 387 75 cents.
7. In30£how many dollars and cents, same curren¬
cy? Ans\ 375 00 pents.
,8. In 9£ 16s., how many dollars and cents, same cur¬
rency? Ans. 324 50 cents.
9. In 942£ of New Jersey, Pennsylvania, Delaware
and Maryland currency, how many dollars and cents,
a dollar being 90 pence? Ans. 32512 00 cents.
10. In 12£ how many dollars and cents, same cur¬
rency? Ans. 332 00 cents.
11. In86£ 6s. 5d., how many dollars, cents and mills,
same currency? Ans. 3230 18cts. 8m.
12. In 56£ S. Carolina and Georgia currency, how
many dollars and cents, being 56 pence in a dollar?
Ans. 3240 00 cents.
' 13. In 21£ how many dollars and cents, same curren¬
cy1 Ans. 390 00 cents.
110
EXCHANGE,
14. In 460£ and 16s., sterling' pnoney, how many dol¬
lars and cents, being 54 pence in a dollar?
Ans. $2048 00 events.
To bring Dollars or Dollars and Cents to Pounds, Shil¬
lings, &c,
rule.
Multiply the dollars or'dollars and cents by the nUm-
ber of pence which make a dollar *of thp currency inl-o
which you wish to bring the given sum. The answer
will be pence, which bring to pounds.
Note.—If there be cents in the given sum, two figures must
be cut off from the r^ght of the product, before bringing them
into pounds, &c.
examples.
1. In 03 dollars how many pounds, &c. sterling, a
dollar being 54 pence?
$
33
54
132
165
]2)1783d.
210)1418—6d.
Ans. 7£ 8s. 6d.
2. In 1000000 dollars how many pounds, same cur¬
rency? Ans. 225000£.
3. In 150 dollars 25 cents, how many pounds, &c.
New England, Virginia, Kentucky and Tennessee cur¬
rency, a dollar being 72 pence? Ans. 45£ Is. 6d.
4. In 2070 dollars, New England, Virginia, Ken-
Exchange.
Ill
lucky and Tennessee currency', how many pounds,
&c., a dollar being^ pence? Ans. 621£.
5. In 24 dollars 50 cents how many pounds and shil¬
lings, &c., in New York and North Carolina currency*
a dollar being 90 pence? Ans. 9£ 16s. 0d.
6. In 2512 dollars, how many pounds of New Jersey,
Pennsylvania, Delaware and Maryland currency, a doU
lar being 90 ftence? Ans. 942£.
7. In 90 dollars, how many pounds South Carolina
and Georgia currency, a dollar being 56 pence?
Ans. 21£.
To change the currency of one State or courttry into
that of another.
RULE.
Place the sum you wish to change in the third place—
the number of shillings in a dollar Uf that currency in¬
to which you wish to change it, in the second—nrtd the
number of shillings in a dollar of that currency you
wish to change, in the first. Proceed by the Rule of
Three.
1. What is the value of 50£, Tennessee currency, in
New York?
S. S. £.
6 : 8 :: 50
8
6)400
Ans. 66£ 13s. 4d.
2. What is the value of 500£, Massachusetts curren¬
cy, in Pennsylvania? Ans. 625£.
3. What is the value of 100£ South Carolina, or
Georgia currency,in Kentucky? Ans. 128£ lis. 5d.-f-
4. What is the value of 750£ New Hampshire cur¬
rency, in North Carolina? Ans. 1000£T
112
vulgar fractions.
VULGAR VRACTIOiVS.
A Vulgar Fraction is a part of a whole number,
and is read by first mentioning the upper part of the
fraction, and then the lower, thus: '•£, f, &c. The
upper part of the fraction is called the numerator, and
shows the part of a whole number expressed by the
traction. The lower number is called the denomi¬
nator, and shows the number of such parts contained
in a whole number. Vulgar Fractions are either
proper, improper, compound ormixed. A proper
fraction has its numerator less than its denominator,
ass, I, &c. An improper fraction has its numera¬
tor greater than its denominator, as -f, &c. A
compound fraction ifc a fraction of a fraction, with
thft word of expressed between them, as i of ■§, of
I, &c. A mixed number is a whole number and a
fraction, as 5§, 8|, &c.
REDUCTION OF VULGAR FRACTIONS.
Case 1.
To reduce a fraction to its lowest terms.
Rule.
Divide the numerator and denominator continually
by any number that will divide them both without a re¬
mainder. When they cannot be divided by any num¬
ber without a remainder, the fractiou is then at its low¬
est terms.
examples.
1. Reduce to its lowest terms.
?4)f4=2 Ans.
2. Reduce to its lowest terms.
3. Reduce A|. to its lowest terms.
4. Reduce to its lowest te.rms.
5. Reduce^?- to its lowest ferms.
b. Reduce 144. to its lowest terms.
2 3 4
Ans. 4
Ans. 4
Ans. 4
Ans. ^
Ans.
VULGAR FRACTIONS.
113
Case 2.
To reduce a mixed number to an improper fraction.
RULE.
Multiply the whole number by the denominator of
the fraction, and add the numerator to the product for
a new numerator, under which place the given denom¬
inator.
examples.
1. Reduce I If to an improper fraction.
Ans. y.
new numerator. 57
denominator. IT
2. Reduce to an improper fraction.
Ans. y.
3^ Reduce 141 to an improper fraction.
Ans. y
4. Reduce 99T8T to an improper fraction.
Ans. 1ff7
case 3.
To reduce an improper fraction to a whole or mixed
number.
rule.
Divide the numerator by the denominator.
examples.
1. Reduce 4Ty to its proper terms.
114 "vulgar Fractions.
17)400(Ans. 234^
34
60
51
9
Reduce "J to its proper terms. A us. 22-1
3. Reduce ai. to its proper terms. Ans. 5-^
4. Reduce yj to its proper terms. Ans. 2 £4
Note.—Case 2d. and 3rd. prove each other.
Case 4.
To reduce compound fractions to single ones.
rule.
Multiply all the numerators together For a new nu¬
merator, and all the denominators/or a new denomin¬
ator; which reduce to their lowest terms.
examples.
1. Reduce I of | of f of | to a single fraction.
Ans. »
1X2X3X4=; 24=
24) (b
2X3X4X5= 120
2. Reduce | of I of | to a single fraction.
Ans. f.
3. Reduce ^ of J. of 4 to a single fraction,
Ans.
4. Reduce 4| of of 4 to a single fraction.
Ans.
VULGAR FRACTIONS.
115
Case 5.
To find a common denominator, viz: one whose de¬
nominators are all alike.
Rule.
Multiply all the denominators together for a common
denominator, into which divide each denominator, and
multiply the quotient by its own numerator for a new
numerator, and plaqe the new numerator over the
common denominator.
examples.
1. Reduce i, ■§ and % to a common denomina¬
tor.
I | I 12 xl = 12
3 SX2= 16 new numerators.
— 6X3= IS
12
2
Divide by 2,3,4. 24 common denominator. Ans. 12. 1A.1A.
7 2 4'n'2 4'
2. Reduce f and | to a common denomina-
tor. Ans. Al, 41, 44.
1 "7o 6-i7 6 4<7 6 4
3. Reduce •§> to a common denominator.
Ans 7 3 5 560 504. 720
, 1^0' ¥47' TSTo^TXTT
4. Reduce 5, and f, to a common denomina¬
tor Ans 144 192 340 252
tU1, AU3' 2"8¥1 2¥¥' 2"5T» 2 8T'
Case 6*
To reduce the fraction of one denomination to the
fraction of another, but greater, retaining the same
value.
rule.
Make the fraction a compound one, by comparing it
with all the denominations between it and that to
which it is to be reduced; which fraction reduce to a
single one.
116 VULGAR FRACTIONS.
EXAMPLES.
1. Reduce f of a pennyweight to the fraction of a
pound, Troy.
„ if IT of A , sh^J=zh A°*
2. Reduce f of a nail to the fraction of a yard.
Ans. t|t yd.
3. Reduce | of a cent to the fraction of a dollar.
Ans. -^4^ dollar.
4. Reduce I of a pint to the fraction of a hogshead.
Ans. hhd-
Case 7.
To reduce the fraction of one denomination, to the
fraction of another, but less, retaining the same val¬
ue.
npLE.
Multiply the given numerator by the parts of the de¬
nominator between it and that to which it is reduced,
for a new numerator, and place it over the given de¬
nominator, which reduce to its lowest terms.
examples.
1. Reduce t4q of a dollar to the fraction of a cent,
Ans. 4 cent.
cts.
I_v I J) 0—glnuolo 5
TToX l — I / l liicf 9"
2. Reduce ^y of a pound, troy, to the fraction of
an ounce. Ans. | 02.
3. Reduce ¥§ £ of a ewt. to the fraction of a pound,
avoirdupois. Ans. | lb.
4. Reduce-^3^4 of a day to the fraction of a min¬
ute. Ans. 44 m*n'
Case 8.
To reduce a fraction to its proper value.
VtJLGAR FRACTIONS. 117
role.
Multiply the numerator by the next lowest denom¬
ination, and divide by the denominator,
examples.
1. Reduce f of a dollar to its proper value.
4
100
5)400
Ans. 80 cents.
2. Reduce § of a dollar to its proper value.
Ans. 75 cents.
3. Reduce i of a day to its proper quantity.
Ans. 6 hours,
4. Reduce A of a mile to its proper quantity.
Ans. 4fur. 125yd. 2ft. lin. 1.
5. Reduce-A- of an acre to its proper quantity.
* Ans. 1R. 10P.
0. Reduce T9g. of a year to its proper quantity.
Ans. 32Sda. 12hr.
Case 9.
To 'reduce any given value or quantity to a fraction of
any greater denomination of the same kind.
Rule.
Reduoe the given sum to the lowest denomination
mentioned for a numerator, and the denomination of
which you wish to make it a fraction to the same name
for a denominator.
examples.
1. Reduce 60 cents to the fraction of a dollar.
Ans. | dollar.
118
VULGAR FRACTIONS.
2. Reduce 90 cents to the fraction of a dollar.
3. Reduce 9 ounces, troy, to the fraction of a
4. Reduce 9oz. 2dr. avoirdupois, to the fraction
a pound. Ans. -£lb.
5. Reduce 3qr. 3na. to the fraction of a yard.
Ans. i
5. Reduce 7 months to the fraction of a year.
ADDITION OF VULGAR FRACTIONS.
Reduce the fractions to a common denominator;
then add all the numerators together, and place their
sum over the common denominator. If fractions be of
different denominations. And their value seperutely, and
add as Compound Addition.
Note.—If mixed numbers be given reduce them to improp¬
er fractions, or only use the fractional paft in performing the
operation. Then add the whole numbers, as in Simple Addi¬
tion. If compouud fractions be given-reduce them to single
ones.
Ans. dollar.-
Ans. 3 lb.
Ans. j\ year.
rule.
examples.
1. Add 5, i and ^ together.
Hi 8
8)
Ans. s
2 32
— 16
8 —
Divide by 8, 2, 4)64
VULGAR FRACTIONS,
2. Add \ and 77 together.
3. Add 2, u, T9^ and | together.
A \-rmn
TT' tt> TT — TT together.
. 12 0*
Ans. i®.
Ans. 11.
Ans. ll£4r.
Ans. 13.JL.
iiuu 4, 2 fx.iu 4
f>. Add 3i, 8^ and ± together.
7. Add 74 and 54 together-
8. Add 4 of an acre to T7g- of a rood.
Ans. 2R. 14P.
9. Add i of a mile to T7g- of a furlong.
Ans. 6fur. 2SP.
10. Add | of jj and \ of t7j together. Ans. |9.
11. Add 2 of g and £ of Altogether. Ans. |£.
MULTIPLICATION OF VULLAR FRACTIONS.
Multiply the numerators together for n new nmtier-
tor, and the denominators lor a now denuminaio
No-ri;.— If compound tractions be given, reduce them to sin¬
gle ones; or, if mixed numbers, reduce tliem to impioper frac¬
tions; and proceed as before.
1. Multiply i byf, 4Xf=f 2) J. Ans. 4.
2. Multiply I by|. Ans. T'ff.
3. Multiply T\ by 4. Ans. 7\.
4. Multiply 4i by ■§. Ans. 31.
5. Multiply 4 of | by ^ of ±*. Ans.
S. Multiply i of 7 by 4. Ans. 12.
4XAX4=A 4)7
II.
RULE.
EXAMPLES.
120
VULGAR FRACTIONS.
SUBTRACTION OF VULGAR FRACTIONS.
rule.
Reduce compound fractions to single ones, and mix¬
ed numbers to improper fractions. Then reduce these
fractions to a common denominator, and subtract the
less numerator from the greater, and place the differ¬
ence over the common denominator.
Note.—When the fractions are of different denominations
reduce them to their proper value, each seperately, and take
their difference by Compound Subtraction.
examples.
1. From I take -JL. Ans.
8 12x5=60
_ 8X5=40
Divide by 8, 12)96 —
4)20 g
2. From I take Ans.
3. From take Ans.
4. From T7T take Ans.-J^.
5. From h of ■§• take f of Ans. -J..
6. From | of -A. take i of |. Ans.
7. From | of a league take of a mile.
Ans. lm. 2fur. 16p.
V. From of a yard take -§ of an inch.
Ana
Note.—When fractions or mixed numbers are to be subtrac¬
ted from whole numbers, subtract the numerator of the frac¬
tion from its denominator, and under the remainder place the
denominator; then carry one to be subtracted from the whole
number.
9. From 5 take ^ Ans. 476x.
VULGAR FRACTIONS. 121
10. From 10 take Ans. 9JL.
11. From 9 take5£. Ans. 3h.
12. From 25 take 24-®,;.. Ans. 1.
10 o
DIVISION OF VULGAR FRACTIONS.
RULE.
Reduce compound fractions to single ones, and mix¬
ed numbers to improper fractions. Then invert the
dividing term, and multiply all the numerators into
each other for a dividend, and denominators for a di¬
visor.
EXAMPLES.
1. Divide h by 5. Ans. •§.
inverted |X | 2)|—§.
2. Divide 6 by §. Ans. 48.
3. Divide a by 3. Ans. ^7.
4. Divide |~L by An£, 1||.
5. Divide 6| by Ans. 19|.
0. Divide f of £ by h of Ans. -§•?.
7. Diyidef of g by 4 of f. Ans. I5.
8. Divide | of 5 by | of i. Ans. lpi.
9. Divide 4A by «. of 4, Ans- 2^.
10. Whdt part of 33-L is 28||. Ans. a.
RULE OF THREE, IN VULGAR FRACTIONS.
ROLE.
State as in whole numbers. Then invert the first
term, and multiply all the numerators together for a
dividend, and denominators for a divisor. If mixed
I
122
VULGAR FRACTIONS.
numbers be given, reduce them to improper fractions;
or componnd fractions to single ones. If a whole
number, place thus: f, &c,
EXAMPLES.
If f of a yard of cloth cost f. of a dollar, how
much will | of a yard cost at that rate?
Ans. 01 60 cts.
Inverted |Xf X|=5]0)8J0
01 60 cts.
;2. If f of an ounce of indigo cost $ of a dollar,
how much will § of an ounce cost?
Ans. 23T7r cents.
3. If 1| bushels of coril cost 01 g, how much
will 60 bushels cost at that rate?
Ans. 038 57f cts.
4. If 2h bushels of oats cost 50 cents, what cost
13£ bushels at that rate?
Ans. $2 65 cents.
5. IIow many yards of linen, | wide, will be suf¬
ficient to line 20 yards of baize that is 3 of a yard
wide? Ans. 12 yd.
6. If | of a pound of cinnamon bring f of a dol¬
lar, what will If lb. come to?
. Ans. 02 74f cts.
7. What will $ of 2| cwt. of chocolate come to,
when 6£ lb. cost £ of a dollar?
Ans. 010 76if cts.
8. When 10 men can finish a piece of work in
VDiGAR FRACTIONS. 123
20| days, in how many days can 6 men do the same?
Ans. 34* da.
9. How many pieces of stuff at $20| per piece
are equal in value to 240*. pieces, at $12! per piece?
Ans. 149T\yT-
10. If ! of |- of $ of 60 cents will pay for a bush¬
el of potatoes, how many bushels will $1 60 cts.
pay for? Ans. lOf bu.
DOUBLE RULE OF THREE IN VULGAR
FRACTIONS.
ROLE.
Prepare the terms, if necessary, by Reduction.—
"State as in whole numbers. Then iuvertthe two divi¬
ding terms, and multiply all the numerators together
for a dividend, and the denominators for a divisor.
EXAMPLES.
1. If ! of a dollar, in T\ of a year, gain yT of a dol¬
lar interest, how much will i of a dollar gain ir^ |. of
a year? Ans. 5A cts.
$ y. $ _
principal ! : T9^ : t interest.
•g : «
Inverted f X y X 8x JxVT=l08)00)600|00=5£.
540
60
2. If 2$ yards of cloth, 1| yards wide, cost $3 j,
what is the value of 38s yards, 2 yards wide?
Ans. $76 50 cts.
3. If $50 in 4Ty months gain 2$ dollars interest,
124
DECIMAL P^ACfT'IdJir^
in what time will $15-1. gain $2?
Ans. monthaf,
4. If 4 men in 5| days eat 71 lb. of bread, how
many pounds will 20 men eat in of a day?
Ans* 5ta.a. lb,
5. If 90 dollars in | of a year gain $4| interest,
in what time will 900 dollars gain 20 dollars interest?
Ans. 4^ months*
DECIMAL FRACTIONS.
A Decimal Fraction is a part of a whole number
or unit, denoted by a point placed to the left of a figure
or figures; as .2, . 18,. 110. The first figure afterthe
point denotes so many tenths of a unit; the second, so
many hundredths; the third, so many thousandths,
and so on.
Decimal Fractions are read in the same manner as
vulgar fractions. .5 is equal to, and reads as
,10 ,l20Tyff0^, and so on. A mixed number
consisting of a whole number and a decimal, as 12 Ap
thus 12.5. Whole numbers, counting from the right
towards the left, increase in a tenfold proportion;
but decimals, counting from the left towards the
right, decrease in a tenfold proportion, as will be bet¬
ter exemplified in the following table:
decimal fractions. 125
TABLE.
WHOLE NUMBERS. DECIMALS.
222222231 .1 22222222
S?s§°?s 3 s!
zs 5, o- «
rv st! uc » •
2cr°§5°g
~ "St"'
^ ^ H £ $ -3 o g ® S"s=i ft: S
ts^ —- • i—z 21 ^ Cu M O- ? E 2 s- o tn «-J
so
? 3-ES5 S-3
OS* ' ^ §
c co tj &i 3 h »-* ^
a »
S» 3 2,»1 fit
s ft. " -j _, & £ t)
ft.» • 3 "3 r' 2. S3
Note—Ciphers annexed to decimals, neither in¬
crease or decrease themj thus, .4, .10, .50, being;
tV» tV°o' To°o> are same value; but ciphers
prefixed to decimals, decrease them in a tenfold pro¬
portion, thus, .04,.010, .050,beingTJ»T,
&c.
ADDITION OF DECIMALS.
rule.
Writedown the given numbers under each other,
viz:—Units under units, tens under tens, &c., and add
as in addition of whole numbers; observing to set the
point in the answer under those of the given number.
examples,
(1.) 2.12 (2.) 36.12 (3.) .7324
.103 3.112 .0962
15.115 .12 .132
.74 16.182 .09
18.078 55.534 1.0506
4. Add 56.12, .7,1. 314,5337.01 and .15 together.
Ans. 5895.294
126
decimal fractions.
5. Add 361.04, .120, 78.0006, 101.54, 8.943 and\3tt>-
gether. Ans. 549.9436.
MULTIPLICATION OF DECIMALS.
RULB.
Multiply as in whole numbers, and point off as many
figures in the product for decimals a? there are decim¬
als in both factors. If there are not so many figures
in the product as there are decimal figures in both fac¬
tors, place ciphers to the left of the product to supply
the deficiency.
examples.
1. Multiply 5.11 by .122
5.11
122
122
610
.62342
2. Multiply 51.20 by 38.03
3. Multiply 4560. by .3720
4. Multiply .283 by .003
5. Multiply3.92 by 198.
6. Multiply .28043 by .0005.
SUBTRACTION OF DECIMALS.
Rule.
Place the numbers as in addition, with the less un¬
der the greater; and subtract as in whole numbers, set¬
ting the point in the answer under those in the given
numbers.
EXAMPLES.
1. From 32.453 take 1.33
1.33
Ans. 2093.7460.
Ans. 1698.3200.
Ans. .000855.
Ans. 768.32.
Ans. .000140215.
Ans. 31.126
2. From 18.16 take 9.125
3. From 100. take .25
Ans. 9.035.
Ans. 99.75..
DECIMAL FRACTIONS.
127
4. Prom 441.2 take 128.9
5. From 456. L lake 111.9
Arts. 312.6.
Ans. 344.2,
DIVISION OP DECIMALS.
Rule.
Divide as in whole numbers; then observehow many
more decimal figures there are in the dividend than di¬
visor, and point oil" t int number of decimal figures in
the answer. Or if there be not figures enough in the an¬
swer, annex ciphers until there be a sufficient number.
Note.—If the dividend be not l irge enough to contain the
divisor, annex ciphers until it will be; or if there be a remain¬
der, proceed in like manner.
4.21) 118.63( Ans. 35.3040
126 3
2233
$105
128.0
1263
17.00
1684
examples.
1. Divide 148.63 by 4.21
160
2. Divide 19.25 by 38.5
3. Divide .2142 by 3.2
4. Divide 210. by 240.
5. Divide .1606 by 4.4
6. Divide 3. by 4.
Ans. .5.
Ans. .066.+
Ans. .875.
Ans. .365.
Ans. .75.
7. Divide 275. by 3842.
Ane. .071577.+
128
decimal fractions.
REDUCTION OP DECIMALS.
Case 1.
To reduce a Vulgar Fraction to a Decimal.
Rule.
Annex ciphers to the numerator, an<} divide by the
denominator. If compound fractions be given, reduce
them to single ones, and then to a decimal.
examples.
1. Reduce to a decimal. A Ans. .5..
2)1.0
.5
2. Reduce I to a decimal. Ans. .332,
3. Reduce f to a decimal. Ans. .75.
4. Reduce § to a decimal. Ans. .375.
5. Reduce A of # to a decimal Ans. .333.+
Case 2.
To reduce any sum or quantity to the decimal of a
higher.
Rule.
Reduce the given sum to the lowest denomination
mentioned for a dividend, and one of that denomina¬
tion of which you wish to tnakea decimal to the same
denomination for a divisor. The quotient will be the
answer.
examples.
1. Reduce 2qr. to the decimal of a yard. Ans. .5.
yd.
1 4)2.0
4
.5
4
2. Reduce 2qr. 2na. to the decimal of a yard.
Ans. .625.
3. Reduce 2qt. lpt. to the decimql of a hhd.
Ans. .00992+.
4. Reduce 10g. to the decimal of an ounce, apotheca¬
ries weight. Ans. ,.02083.+
DECIMAL FRACTIONS.
129
5. Reduce 5 mini to the decimal of an hour.
Ans. .05333.4-
6. Reduce 2r. 4p. to the decimal of an acre.
Ans. .525t
Cask 3.
To reduce a decimal fraction to its proper value.
Rule.
Multiply the given fraction continually by the next
lowest denomination than that of the given sum, for
the proper value.
examples.
1. What is the value pf .75 of a dollar? Ans. 75cts.
100
75.00
2. What is the value of .375 of a dollar? Ans. 37Jcts.
3. What is the value of .Oof an acre? Ans.3r.24p.
4. What is the value of .436 of a yard?
Ans. lqr. 2na. .076.
5. What is the value of .71 of 4 ounces, troy?
Ans. 2oz.l6dwt. 19.2gr.
6. What is the value of .86 of cwt?
Ans. 3qr. 12 lb. 5oz. 1.92dr.
7. What is the value of .07 of a barrel of 32 gallons?
Ans. 2gal. l,92pt.
8. What is the value of .235 of a day?
Ans. 5hr. 3Smin. 24sec.
RULE OF THREE IN DECIMAL^.
Rule.
Stato as in whole numbers, only observing when
you multiply and divide, to place the decimal points
according to the rules of multiplication and division of
decimals.
examples.
1. If 6.4 lb. of coffee cost 1.22 dollars, what cost
25.61b. 6.4 : 25.6 ; : 1.22? Ans. $4 88 cents.
2. If 1.4 lb. ot sugar cost .16 of a dollar, what will
30cwt. lqr. 22.5 lb. come to? Ans. $3S9.77l.+
130 involution; or raising op powers.
3. If I sell lqr. of cloth for $2,345, what is it per
yard? Ann. $9.38.
4. How many pirees of cloth at $20.8 pel' piece are
equal in value to 240 pieces at $12.6 per piece?
Ans. 145.38.-f-
5. How lone will 3 men he in performing' a piece of
work which will occupy 5 men for 40.5 days?
Ans. 67.5 days.
6. How much muslin .75 of a yard wide will lino
25,5 yards of clotty thai^ is 5 quarters wide?
Ans. 42.5 yhrds.
INTOLITTSOiY,
©R RAIS21TO ©F POWERS.
A power is the product produced by multiplying any
given number into itself a certain number of times.
Thus: 3x3=9 the square or second power.
3x3x3=27 the cube or third power of 3.
3x3x3x3x=81 the fourth power of 3, &c.
The number which denotes a power is called its in¬
dex. Any number multiplied by the same sum one
time, the product is its square. Thus, 2 by x2=4the
square of2, &c. Any number multiplied into its square,
the product will be the cube. Thus, 2x2x2=9 the
cube of 2. When any power of a vulgar fraction is
required, first raise the numerator to the required pow¬
er for a new numerator, and then raise the denomina¬
tor to the required power for a new denominator.—
Thus the third power of -!fx3X-?=
Ans. J*7 the required powers.
SQUARE ROOT.
131
TABLE OF THE FIRST NTNE POWERS.
1
o,
o>
7? '
QO
<o
J
CO
>8
C
ET
~
"Sr
p-
S"
p*
0 '
jS
3-
T
•d
"Z
•Jl
it
O)
Ss
o
%
%
§
U)
2
2
2
n
2
1
1
1
~~ 1
1
1
1
1
1
2
4
8
16
32
64
128
256
512
.>
9
27
81
243
729
2187
6561
19683
4
16
64
256
1024
4095
16384
65536
262144
5 25 125
625
3125
156ao
78125
590625
195s125
6,36 216
1296| 7776
46656
2799-6
1679616
10077696
7|49
34 >
24011168 ,7
117619
823543
5764811
40353607
8
64
512 4096 32768
729 6561 59049
267144
2.J97152 16777216
134217728
9|81
531441
4782969
43046721
387420489
EXAMPLES.
1. What is the square of 8? Ans. (>4.
2. What is the square of 9? Ans. 81.
3. What is the cube of 4? Ans. *54.
4. What is the cube) of 5? Ans. 125.
5. What is the cube or third power of .203?
Ans .(MS191447.
6. What is the Gth power of 2 8? Ans. 481.890304.
7. What is the 8lh power of J?
Ans. •g-y-J-3^-
The root of a number is that which will produce that
number by being multiplied by itself a given number
of times; thus: '2 is the square root of 4. because twice
2muke4; & 4 is the cube root of 64, because 4x4x4=
make 64, and so on.
SQUARE ROOT.
When the square root of any given number is re¬
quired
RULE.
Seperate the given number into periods of two fi-
132
Square root.
gureseach, begining at the units' place, find the great¬
est square contained in the left hand period, and set
its root ou the right of the given number. Subtract
said square from the left hand period, and to the re¬
mainder bring down the hext period for a dividend.—
2d. Double the root for a divisor, and try how often
this divisor is contained in the dividend, omitting the
last figure, and place the result to the right of the as¬
certained root; and to the right of the number pro¬
duced by doubling the ascertained root. Multiply and
subtract as in division; and bringdown the next pe¬
riod to the remainder for a dividend. Double the as¬
certained root, for a divisor, qnd proceed as before, till
all the periods are brought down.
Note.—if the square root of a whoTe number & decimal are
required, point the whole number from right to left; then be¬
gin with the decimal, and point from left to right; if there be
only one figure at the last, place a cipher to its right to make
an even period.
examples.
1. What is the square root of 451594?
45.15.84(Ans. 672 root.
36
127)91-5
899
1342)2684
2694
2. What is the square root of 106929?
3. What is the square root of 6.9169?
4. What is the square root of 393756?
5. What is the square root of 10.4976?
6. What is the square root of 18.3621?
7. What is the square root of 160000?
8. What is the square root of .250000?
9. What is the square root of 5?
Ans. 827.
Ans. 2.63.
Ans. 627+
Ans. 3.24.
Ans. 4.28+
Ans. 400.
Ans. .500.
Ans. 2.23+
sqture root.
133
Note.—When the square root of a vulgar fraction is re¬
quired, extract the square root of the numerator for a new
numerator, and the square root of the denominator for a new
denominator. If there be a remainder, either to the numera¬
tor or denominator, reduce the fraction to a decimal, and ex¬
tract the square root thereof; or if there be a mixed number,
reduce it to an improper fraction, and proceed as before.
10. What is the square root of Ifff? Ans.
11. What is the square root of ||«o? Ans.
12. What is the square root of Ans. |.
13. What is the square root of Ans. |.
14. What is the square root of 27T9g? Ans. 54*
15. What is the square root of 3<H? Ans. 5T5^.
16. A certain young man gave 484 apples to a num¬
ber of girls, each girl received as many apples as there
were girls; how many girls were there? Ans. 22.
17. A person being desirous to lay off 3 acres, 2
roods, 5 poles of land, in such a manner as to form a
square field, what must be the length of one of its
squares? Ans. 23.76 poles.-f-
18. The square of a certain number is 124600, what
is that number? Ans. 352.+
Notx.—To find the longest side of a right angled triangle.
Square each number, and extract the square root of their sum.
If the shortest side be required,- extract the square root of
their difference.
19, Suppose two men depart from Baltimore; one
>of them travels due east 90 miles; the other due north
40 miles; how far are they asunder?
Ans. 98.48 miles.+
30. Suppose a wall be 20 feet high, and be surround¬
ed by a creek 50 feet wide; how long must a line be to
reach from the top of the Wall to the opposite bank of
the creek? Ans. 53.85 feet.+
21. Said James to Joseph, I see a tree known to be
CUBE &00T.
^00 feet high, and from the spot where I stand it is 40-
feet to its root, but I demand the distance from where I
stand to it's top? An5, 107.70feet.
22. A Pertain castle which is 45 feet high, is surround¬
ed by a ditch 60 feet broad-. What lelugth must a ladr
der be to reach from thy outside ol^ the ditch to the top
of the castle? Ans. 75 feet.
23. What is the height of a steeple when a line 204
fpetlong will reach from the top of the steeple to the
opposite hank of a river known to by 41 feet broad?
A us. 190.83 feet.-f-
24. A certain geheraljiasan army of 5625 men; how
many must lie place -in ratili and file to form them into*
a square? Ans. 75 men.
25. Suppose a ladder1 60 feet long lip s > planted as'
tp reach a windodfr1 37 feet from thy ground on one side-
of the street, and without moving" if at thy fyot wilL
Teach p window 23 feet high on the ptlier side. What
is thy breadth of the street^ Anst. 102.64 feat*
CTRJS ROOT.
When the cube root of ppy hummer i* required,
RUl.K.
1st. pSeperate the given rt umber into periods of three
figures,each byginn'mg at'ihe urtits* place. 2nd. Find
the greatest yObe contained in the left hand period,
and set its root on the right of the given number. 3rd.
Subtract said cube from the left hand period; bring
down the next period to the remainder for a dividend,
4th. Square the root and multiply the square by 3 for
a defective divisor^ 5th. Try how often the defective
divisor is contained in the dividend, omitting the two
right hand figures, and place the number of times it is
contained to the right of the ascertained root, and its
square to the right of the defective divisor, supplying
the place of tens with a cipher, if the square be less
than 10, 6th. Multiply the last figure of the root by
CTlBJi BOOT,
135
all the figures in It previously ascertained; multiply
that product by 33; and acid their products to the divi¬
sor to complete it. 7th. Multiply and subtract, as ia
Division, bth. And to the remainder bring clown the
next period for a new dividend. 9th. Find a divisor
as before: and thus proceed until all the periods are
brought down.
Notb.—-When remainders occur annex ciphers for decimal
periods; and point dhcimuU as in the Square Hoot.
EXAMPLES,
1. What is the cube root of 10793S61? AnS. 221.
10793.861(221,
8
Defective divisor &, square of 2= 1204)279,1
-f"120=»complete divisor 1324)2048
Defective; divisor & square of 1=145201)145'.861
-f-660=compleie divisor 145861)145,861
2. Whatisthe cube root of 16191277? Ans. 253.
3. Whatisthe cube root of 5735339? Ans. 179.
4. What is the cube root bf 7552611? Ans. 196.+
5. What is the cube root of 12.113347? Ans. 2.29.4-
6. What is the cube root of .378821? Ans. .72.4-
Note.—-When the cube root, of a Vulgar fraction is requir¬
ed reduce it to i»s lowest terms, and extract the cube root of
the numerator and of the denominator. If there be a re¬
mainder to the numerator or denominator, reduce the fraction
to a decimal, and extract the cube root thereof. When mixed
numbers are given reduce them to improper fractions, or to a
•decimal, and proceed as before.
7. What is the cube root of | *°? Ans. ^
'8. What is the cube root of •/Tr4ff8ff Ans.
9. What is the cube root of 36f£? Ans. 3.32+
136
SINGLE POSITION.
10. There has been a cellar dug, out of which has
been taken 3456 cubical feet; what is the length,
breadth, and depth of it?
Ans. 15ft. 4-
POSITION.
Single position is used when it is required to make-
use of only one supposed number to find an unknown
numberj
RULE.
Suppose any number most suitable, and proceed
withitas if itwere the true one; setting down there-
suit, which is the first term; the given number the se¬
cond; the supposed number the third. Proceed by
Rule of Three. The quotient will be the number
sought.
EXAMPLES.
1. A person having about him a certain number
of dollars, said if a h a ip and a | were added togeth¬
er, the sum would he 90; how many had he?
12 (Supposed.)
120
40
30
20
9 :90 : : 12(Ans. @120. $90 proof.
2. A merchant received a number of dollars, said
i, f, £ and | of the number is 90; what number of
dollars has he? Ans. $75.
3. A. and B. having found a purse of money,
SINGLE JPOSITION. 1#7
disputed1 who should have it; A. said that and
^of it amounted to 35 dollars, and if B. could tell
him how much was ip it he shpdld have the whole,
orherwise he should hafe nothing; how4 much did
the purse contain?
Ans. $100.
4. A person alter spending ^ apd § of his moneys
had 26f dollars left, how ,much had he at first?
Ans- $160.
5. A certain sum of mohey is to be divided a-
rag 5 men in such a manner that A. shall-have
C^s, D. ^-g, and B. th&Temaincler, which is
40 dollars; what Js the sum?
JiXiS. $1001.
6. A gentleman hcipg jgiSKed his age, replied, if
the years of my life were dopbled and 4 of the pro¬
duct divided by 3, the^bsiilt would be 14; what was
his age?
Ans- 35 years.
7. In a certain web of clofh there is \ blue, $
black, and 9 yard,s white, how many yards are there
in the web? Ans, 54 yards.
8. A country clown, a lovely maid ad<Jress*d,
Whose wit and beauty charm'd his breast.
The youth, unskiil'd in numbers, Wish'd to know
The age of her he lov^d so.
The answer made, with a sarcastic air,
And manner, suited to the fair;
My age in years, if multiplied by three,
Two sevenths of that product thribble be,
The square root of the power ninth, which is four.
Tell me my age, or never court me more?
Ans. 14 years.
J
138
DOUBLE POSITION.
BOTEEE POSITION.
Double position teaches to find the true number by
making use of two supposed numbers.
rule.
Suppose two numbers most suitable, and work with¬
en eh according1 to the nature of the question, observ¬
ing the errors of the result. Multiply the errors Of each
operation into the contrary"supposed number. If the
errors be alike, i. e. both too much or both too little,
take their difference for a divisor, and the difference
of the products for a dividend; but if the errors be un¬
like, <that is, one too great and the other too small, take
their sum for atlivisor, and the sum of the products lor
a dividend. Proof as in Single Position.
examei.es.
1. A.B.undC. would divide $100 among them, bo¬
ss that A. may have 5 more than B. and B. 10 more
than O. The share of each is required.
Suppose A 50 Again suppose A 45
B 45 B 40
C 35 C 30
130 115
100 100
30 error too much. 15 error too much.
2d supposed No. 45 50 1st suppos'd no.
750
error 30
error 15
difference 15 15)600( r A 40,
B 35.
)600( r A 40,
600 Ans. < B 35.
CC 25.
»0
Proof. 100
2. A laborer engaged himself for50 days upon these
conditions: that for every day he worked he should
ALLIGATION.
159
receive one dollar; and that for eVery day he was idle
he should forfeit 50 cents. At settlement he received
$37 50 cents. How many days did he wprk, and how
many was he idle? Arts, worked 35, idle 15 days.
3. Bought cloth for a coat at $8 per yard, and linen
to line it at $L per yard. The number of yards \Vas
12, and the whole cost $42; how rpany yards were
thereof each? Ans. 6 yards each.
4. A fanner having driven his cattle to market, re-,
ceived for them all, $ j30; heing jiaid at the rate of $24
per ox, $16 per cow, and $6 per chlf. There were as
many oxen as cows, and four times as pinny calves;
how many were there of ettch?
An<*. 5 oXen, 5 cows and 28 calves.
5. A man wljqn driving sheep td market, was asked
where he was going with his score of sheep? who an¬
swered he had no scon; but if he had as many more,
half as many more and t wo sheep and a half, he would
have a score. How ipany had he?
Ans. 7 sheep.
A1LLI&ATION.
Alligation is a rule for mixing sipiples of different
qualities in such a manner that the composition may
be of a middle quality. When the quantity and rates
of the simples are given to Cnd the rate of mixture,
compounded of their simples.
Rdlb.
Find the value of each quantity according to their
respective costs; then divide their whole value by the
sum of the several quantities.
examples.
1, If 4 pounds at 20 cents per pound, 6 pounds at 25
eents; and 6 pounds at 30 cents per pound be mixed
together, what will a pound of the mixture be worth!-
140
ARITHMETICAL PROGRESSION.
lb. cts.
4 at 20= 80
6 at 25= 150
8 at 30= 240
18 18)470(Ans. 26 cents.4-
36
110
108
*2
2. If a person have 4 lb. of tea at 90 cents per lb., 8
lb. at 75 cents per lb., an J 6 lb. at 110 cents per lb., to
railx tftgether, what will a pound of the mixture be
tkrorth? A lis. 90 cents.
3. If 4oz. of silver worth 73 cents per ounce, be mel¬
ted with 8oz. worth 60 cents per oz., what will loz.
of the in'xture be woi th? Ans. 65 cents.
4. A fanner minted 20 bushels of wheat, at 50 cents
per bushel, 3'J bushels of rye at 40 cents per bushel,
with SO bushels of corn utx.0 c'cnts per bushel, what is
the worth of one? bushel of the mix tyre?
Ans.35^ cents.+
5. A grocer has 2ewt. of fcoflee at $25 per cwt.—
4cwt. at $20 50 eenia per cwt., and 7c\Vt. at $18 62J
cents per cwt., whiiih he w ill mix together; what will
lewt. of this mixture he worth? Ans. $20 lir£ Cents.
ARITHMETICAL FRH©RE§@ION;
Any rank or series of numbers increasing or de¬
creasing, is by a common difference in Arithmetical
Progression, as 1, 2, 3, 4, 5, 6:—6, 5, 4, 3, 2, 1;—1,
3,5, 7,9, 11;—11,9, 7,5, 3, 1. There are five things
to be particularly attended to in Arithmetical Progres¬
sion, the first and last terms; the number of terms; the
common difference, and the sum of all the terms.
ARITHMETICAL PROGRESSION. 141
Case 1*
The first tel*m. common'difference, and nuinbbr of
terms being given to find the last term and sum of all
the terms.
ROLE.
Multiply the number of terms less one, by the com¬
mon difference; to that product add the firstterm; the
sum is the last term. Add the first and last terms to¬
gether, artd multiply their sum by the number of terms,
and half the product will be the sum of all the terms.
examples.
I. What is the last term and sum of all the terms of
an Arithmetical Progression, whose firstterm is 2; the
common difference 4, and,number *>f terms 13.
number of terms 13—1^1,2 2-^-50=52 first & last terms,
common difference 4 13 number of terms.
48 156
first term. + 2 52
the last term. 50 2)676
Sum of all the terms. 338 Answer.
2. A man sold 40 yards of linen at 2 cents for the
first yard, 4 cents for the second, increasing 2 cents ev¬
ery yard; what did they amount to? Ans. $16 40cts.
3. Uought 15 yards of lirteo. at 2 cents for the first
yard, 4 cents for the second, 0 cents for the third, &c.
increasing' 2 cents every yprd; what was the cost of
the last yard, and what was the cost, of the whole?
Ans. The last yd. cost 30ets.— the whole $2 40cts.
4. Twenty persons gave charity to a poor woman;
the first gave 6 cents, the second 8 cents, and so on ip
arithmetical progression; how muqh did the last per¬
son give, and what sum did the woman receive?
Ans. The last person gave 44cts.—she received S5,
5. A man on a journey travels the first day 10 miles.
142
ARITHMETICAL PROGRESSION
the second 14 miles, increasing14 miles every day: how
many miles did he travel the tenth day, and bow many
miles did he travel jn all?
Ans. Tenth day 46 miles—in all 280 miles.
6. Suppose a numbei* of stones were laid ayard dis¬
tant from each other for the spare of a mile; and the
first a yard from a basket; what length of ground will
that man travel over who gathers them Up singly re¬
turning with them one by one to the basket?
Ans. 1761 miles.
Cask 2.
When the two extremes and the number of terms arc
given to find the cbinmou din -rence.
rule.
Subtract the less extreme frotp the greater, and di¬
vide the remainder by one less than the number of
terms; the quotient will bd the common difference-
examples.
7. The extremes beirtg 20 and 40: and the number of
terms 6; what is the Common difference?
Number of terms 6 40) 17, .
l oq f i-xtiemw.
One less 5 5)20
Ans. 4 Common.
8. A man had 10 sons whose several ages differed
alike; the youngest was 3 years old, and the eldest48;
what was the common difference of their ages?
Ans. 5 years.
9. 'A man is to travel from'Boston to a certain place
in 9 days, and to go but 5 miles the first day, increas¬
ing every day by an equal excess, so that the last day's
GEOMETRICAL PROGRESSION.
143
journey may be 37 miles. Required thn daily increase.
Ans. 4 miles.
10. A man received charity from 10 different persons;
the first gave him 4 cents, the last 49 cents, in arith¬
metical progression; what was-the common difference,
and what did the man receive?
Ans. Received $2 65cts.—common difference Sets.
11. When a debt is paid at8 different payments, in
arithmetical progression, the first payment to be $21;
"the last $173; what is the Common difference, and
what each payment, and what was the whole debt?
Ans. Common difference $22—Second payment $43
—Third payment $05, &c.—-The whole gum $784.
Geometrical Progression is the increase of a series
of numbers by a common multiplier, or decrease by a
common divisor, as 4, 8, 18, 32, 64;—61, 32, 16, 8, 4.
The multiplier ©r divisor by vt'hioh any series is in¬
creased or decreased is called the ratio.
Cask.
To find the last term and sum of the series.
rule.
Raise the ratio to a power \vhose index is one less
than the number of terms given in the sum. Multi¬
ply the product by the first term, and that product by
the ratio. From this last product subtract the first
term, and divide the remainder by a number that is one
less than the ratio. The quotient will be the sum of
the series.
examples,
1,. If 1 buy 18 bushels of wheat, and pay 2 cents for
the first bushel, 4 fpr the second, 8 for the third, &«.,
*k>a bling to the last, how much must I pay?
144
GEOMETRIC!. PROGRESSION.
a
T3
a,
J5
Ratio 2, 4, 8, 16, 32, 64, 128,
IBS
1024
■256
128
16384 14(h power*
8 3rd power.
131072 17tti power.
2 First term.
262144
2 Ratio.
524288
2 First term.
Divide by Ratio 2 1=1)524286
Ans. $5242 86 cts.
2. A man taught school 21 days, and received for
the first day 1 cent, for the second 2, for the third 4, and
so on, until the last. What spm did he receive?
Ans. 20971 dollars 51 cents.
3. A gentleman whose daughter was married on a
new year's day, gave her »!1, promising to triple it on
the first day of each month in the year. What did her
portion amount to? ' Ans. $205720.
4. What sum would pwrchestrtt horse' with 4 shoes,
and six nails in each shoe, at £ of a cent for the first
nail, a half for the second, a cent for the third, &c.,
doubling to the last? Ans. $41943 03^ cts
5. A merchant sold 20 bushels of clover seed, at 1
COMPOUND INTEREST, BY DECIMALS. 145
eent for the first bushel, '4 for the second, 16 for the
third, and so on; in quadruple proportion. What sum
did he receive, and how much did he gain by the sale,
supposing he gave $5 per bushel for the seed!
&na $ $3665038759 25 ctg. sum received.
An8, I $3665038659 25 cts. gained.
COMPOUND INTEREST, BY DECIMALS.
The ratio in Cohnpound Interest is the amount of 1
dollar for 1. year, which is found as follows:
100 : 104 : : t (101 amount for 1 year at 4 per ct.
Note.-—"ffte 4th root of the ratio will be the quarterly a-
mount—Tl(e square root the half yearly amount—and the pro¬
duct arising from the ha)f yearly and quarter yearly multipli¬
ed together, the three quarter yearly ^mount, as follows:
Thus# %/!.04=1.009353 quarterly amOunt; and
*\/l 04=1.019804 half yearly amoUht; then 1.0C9853X
1.019804=1.029852, amount for 3 qrs. oC a year at 4 per
cent,
Note..—The 4th root is found hyextracting the square root
of the Square loot. The ^atio jnvpUed tp the power, whose
ipdex is the time, is, the amount of one dollar for that time, as a
square for two yeari, a cube for three yeuiJs, &©.
Thus: 1.01xA04x 1.04=1.124884, amount of 1 dollar
for three years, at 4 per cent.
When the ratio is io be involved tcryears an<Tquar¬
ters, the power for the -yea us-must he inultiplietlrtryTtiC"
quarterly amount. 1
Thus: 1.1910160x 1.014874=1.2TS4929, amount for 31
years, at 6 per cent.
The power of 1 dollal* may' also be obtained for
months a»d days, nearly, by adding the monthly sim-
*46 COMPOUND INTEREST, BY DttClMALS|.
pie interest of 1 dollar, or proper phrts thereof to the
amount of Ihe quarter next preceding the given time,
for what that time exceeds the shiu quarter, ps fol¬
lows:
Amount for ^ yean. f=1.029563; For 4J years,*=1.318873.
Int. of $1 for i mo* *=* .00530(1 —> .006000.
One sixth for 5 days. — .1)00833 ■— .000833.
For 7 months, 5 days=l.Q35396. for 4y.l0mp.5da.=l.324706.
T1BIE 1.
Amount of $1 for a year, $£ for Qifdrlcrd at Compound Iniereft
— ;— '-n-j ■ r nIr4-1 <—r-e—y—
Rate
pr ct.
Ratio.
For three
Quarters.
f
For two
Quarters.
Hlr—
For one
Qyarler.,
Simple Int
of $1 for
1 teonth.
3
1-03
1.023416
1.014889
1.007417
11.002500 '
n
1.030
1-026137
1.01734$
lr'J08637
.002917
4
1.04
1.029852
1.019304
,1.009853
*003333
4J
1.045
1,033563
1-022252
1 011065
.003750
5
1.05
1.037270
i-024695
1.012273
.004167
Si
1.055
1-P4097S
14)27132
1 013475
*004583
6
1.06
4.0^4671
1.029536
1 014674
.005000
61
1.065
1.048304
4.031988
1.015868
.005417
r
1.07
1,052053
1.034408
1.017058
.005833
COMPOUND INTEREST, V? DECIMALS. 147
TABLE 2.
Pfhewinir the amalmt of one dollar from one year to forty.
yr.|-i perceiu|4£ prcent[5 per ceiit|5£ pt* cei*t| 6 per cent
1.1.O40JOOO 1.0450000 1.0500000|1.055000u
2 1.0316000 1.0920250 1 1025000 1.1130250
S 1.1243640 1.1411661 1 157625U 1.1/42413
1.1698585 1 1925186 I 2155062 1.2388246
5 1.2166529 I 2461819 1.2762815,1.3069598
6 1.2653190 1 3022601 l.340'J956 1.3788426
7 1.3159317 1 3608318 1 4071004 1.4546789
1.3685690 1,4221006'1.4774554 1.5346862
1.4233118 1.4850951 1.4513232 1.6190939
1.4802442 1.552959 4 1.6238946 1 7081440
1.5394540 1.6228 >39 1.7103393 1.8920919:
1.60103211.69583141 79-58533 1.9012069
1.6650735 1.772196ill. 8856491 2.0057732
1 7316764,1 8519449,1 9790316 2 1160907
l.8009435jl.935282412.0789281'2.2324756
1.6729812 2.0223701)2.1828745 2.3552617
1.947901)5 2.1133768 2.292018 >'2.4848011
2.0258161 2 2084787 2 4 <66:92 2 6214652
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
2.10684912 3076693
2.191123112.4117140
2.2787680'2.5202411
2 3699187i® .6336 520
2 5260502 2 7656458
2.6532977,2 9177.563
2 785962",|3 0782329
2 92.52607(3 2475J57
2.4647155 2.7521663 3.0715237)3.4261502
2.563304ll2 8760138,3.2250999 3 604588
31 373T343241X91385744"53R9393F
32
33
34
35
36
37
38
39
40
2.6658363 3 00543413.3863549
2.7724697,3 1406790 3 5556726
2,8833635 3 2820095 3 7334563
2.9987033 3.4296999 3.S201291
3.1186514 3.5840354 4.1161356
3 2433975 3.7453181 4 3 219423
3.5Q&0537?i^09998i &
3.6481831 4 2740301
3.7943163 4.4663015
3.9460839 4.6573478
4.1030325 4 8773784
4.2680898 5 0968604
4.4388134
4.6163659
4.8010206
5.3262192
5 5658990
5.8163645
5.0031885
3.8133919
4.0231379
4,2443999
4.4778419
4 7241232
4.9839469*
5-12580671
4 T640444.^-Jti7?fiO8
5 8523600
5.2533473 6 1742398
5 5160152 6-5138230
5 7918101 6 8720832
6 0314069 7.2500478
63854772
6 7047511
7-0399887
7 6488004
8 0694844
8.513306C
1.060U0UO
1.1360000
1.1910160
1 2624769
1.3382256
1.4185191
1.5036302
1..5938480
1.68947.89
1 7908476
1 8982985
2.0121964
2.1329282
2 260y039
2 3965581
2 5403517
2 6927727
2.8543391
3.0255995
3.2071355
3.3995636
o. 6035374
3 8097496
4 0489346
4.2918707
4.5493829
4.8223459
5.1116867
5.4183870
5 7434912
6.0881007
6.4533867
678403]39y
7.2510253
7.6860868
8.1472520
8 6360871
91542523
9 7035074
10.2857178
148 COMPOUND INTEREST, BT DECIMAL'S.
Compound Interest is that in which the interest of 1
year is added to the principal, and that amount is the
principal for the second year, and so On for any num¬
ber of years.
Case 1.
The principal time and rate given to find the amount.
Rule.
Multiply the principal by the ratio involved to the
time, which may be taken from table 2, and the pro¬
duct will be the amount, from which subtract the prin¬
cipal for the compound interest.
examples. .
1. What is the compound interest and amount of
$300 for 3 years, at 5 per cent.
1.05x1.05x1.05=1.1576250
300
f $347.28.7.5000 amount.
Answer J
[ $47.28.7 interest.
2. What is the amount of $500 for five years, at ft
percent? Ans. $669.11.2.
3. What is the compound interest of $100 for four
years, at 5 percent? Ans. $21.55.
4. What is the amount of five dollars for 20 years,
at six per cent? Ans. $16.03.5.
5. What i^ the compound interest of 1(100 dollars
for thirteen years at six percent per annum?
Ans. $1132.92.8.
6. What is the n mount oftJO dollars for II years, at
6 per centl— ~ A~nfc.i$tM.i)l,.4m.-{-
7TWhat is the amount of 12 dollars for one half
year, at 6 per cent? Ans. $12*35.4.
case 2.
The amount, time and rate per cent given to find the-
principal.
COMBINATION.
149
rule.
divide the amount by the ratio involved to the time
in tyble 2.
examples.
l.YVhat principal pht to interest will amount to $400
in fiv^ years, at 6 per cent?
1.3382256)400:1)000000 Ans. $298.90.3.
S. VYhat principal put to interest will amount to
$1500 ii) 7 years,at 5$ per cent?,, Ans. $1031.15$.+
PERMUTATION.
Permutation is used to show how many ways thing's
may be varied in place or succession.
* "rule.
Multiply all th$ terms of the series continually, from
one to the giv^n number inclusive,, and the last product
will be the answer required.
examples.
1. In how many different positions can ten persons
place themselves round a table?
lx2x3x4x5x0x7x^X9x!0=Ans. 3628800.
2. The church it) Boston has 8 bplls; how many chan¬
ges may be rung op them? Ans. 40320.
3. In what time will a person make all the changes
that tbo first 12 letters of the alphabet admit of, al¬
lowing 15 seconds to each change, and 365£ days to a
year. Ans. 227y. 248da. 6h.
COMBINATION.
Combination is used to show- how many different
ways a less number of things can be combined out of
a greater, as hut of the figures 1, 2, 3, 4; fourcombi-
matoins, 12, 34 and 43 may be performed.
ISO
DUODECIMALS.
RULE.
Take a series proceeding from and increasing &
nnit up to the number to be Combined. Take another
series of as inan^ places decreasing by unity from the
number out of which the combinations are to be made.
Multiply the first continually for a divisor, and the last
for a dividend, the quotient will be the qnswer.
EXAMPLES.
1. IIovC many combinations of 4 persons i» 8?
1x2x3x4— 21 24}lfi8»(70Ans.
8x7x6'x 5=1880 108
2. How many combinations of 10 figures may be
made out of 201 Ans. 184756.
S. How many changes may be rung with 10 bells-
out of 20? Ans. 184756.
DUWDEClMLAXS.
Duodecimo's are parts of a foot; the denomination*
of which increase continually by 12. The denomina¬
tions are,
12 fourths ("") make 1 third.'"
12 thirds 1 second."
12 seconds 1 inch.in.
1.2 inches 1 foot. ft.
ADDITION OF DUODECIMALS.
RULE.
Proceed as in Compound Addition, observing to car¬
ry one for every 12.
DUODECIMALS.
151
EXAMFtRS.
ft.
in.
nt
w.
ft.
in.
M
*t
(1). 6
4
2
i
(2.) 40
7
i
9
6*
8
10
9
li
22
8
7
I
4
13
7
10
3
15
11
9
8
10
19
15
5
2
1
3
0
0
1
Ans. 49
2
3
5
Ans. 80
6
G
"7
9
3. Three planks measure as follows: 10ft. Sin.—14ft.
Cin.—17ft. 9ip. 2". How many leet Go they contain?
Ans. 4Si't. llin. 2"„
SUBTRACTION OF DUODECIMALS.
rut®.
Proceed as in Compound Subtraction, observing th«*
12s.
examples.
ft. in. ". ft, In. ".
(1.) 50 2 11 9 1 (2.) 400 8 7 11 0
17 5 10 11 4 387 9 6 1 4
Ans. 82 9 0 9 9 Ans. 12 11 1 9 8
3. If 19ft. lOin. be cut off from a board which con¬
tains 41ft. 7in., how much will be left? Ans. 21ft. 9in.
MULTIPLICATION OF DUODECIMALS.
Rule.
Set the multiplier in sucji a manner that the feet
thereof may stand under the lowest denomination of
the multiplicand; multiply and carry one for every 12
from one denomination to another; and take parts for
theinches as in Practice.
N»tk Feet multiplied by feet, give feet.
Feet multiplied by inches, give inches.
Feet multiplied by seconds, give seconds.
Inches multiplied by inches, give seconds.
Inches multiplied by seconds, give thirds.
Seconds multiplied by seconds, give fourths.
15?
DUODECIMAL*'
EXAMPLES.
1. Multiply 5ft. Gin. by 2ft. 4in.
in. fit. in.
4|||5 6
2
11 0
1 1G
Ans. 12ft. 10 in.
2. Multiply 54ft. lOin. by 5ft. 7in. Ans. 306ft. lin. 10.f
3. Multiply 9ft. 7in. by 3ft. 6in. Ans. 33ft. Gin. 6".
4. What are the contents of a door measuring1 in
length 6ft. 9in.3"., and in width 3ft. 5ih.?
Ans. 23flt. lin. 7''. 3"'.
5. A certairi partition isSlft. lOin. 4''. long, and 14ft,
7in. 5". high. How many yardst doqs it contain?
Ans. 132yd. 8ft. 7!n. 9". 7'". 8"".
6. If a floor be 79ft. Him by 38ft. llin.. how many
square feet are there in it? L An?- 3100ft. 4in. 4".
7t HoVir many square feet in a board 17ft. 7in. long,
and 1ft. 5in. ivide? ^ns. 24ft. lOin. 11".
8. What wiii he the expense of plastering the walls
of a room 8i't. Gin. high, qnd each of the four sides
16ft. 3in. long, ht 50 cents per square yard?
Ans. $8069.-f-
9. In 40 planks 13ft. long and8in. wide, how many
feet? Ans. 346$ft
10. In 49 planks 22ft. long and llin. wide, how many
feet? Ans. 988ft, 2in.
11. In 17 planks 12ft. long and5in. wide, how many-
feet? Ans. 85 feet.
promiscuous examples.
153
PROMISCUOUS EXAMM.ES.
1. How many bushels of corn at 22 cents per
bushel, can I have for 40 dollars.
Ans. 18lTt bu.
2. If a man's yearly income be $7777, how much
is it per day? Ans. $21 30cts. 6m.-f-
3. My agent sends me word he has bought goods
to the value of 500 dollars 54cts. tipoh my pccount;
what will his commission come to at 4 per cent?
Ans. 20 dollars Sets. 4-
4. A man had in his desk 2176 dollars 55 cents,
he drew out at one time 13 tfpilars 6-4- cents, at
another time 49 dollars 1 cent, and at another 61
dollars 211 cRy after which he deposited at onetime
88 dollars S8| cts.; how much had he in desk after
making the deposit?
Ans, $2142 1"4i-cents.
5. A. is 25 years old, B. 15 years older than A.
and C„ is 12 years older than B. The ages of B.
and C. are required?
Ans. B, 40y."C. 52y.
6. Sold 6 bales of cloth, 5 of which,contained 10
pieces each, and in each* piece were 28 yards; the
other hale contained 16 pieces, and in each piece
were 20 yards. How many pieces and how many
yards were there in all?
Ans. 66 pieces, & 1720yd.
7. If goods which cost 44 dollars, be sold for 62:
dollars, what is the gain per cent?
Ans. 4011 per cent.
K
154
PROMISCUOUS EXAMPLES.
8. If 4 of an ounce cost § of a dollar* what will
| of a pound cost?
Ans. $19 60 cts.
9. If f of a gallon cost 11 dollars, what will Tj of
a ton come to?
Ans. $610 90 cts. 9m.+
10. A person who wa? possessed of 4 of a store
sold l of his share fo)r 551 dollars 62p cents, what
was the whole store worth at that rate?
Ans. 4241 dollars 15£ centd.
11. What will 27cvvt. of iron come to at $4 56cts.
per cwt?
AOs. $123 12 cts.
12. If I buy 100 yards of cloth at 50 cents per
yard, at how much mid 1 sell it per yard to gain
*100 percent? Ans. $1.
13. Bought a quantity of goods for $400, and 5>
months afterwards sold them for $650. How much
per cent per annum was gained by the transaction?
Ans. 150 per cent.
14. What is the interest of $51 621 cts. for 2
years, 3 months and J13 days, at 7b per cent?
Ans. 8 84cts.+
15. IIow often would a wagon wheei turn round in.
rolling1 from Krtoxville to Baltimore; Suppose the dis¬
tance to be 600 miles; admitting the wheel be 5 feet in
•diameter? Ans. 201600 times.
16. Suppose a crib which contains corn in thb ears,
be 25ft. 4in. Jong, 8ft. 5in. wide, and lift. 2in. deep how
many bushels will it contain? Ans. 1190|bu.+
17. Suppose a coal bed be 15fTt. 2in. long, 3ft;. 5in.
wide, and 3ft. Sin. deep. Tell me how many bushels of
coal it will conjoin? Ans. 185| bu.+
18. A crib which contains corn in the ears is 20ft. 6
PkOMiSCUOtJS EXAMPLES.
155
iri. !dn<*; 10ft. lin. deep, and 5ft. lj,in. "wide: how maBy
bushels does it contain? Ans. 611^ bu.-{-
19. A man had $20, which he wished to lay out as
follows: via. in sugar at 10 cents, coffee at 14 cents, &
rice at 11 cents per pound; so as to have an equal quan¬
tity of each. How many pounds must he have?
Ans. 57^1^
20. A corn crib is 5ft. wide at the bottom, and 7ft.
wide at the top, tell me how wide it is oaan average?
Ans. G leei
21. When $25 are multiplied by $25, how much mo-'
ney is there in the product? Ans. $625
22. When $25 are multiplied by 25cts., how much
money is there lathe product? Ans. $6 25cts.
23. When 25 cents are multiplied by 25 cente, how
much money is there in the product? Ans. 6£ cents.
24. How much will 1SJ bushels of corn come to at
18£cts. per bushel? Ans. $3 51 cts. 5m.-|-
25. What will 2J pounds of beef come to at 2J cents
per pound? Ans. 6^ cents.
26. In 48 planks 8 inches wide and 10 feet long, how
many feet? Ans. 320 feet.
27. A house is 20 feet long, and 18 feet wide. How
many feet of plank will be required to cover the floor?
Ans. 360 feet.
28. What is the neat of a hog weighing 294 pounds
gross? Ans. 256| lb. neat.
29. If A can drink a pint of whiskey in 20 minutes;
B one in 30, and C one in 40; in what time can they
drink a pint, when all drinking together?
Divide by 20,30 &40. Suppose 120
3
4
6
13)120(Ans. 9_3_ mill.
117 13
156
PROMISCUOUS EXAMPLES.
Note.—In any question like the above, suppose any number
into which all the given numbers may be divided without any
remainder, then add together their quotients, by which sum
divide the same dividend. The quotient \vill be the answer.
Si). Three young ladies met at their neighbors'for.
the purpose of finishing1 a fine quit, ©aid MI can fin¬
ish it in six hours; said E I can do it in four hours;
said L I can do it in three hours; but we will all work
together. In what time con we finish the quilt?
Ans. I5 hour.
31. There is a cellar dug, that is 20 feet every way,
in length, breadth and depth. How many solid feet of
earth were taken out of it? Ans.SOOO feet.
32. How many bricks 0 inches long and 4 inches
wide, will pave a yard that is 300 feet long and 40 feet
wide? Ans. 4SCC0 bricks.
33. What sum will produce as much interest in live
years as $390 would in 8 years and 4 months?
Am*. $933£.
34. A guardian paid his ward $3090 for $201)fi, whic!^
h<3 had held in possession 8 years. What rate of inter¬
est did ho allow him? Ans. 5.
35. A owes B 1G0 dollars, payable in Sir months;
$150 in 4} months, and $204 in 5} months; but is wil¬
ling to make one payment ofthe Avhoie. In what time
should the payment be made? Ans. 4mo* 2Cdnys.-f-
04. In what time will any sum of money double it¬
self at 5 per cent simple interest? Ans. 20 years.
37. If B tan do a piece of work alone in 10 days,
and C can do it in 19 days, in what time cOn they
finish it, both working together? Ans. 6*|- days.
38. A Band C found a purse of money, containing
$60; whereof A is to have i, B and C i. What
will be'the share of each?
C A's share $27 69 cts. 2m.-{-
Ans. < B's share $18 46 cts. lm.-f-
( C's share $13 84 cts. 6m.X
PROMISCUOUS EXAMPLES.
157
39. A and B traded together; A putin 320 dollars for
five months; B put in 480 dollars for 3 months; and
they gained 100 dollars. What was each man's share
40. WThat is the difference between the interest of
$1000 at 6 per cent for 8 years; and the discount of the
same sum for the same time, and at the same rate of
interest?
Ans. the int. exceeds the discount by $155 G7cts. 5m,
41. Said Dick to Harry, I can place four nines in
such a manner that they will make precisely an even
hundred. Can you do so too? Ans. 99|.
42. What is the sum of the third and half the third of
6^ cents? Ans. 3g cents.
43. How many dollars are there in £200 Tennessee
currency? Ans. $666 66f cents.
44. The clpcks of Italy go on to 24 hours. How
many strokes do they strike in one complete revolution
of the index? Ans.-300.
45. A line 40 yards, long \yill exactly reach from the
top of a fort standing on the brink of a river to the op¬
posite bank, known to be 25 yards from the foot of the
wall. What is the height of the wall? Ans. 31.22yds.
46. What is the value of a slab of marble the length
of which is 5ft. 7in. and the breadth 1ft. lOin. at $2 per
foot? Ans. $20 47cts.+
47. Shipped to New Orleans 4000 lb. cotton at 74cts.
per lb. and 513 yards of muslin at 62£cts. per yard; in
return for which I have received 37cwt. 3qr. of sugar
at 12^ cents per pound, and 44 pounds of indigo at 20
cents per pound. What remains due to me?
48. If the flash of a gun was observed just 1 minute
and 20 seconds before the report. What was the dis¬
tance, supposing the flash to be seen the instant of its
going off, and admitting the sound to fly at the rate of
1150 feet in a second? Ans. 17m.3fur.15p. 4yd.0ft.6in.
49. There is a certain pole^ f of which is in the wa-
of the gain?
Ans.
A's share $53 69cts. lm.-f-
B's share $46 30cts. 8m.-j-
Ans. $83 32J cts.
158
PROMISCUOUS EXAMPLES.
ter. £ in the mud, and 6ft. on dry ground. What is the
whole length of tho pole? ( Ans. 36ft.
50. When § of the number of an Assembly, and 15,
were inet, there were £ and 10 absent. How many
did that branch of the legislature consist of? Ans. 150.
51. Bought goods for $590. and sold the same imme¬
diately for $400. What was the loss per cent?
Ans. 20 per cent?
52. What is the interest of $15000000 for one minute
at 6 per dent per annum? Ans. $1 71 cts. 2m.-(-
53. If the earth be 360 degrees in circumferen6e, and
each degree 60 miles, how long would a man be in
travellinground it, who advances 40 miles a day, reck-
oning365i days a year? Ans. ly. 174da. 18hr.
54. Sold 12 yards of cloth dor $15 20cts. by which
was gained 8 per cent. What was the first cost of a
yard? Ans. $1 17cts. 2m.-}-
55. Bought 12 pieces of white cloth for $16 50cts.
per piece; paid $2 87cts. per piece for dying. For how
much must I Sell them each, to gain 20 per cent?
Ans. $23 24cts.4m.
56. When I, by disposing of a yard of cloth at $7f
gain 56£ cents, what would I gain by selling 3 pieces,
which cost me $400? Ans. $32 14icts.+
57. The yearly interest) of Charlotte's money at 6
per cent per annum exceeds ope twentieth part of the
principal by $100, and she does not intend to marry any
man who is not scholar enough to tell her fortune.-^-.
Pray what is it? Ans. $10000
58. There is a eistern having eight pipes to discharge
it. By the first it may be emptied iu ten minutes; by
the second in 20; by the third in 40; by the 4th in 80;
bythe 5th in 160; by the 6th in 320; by the 7th in 640,
and by the 8th in 1280. In what time will all eight run¬
ning together empty it? - Ans. 5-£T minutes.
59. In 140 planks, each 12 feet long and 9 inches
wide, how many feet? Ans. 1260.
60. At a certain quilting, $ of the girls are eating, £
of them cooking, and 5 at work; I would know how
many girls there are at the place? Ans. 30.
PROMISCUOUS EXAMPLES.
150
61. A hare starts 12 rods before a hound, but is not
perceived by him till she has been up 45 seconds. She
scuds away at the rate of 10 miles an hour, and the
dog on view, makes after at the rate of 16 miles an
hour. Howlong will the course hold, and what space
will be run over from the spot whence the dog started,
until the hare be overtaken? Ans. 2288ft. and 97j- sec.
62. Bought a watch at 10 per cent under its value,
and sold it at 10 per cent over its value, and by so doing
gained $10. How much was the watch worth?
Ans. $50.
63. Bought a horse and saddle for $100. The horse
•was worth seven times as much as the saddle. How
mnch was the horse worth, and how much was the
saddle worth? . 5 H. $37 50
Ans- ^ S. $12 50
64. A owes B 100 bushels of corn, the tub out of
which they expect to measure the same, contains Ibu.
lpe. lqt. lpt> How often must it be tilled to make the
100 bushels? Ans. 77T9T.
65. A and B bought 200 acres of land in partnership,
'for which they paid $600; each paying $300. On divi¬
ding the land A agreed totakeoif of the better end at
■$3 25 per acre, and B off of the other end at $2 75 per
acre; how many acres will each have? •
Ana 5 A 91f acres.
Ans' I B lOSg- acres.
66. If 20 dogs'for 30 groats go 40 weeks to grass,
how many hounds for 60 crowns can winter in that
jplaoe? Ans. 3,000 hounds.
Note A groat ip 4». .or is.
Note.—A crown is 5s.
iNoti.—Count 12 weeks the winter.
CONTENTS.
NtTMERATioJr, - *• .... PAGE 9
Addition, - - * - 10
Multiplication, - 12
Subtraction, - - » r . . . 17
Short Division, - - ..... 19
Long Division, - ...... 20
Tables of Money, Weights and Measures, - 24
Compound Addition, - - 27
Compound Multiplication, ..... 34
Compound Subtraction, ...... 41
Compound Division, ...... 46
Reduction Descending, 49
Reduction Ascending, ...... 53
Rule of Gauging, - - 57
Rule of Two, ....... 63
Rule of Three, 67
Double Rule of Three, ...... 72
Practice, 75
Interest, ----.-7.- 79
Brokerage, --------- 89
Discount, 90
Tare and Tret, ........ 93
Equation, ........ 96
Barter, ......... 98i
Loss and Gain, ........ 109
Partnership, - - - - - - - - 103
Exchange, 105
Vulgar Fractions, - - - . - - - 112
Decimal Fractions, - 124
Involution, or the Raising of Powers, - , - - - 130
Square Root, * 1311
Cube Root, - ....... 134
Single Position, ....... 136
Double Position, - 138
Alligation, 139
Arithmetical Progression, 149
Geometrical Progression, 1 143
Compound Interest by Decimals, ... - - 145
Permutation, ------ 149
Combination, - - - ib.
Duodecimals, 150
Promiscuous Examples
ly their better feeling
jti3^they, said to each other,
our own business^in these mat-
not fall out Jby^fuT~way j—there is
to be done in "the woi^cf;—let us be up
q: master's btTsmesgj—on the grgai-j-ft
we may at least travel together."
well informed of every *sect
^ut of the question)
peats hfS
Did you neVv
much agaijpst Sectt
very charitable as
That thought a"
such enew"
feu''