UC-NRLF 
 
 . APPLETON & CO., New York. 
 
 
LIBRARY 
 
 OF THE 
 
 UNIVERSITY OF CALIFORNIA. 
 
 Received t^Jr . 189 n . 
 
 Accession No. (b 7 J~/ . Class No. 
 
APPLETOHS' MATHEMATICAL SERIES. 
 
 > A 
 
 PRIMARY ARITHMETIC 
 
 BT 
 
 G: P. QUACKENBOS, A. M., 
 
 AUTHOR OF 
 
 "AN ENGLISH GRAMMAR;" "FIRST LESSONS IN COMPOSITION;" "ADVANCED 
 
 COURSE OF COMPOSITION AND RHETORIC;" U A NATURAL PHILOSO- 
 PHY; 1 ' "ILLUSTRATED SCHOOL HISTORY OF THE UNITED 
 STATES J " " PRIMARY HISTORY OF THE UNITED 
 STATES J " ETC. 
 
 UPON THE BASIS OP THE WORKS OF 
 
 GEO. R. PERKINS, LL.D. 
 
 ^^ 
 
 \ 
 
 N 
 D. APPLETON AND COMPANY, 
 
 443 & 445 BKOADWAY. 
 
 1864. 
 
PREFACE. 
 
 This little book, the first of our Series of Arithmetics, presup- 
 poses no knowledge of numbers whatever. It tries to give a cor- 
 rect idea of their value, both absolute and relative, by treating 
 them concretely as well as abstractly from the very outset, pictorial 
 illustrations being freely used for that purpose. We have not 
 sought in its pages to go/ar, but to go thoroughly. It is therefore 
 i confined to the four fundamental operations, a very brief view of 
 fractions, the most important tables of moneys, weights, and meas- 
 ures, and easy exercises under them. These subjects, it is believed, 
 are so treated, as to make the young pupil think for himself, and to 
 lay the right kind of foundation for a mathematical course. One 
 thing is taught at a time, and great care has been taken to present 
 every thing in its proper place. It will be observed that through- 
 out the book slate exercises go hand in hand with mental opera- 
 tions. In the author's opinion, they are indispensable, from the 
 first, for inspiring the beginner with that interest in the subject 
 which is essential to success. 
 
 This book imposes no labor on the teacher, in the way of ex- 
 plaining orally, setting sums, &c. It is thought to contain in itself 
 all that is needed. The author would only ask those who use it to 
 be sure that every lesson is thoroughly mastered, before proceed- 
 ing to the next. Each principle presented, each table, should be 
 perfectly understood and memorized before leaving it, even though 
 it be necessary to repeat the lesson again and again. Time saved 
 by allowing a single lesson to pass unmastered, will be a tenfold 
 loss in the end. 
 
 Entered, according to Act of Congress, in the year 1863, by 
 
 D. APPLETON & CO., 
 
 In the Clerk's Office of the District Court of the United States for the 
 Southern District of New York. 
 
PRIMARY ARITHMETIC. 
 
 LESSON I. 
 
 Touch your head. How many heads 
 have you ? ONE. 
 
 Touch your eyes. How many eyes 
 have you ?. Two. 
 
 Touch the joints of your fore-finger. 
 How many are there ? THREE. 
 
 Touch the fingers of your left hand. 
 How many are there ? FOUK. 
 
 Touch the fingers and thumb of your 
 left hand. How many do they make ? FIVE. 
 
 When we say ONE, TWO, TTTKEE, FOUK, FIVE, 
 what do we do ? 
 
 Answer. We count. 
 
 Count five ; count four ; count three ; count 
 two. 
 
 What are one, two, three, lour, five, called? 
 Answer. Numbers. 
 
 Which is the smallest of these numbers ? 
 Which is the greatest of these numbers ? 
 
COUNTING. 
 
 LESSON II. 
 
 Count the birds on 
 this branch. How 
 many are there ? FIVE. 
 
 If another alights 
 on it, how many 
 will there be ? Six. 
 
 Ifanotherjoins 
 them, how many 
 will that make ? SEVEN. 
 
 If another 
 comes, how 
 many ? EIGHT. 
 
 One more 
 will make 
 
 * how many ? NINE. 
 And one 
 more, how 
 many ? TEN. 
 Count six ; count seven ; eight ; nine ; ten. 
 Which is greater, ten or five ? Two or six ? 
 
 "What do we use, to express numbers ? 
 Answer. Ten characters, called Figures. 
 
 Learn the names of these ten figures, and how 
 to make them neatly on your slate. 
 
 NAUGHT ONE TVTO THREE FOUR FIVE BIX SEVEN EIGHT NINB 
 
 / 2 
 
 / 
 
 I 
 
COUNTING. NUMERATION. NOTATION. 
 
 Count these rabbits. How many are there ? 
 How do we express ten with figures ? 
 Answer. By putting a naught after a one (10). 
 
 Learn the numbers, going up from ten : 
 Eleven // Fourteen /-/ Seventeen 
 Twelve /2 Fifteen /^ Eighteen 
 Thirteen /J> Sixteen /^ Nineteen / <? 
 Twenty . . . 20 
 
 Eead these numbers : 13 ; 7 ; 19 ; 11 ; 9 ; 2 ; 
 20 ; 12 ; 5 ; 16 ; 3 ; 10 ; 4 ; 18 ; 6 ; 15 ; 8 ; 17. 
 
 Write in figures, six ; ten ; three ; eighteen ; 
 eight ; twenty ; two ; twelve ; fourteen ; five. 
 
 What is the reading of numbers called? 
 Answer. Numeration. 
 
 What is the writing of numbers called? 
 Answer. Notation. 
 
COUNTING. 
 
 LESSON IV. 
 
 ISTow we have some marks in different rows. 
 Count those in each row. 
 
 The number of marks is given after each row ; 
 then come the written figures that represent this 
 number, then the printed figures. 
 
 I ONE </ 1 
 
 .Two -22 
 
 THREE 3 3 
 
 , FOUR ^ 4 
 
 FIVE & 5 
 
 Six ^6 
 
 SEVEN y 7 j 
 
 EIGHT <? 8 
 
 NINE y 9 
 
 TEN /^ 10 
 
 ELEVEN // 11 
 
 TWELVE /^ 12 
 
 THIRTEEN /c? 13 
 
 FOURTEEN -/ 14 
 
 | FIFTEEN ^ 15 
 
 || .... SIXTEEN /^ 16 
 
 Ml .... SEVENTEEN <// 17 
 
 [111 ... EIGHTEEN /<f 18 
 
 | 1 | | | ... NINETEEN // 19 
 
 | | | | | [ . . TWENTY 20 20 
 
 Which is greater, twenty or ten ? 11 or 18 ? 
 
COUNTING. 
 
 LESSON V. 
 
 Twenty-seven 27 
 Twenty-eight 28 
 Twenty-nine 29 
 
 Learn the twenties : 
 
 Twenty-one 21 Twenty-four 24 
 Twenty-two 22 Twenty-five 25 
 Twenty-three 23 Twenty-six 26 
 
 In the twenties, which figure remains the 
 same, and which does not ? 
 
 Answer. The left-hand figure remains the 
 same 2. The right-hand figure changes. 
 
 What comes after 29 ? Answer. Thirty (30). 
 
 Learn the thirties : 
 
 Thirty-one 31 Thirty-four 34 Thirty-seven 37 
 
 Thirty-two 32 Thirty-five 35 Thirty-eight 38 
 
 Thirty-three 33 Thirty six 36 Thirty-nine 39 
 
 What is the left-hand figure in all the thirties ? 
 Which figure changes ? 
 
 What comes' after 39? Answer. Forty (40). 
 
 Learn the forties : 
 
 Forty- one 
 Forty-two 
 Forty-three 
 
 41 Forty-four 44 
 42 Forty-five 45 
 43 Forty-six 46 
 Fifty .... 5 
 
 Forty-seven 47 
 Forty-eight 48 
 Forty-nine 49 
 
 
 Which 
 28 or 38? 
 
 is greater, fifty or forty ? 49 or 39 ? 
 26 or 17? 9 or 15? 15 or 30? 
 
 Count 
 
 from 1 to 50. Count from 20 to 1 
 
 backwards 
 
 ; twenty, nineteen, eighteen, &c. 
 
8 COUNTING. 
 
 LESSON VI. 
 
 Learn the numbers, going up from fifty : 
 
 Fifty 50 
 
 Sixty-seven 67 
 
 Eighty-four 84 
 
 Fifty-one 51 
 
 Sixty-eight 68 
 
 Eighty-five 85 
 
 Fifty-two 52 
 
 Sixty-nine 69 
 
 Eighty-six 86 
 
 Fifty-three 53 
 
 Seventy 70 
 
 Eighty-seven 87 
 
 Fifty-four 54 
 
 Seventy-one 71 
 
 Eighty-eight 88 
 
 Fifty-five 55 
 
 Seventy-two 72 
 
 Eighty-nine 89 
 
 Fifty-six 56 
 
 Seventy-three 73 
 
 Ninety 90 
 
 Fifty-seven 57 
 
 Seventy-four 74 
 
 Ninety-one 91 
 
 Fifty-eight 58 
 
 Seventy-five 75 1 Ninety-two 92 
 
 Fifty-nine 59 
 
 Seventy-six 76 
 
 Ninety-three 93 
 
 Sixty 60 
 
 Seventy-seven 77 
 
 Ninety-four 94 
 
 Sixty-one 61 
 
 Seventy-eight 78 
 
 Ninety-five 95 
 
 Sixty-two 62 I Seventy-nine 79 
 
 Ninety-six 96 
 
 Sixty- three 63 Eighty 80 
 
 Ninety-seven 97 
 
 Sixty-four 64 
 
 Eighty-one 81 
 
 Ninety-eight 98 
 
 Sixty-five 65 
 
 Eighty-two 82- 
 
 Ninety-nine 99 
 
 Sixty-six 66 
 
 Eighty-three 83 
 
 One hundred 100 
 
 How many figures does 100 contain ? 
 
 "What is the greatest number that can be ex- 
 
 pressed with two figures ? Answer. 99. 
 
 What is the greatest number that can be ex- 
 
 pressed with one figure ? Answer. 9. 
 
 Name in order the numbers between 1 and 
 
 100 that contain naught. 
 
 Ans. 10, 20, 30, 40, 50, 60, TO, 80, 90, 100. 
 
COUNTING. 
 
 LESSON VII. 
 
 Here is a factory ten stories high. How many 
 windows are there in each story ? 
 
 Count the windows in the two lowest stories. 
 How many do you find? How many rows of 
 10 each make 20 ? How many tens in 20 ? 
 
 Count the windows in the three lowest stories. 
 How many tens in thirty ? 
 
 Add another row of windows, and how many 
 do you find ? How many tens in forty ? 
 
 Count the windows in the five lowest rows. 
 How many tens in fifty ? 
 
 How many tens in 60 ? How many tens in 
 70 ? How many tens in eighty ? How many 
 tens in 90 ? 
 
 Count all the windows. How many are there ? ! 
 How many rows of 10 each make 100 ? How 
 many tens in one hundred ? 
 
10 UNITS. TENS. 
 
 LESSON VIII. 
 
 Learn this table : 
 
 20 is 2 tens. 
 30 is 3 tens. 
 40 is 4: tens. 
 50 is 5 tens. 
 
 60 is 6 tens. 
 70 is 7 tens. 
 80 is 8 tens. 
 90 is 9 tens. 
 
 Which figure shows the number of tens ? 
 Answer. The second, or left-hand figure. 
 
 What is the second place called ? 
 Answer. The place of tens. 
 
 What is the first, or right-hand place called? 
 Answer. The place of units. 
 
 Write down 22. What figures do you use ? 
 
 Have these twos the same value ? 
 Answer. ~No. The 2 in the second place is 
 ten times as great as the 2 in the first place. 
 
 Why is this ? 
 
 Answer. Because the 2 in the second place 
 denotes two tens, or twenty ; the 2 in the first 
 place denotes two units, or two. 
 
 What, then, is the effect of removing a figure 
 from the first place to the second ? 
 
 Answer. Its value is increased ten times ; 20 
 is ten times as great as 2. 
 
 Write down the numbers from 1 to 100. 
 
UNITS. TENS. 11 
 
 LESSON IX. 
 
 How do you write six tens ? 
 
 Ans. 6^ in the second place denotes six tens. 
 As there are no units, I put a after it 60. 
 
 How do you write six tens, one unit? 
 
 Ans. 6 in the second place denotes six tens ; 
 1 in the first place denotes one unit 61. 
 
 Head this number. Ans. Sixty-one. 
 
 How must a column of numbers be written ? 
 Ans. So that units may stand under units, and 
 tens under tens. 
 
 Write the following : Four tens, three units ; 
 nine tens, nine units ; three tens, seven units ; 
 eight tens, two units ; five tens, two units ; two 
 tens, five units ; one ten ; seven tens. 
 
 Read the numbers just written. 
 
 Mention the tens and units in the following 
 numbers, and then read them : 80 (eight tens, 
 eighty] ; 75 (seven tens, five units, seventy-five) ; 
 69 ; 93 ; 41 ; 28 ; 7 ; 50 ; 17 ; 32 ; 84 ; 22 ; 61 ; 
 14 ; 57 ; 46 ; 70 ; 11 ; 98 ; 23. 
 
 "Which is greater, a ten or a unit ? 
 
 How can you turn three into thirty ? 
 
 Count from 100 to 75 backwards. Count 
 from 50 to 20 backwards. 
 
 Write down in columns the numbers in order, 
 going backwards from 100 to 1. 
 
12 HUNDREDS. 
 
 LESSON X. 
 
 How much do 10 tens make ? 
 
 Ans. One hundred 100. 
 
 Which figure shows the number of hundreds ? 
 
 Ans. The third figure 1. 
 
 How, then, do we write two hundred? 
 
 Ans. By putting a 2 in the third place 200. 
 
 Learn the even hundreds : 
 
 One hundred 100 
 
 Two hundred 200 
 
 Three hundred 300 
 
 Four hundred 400 
 
 Five hundred 500 
 
 Six hundred 600 
 
 Seven hundred TOO 
 
 Eight hundred 800 
 
 Nine hundred ... 900 
 
 How many times greater is 1 in the third 
 place than 1 in the second place ? 
 
 Ans. Ten times ; 100 is ten times 10. 
 
 What is the effect, then, of removing a figure 
 one place to the left? 
 
 Ans. Its value is increased ten times. 
 
 Name the places, going from right to left. 
 
 Ans. UNITS, TENS, HUNDREDS. 
 
 Count from 100 to 200. Thus : One hun- 
 dred and one^ one hundred and two, &c. 
 
 Write the numbers from 100 to 200. Thus : 
 
 101 104 107 110 113 116 
 
 102 105 108 111 114 117 
 
 103 106 109 112 115 118, &c. 
 
NUMERATION. NOTATION. 13 
 
 LESSON XI. 
 
 What is Numeration ? 
 
 Answer. The art of reading numbers. 
 
 What is Notation ? 
 
 Answer. The art of writing numbers. 
 
 I 
 
 EXERCISE IN NUMERATION. 
 
 Read the following numbers : 
 
 198 
 
 912 
 
 15 
 
 853 
 
 4 
 
 909 
 
 611 
 
 1 
 
 268 
 
 309 
 
 200 
 
 88 
 
 82 
 
 79 
 
 41 
 
 470 
 
 224 
 
 625 
 
 703 
 
 816 
 
 526 
 
 6 
 
 36 
 
 64 
 
 434: 
 
 349 
 
 62 
 
 518 
 
 147 
 
 517 
 
 EXERCISE IN NOTATION. 
 
 Write these numbers in figures : 
 Eighty-three ; Fourteen ; Two 'hundred and 
 sixty ; Nine hundred and forty-eight ; One hun- 
 dred and nine; Twelve; Ninety-one; Seven 
 hundred and fifty-seven ; Thirty-four. 
 
 Three hundred and fifteen ; Seventy -two ; 
 
 Six hundred and twenty-four ; One hundred ; 
 
 | Four hundred and seven ; Eight hundred and 
 
 eleven ; Eighty-eight ; Five hundred and forty ; 
 
 Fifty ; Seven hundred and twenty ; Ninety-nine. 
 
 COUNTING. Count from 800 to 900. 
 
 
ADDITION. 
 
 LESSON XII. 
 
 Look at the picture. You see one chimney in 
 one part of the roof, and one chimney in another 
 part ; how many chimneys do you see in all ? 
 Count them. One and one are how many ?. 
 
 One sheep is feeding by itself, and two sheep 
 are feeding together ; how many sheep are there 
 in all ? One and two are . 
 
 One boy and three girls are walking. How 
 many in all are walking ? One and three are . 
 
 One dog is lying down, four dogs are running ; 
 how many dogs are there altogether ? One and 
 four are . 
 
ADDITION. 15 
 
 There is one window on one side of the house, 
 and five windows on another. How many win- 
 dows are there altogether ? One and five are . 
 
 There is one girl jumping the rope, and six 
 girls not jumping it. Plow many girls are there 
 in all? One and six are . 
 
 On the lawn we see one boy and seven girls ; 
 counting the boy and girls together, how many 
 are on the lawn? One and seven are . 
 
 One tree stands on one side of the house, and 
 eight trees on the other. How many trees do 
 you count altogether ? One and eight are . 
 
 One chicken by itself, and nine chickens in a 
 group ; how many chickens in all ? One and 
 nine are . 
 
 One hen and ten chickens ; counting hen and 
 chickens together, how many do you find ? One 
 and ten are . 
 
 "What yon have just answered, will now be 
 put in a table. Learn it perfectly. 
 
 1 and 1 are 2. I 1 and 6 are 7. 
 1 and 2 are 3. 1 and 7 are 8. 
 
 1 and 3 are 4. 
 1 and 4 are 5. 
 1 and 5 are 6. 
 
 1 and 8 are 9. 
 1 and 9 are 10. 
 1 and 10 are 11. 
 
 
 
 When you put numbers together, to find how 
 much they make, what is the process called 2 
 A?is. Addition. 
 
16 
 
 ADDITION. 
 
 LESSON XIII. 
 
 TYTiatis Addition? 
 
 Ans. Addition is the process of uniting two 
 or more numbers in one. 
 
 "When you unite two or more numbers in one, 
 what do you find ? Ans. I find their Sum. 
 
 Two men are riding ; one is walking by their 
 side ; how many men does that make? Add 2 and 1. 
 
 Jane has two kittens ; her sister also has two. 
 How many kittens have both ? Add 2 and 2. 
 
 Jane had two dollars, and her father gave her 
 three more. How many had she then ? 
 
 Learn the Tables so as to say them forward 
 and backward, in order or skipping about. 
 
 2 and 
 2 and 
 
 are 3. 
 are 4. 
 
 2 and 3 are 5. 
 2 and 4 are 6. 
 2 and 5 are 7. 
 
 2 and 6 are 8. 
 2 and 7 are 9. 
 2 and 8 are 10. 
 2 and 9 are 11. 
 2 and 10 are 12. 
 
ADDITION. 17 
 
 LESSON XIV. 
 
 3 and 1 are 4. 
 
 3 and 2 are 5. 
 
 3 and 3 are 6. 
 
 3 and 4 are 7. 
 
 3 and 5 are 8. 
 
 3 and 6 are 9. 
 3 and 7 are 10. 
 3 and 8 are 11. 
 '3 and 9 are 12. 
 3 and 10 are 13. 
 
 [Let the pupil in all cases add each number as a whole, 
 and not "by counting or taking one unit at a time. Say three 
 and three are six ; not three, four, Jive, six.] 
 
 1. A regiment marched three miles before 
 dinner, and five miles after dinner. How far 
 did it march in all ? Add 3 and 5. 
 
 2. If you have 3 marbles in one pocket, and 
 7 in another, how many have you in both ? 
 
 3. Three horses are in the stable, and six are 
 in the field. How many horses in all ? 
 
 4. Ruth bought three books; she had ten 
 books before. How many has she now ? 
 
 Now you have some sums in addition to do 
 on your slate. Copy the figures in each column, 
 add them, and set down the sum below the line. 
 
 1127859 10 
 12331321 
 
 1 10 9 8 74 65 7 
 1 1 1 2 10 21 1 
 
 1 1 2 1 12 11 2 
 
18 
 
 ADDITION. 
 
 LESSON XV. 
 
 How many are 1 and 4? ->{ 'J'-/Hcvr 
 
 How many are 4 and 1 ? /Hcww w 
 
 How many are 2 and 4 ? 4 and 2 ? 
 How many are 3 and 4 ? 4 and 3 ? 
 When you are adding numbers, does it make 
 any difference which you take first ? 
 
 Here are four eggs in 
 one bird's-nest, four in 
 another; count how many 
 there are in both. Add 
 4 and 4. 
 
 Four kittens are running one way, and five 
 the other ; how many in all ? 4 and 5 make . 
 
 Four kittens and six rats ; how many do they 
 
 make together ? 
 
 How many are 4 and 6 ? 
 
 4 and 1 are 5. 
 4 and 2 are 6. 
 4 and 3 are 7. 
 4 and 4 are 8. 
 4 and 5 are 9. 
 
 4 and 6 are 10. 
 4 and 7 are 11. 
 4 and 8 are 12. 
 4 and 9 are 13. 
 4 and 10 are 14. 
 
SUMS IN ADDITION. 19 
 
 LESSON XVI. 
 
 1. Harry gets four good marks on Monday, 
 and seven more on Tuesday ; how many does he 
 get both days ? How many do 4 and 7 make ? 
 
 2. I have four fingers on each hand ; how 
 many have I on both ? What is the sum of 4 
 and 4? 
 
 3. If four cars leave in one train, and ten in 
 another, how many leave in both ? Add 4 and 10. 
 
 4. Ida had one pencil, then she bought three, 
 and the next day her father gave her seven more ; 
 how many had she then in all? 1, 3, and 7, 
 make how many ? 
 
 5. A toyman sold two dolls in the morning, 
 two in the afternoon, and nine in the evening ; 
 how many did he sell altogether ? 2 and 2 added 
 to 9 make how many ? 
 
 6. If I give four dollars for a vest, and eight 
 dollars for a coat, how much do both cost me ? 
 
 Do the following sums on your slate. Be 
 sure to set units under units, tens under tens. 
 
 Add twenty-three and thirty-four. Add one 
 hundred, twelve, and three hundred and forty- 
 three. Add forty -four to four hundred and one. 
 Add four and eleven. Add seventy-four and 
 two hundred and two. Add ninety-four and 
 three hundred. 
 
20 
 
 ADDITION. 
 
 LESSON XVII. 
 
 How many are one and five ? >( -JHH 
 How many are five and one 2 -JHHHH 
 How many are 2 and 5 ? 5 and 2 ? 
 How many are 3 and 5 ? 5 and 3 ? 
 
 Five lilies and four roses ; how many of both ? 
 
 Five boys are sailing in one boat, and five in 
 another. Count how many there are in both. 
 
 Five tops are lying on the floor, and six are 
 spinning ; how many do you see in all ? 
 
 How many are 5 and 7? 11111 1 1 I 1 1 I I 
 How many are 5 and 8? Mill I I Ml II I 
 How many are 5 and 9? Mill I Mill III 
 How many are 5 and 10? Mill M I I II 11 I I 
 "Which is the greater, five, or ten ? 
 
 5 and 1 are 6. 
 
 5 and 2 are 7. 
 
 5 and 3 are 8. 
 
 5 and 4 are 9. 
 
 5 and 5 are 10. 
 
 5 and 6 are 11. 
 
 5 and 7 are 12. 
 
 5 and 8 are 13. 
 
 5 and 9 are 14. 
 
 5 and 10 are 15. 
 
SUMS IN ADDITION. 21 
 
 LESSON XVIII. 
 
 1. Five years ago Mary was nine years old ; 
 how old is she now ? How much are 5 and 9 ? 
 
 2. We have five toes on each foot ; how many 
 toes have we in all ? What is the sum of 5 and 5 ? 
 
 3. Horace has five marbles in one bag, and 
 ten in another ; how many has he in both? Add 
 5 and 10. 
 
 4. Five pigs are in the orchard, and seven in 
 the sty. How many pigs are there altogether ? 
 
 5. Louise has three cents, Mary two, and 
 George eight ; how many cents have all three ? 
 
 6. Susan has four books ; if her brother gives 
 her one more, and her sister two, how many books 
 will she have ? Add 4, 1, and 2. 
 
 7. Richard caught five fish, and Ben six ; how 
 many did both catch ? How many are 5 and 6 ? 
 
 8. The first story of a house contains two 
 rooms, the second three, and the third three ; how 
 many rooms does the whole house contain? 
 
 Here are some sums for your slate. Read 
 each of the numbers added, and also the answers. 
 
 (10) (11) (12) (13) (14) (15) 
 
 4 403 927 8 5 765 
 14 515 20 610 372 121 
 51 30 32 41 112 102 
 
22 
 
 ADDITION. 
 
 ESSON XIX 
 
 How many are one and six? ->(- ->H 
 How many are six and one ? ->HHc"/ 
 How many are 2 and (3 ? 6 and 2 ? 
 How many are 3 and 6 ? 6 and 3 ? 
 How many are 4 and 6 ? 6 and 4 ? 
 How many are 5 and 6 ? 6 and 5 ? 
 
 Here we have six flies and six spiders, 
 and spiders, how many are there? 
 
 Flies 
 
 Six squirrels are eating, seven are running ; 
 count how many there are in all. 
 
 If you put six forks and eight forks together, 
 how many will that make ? 
 
 How many are 6 and 9? 1 1 I I 1 1 I I I I I 1 I 1 ! 
 How many are6 andlO? I 1 I I I I I I I 1 I I I 1 1 I 
 
 6 and 1 are 7. 
 6 and 2 are 8. 
 6 and 3 are 9. 
 6 and 4 are 10. 
 6 and 5 are 11. 
 
 6 and 6 are 12. 
 
 6 and 7 are 13. 
 
 6 and 8 are 14. 
 
 6 and 9 are 15. 
 
 6 and 10 are 16. 
 
SUMS IN ADDITION. 23 
 
 LESSON XX. 
 
 1. Troy is six miles above Albany, and Lan- 
 singburg is three miles farther ; how far is Lan- 
 singburg from Albany ? 6 and 3 make how many ? 
 
 2. If I have 6 dollars in my pocket, and 9 in my 
 purse, how much have I in all ? Add 6 and 9. 
 
 3. Three dogs, and three dogs, and three dogs, 
 make how many ? How many are 3, 3, and 3 ? 
 
 4. Two ships, four schooners, and ten brigs, 
 are in port ; how many vessels does that make in 
 all ? What is the sum of 2, 4, and 10 ? 
 
 5. A baker sold six loaves of wheat bread, and 
 two of rye ; how many loaves did he sell in all ? 
 
 6. Mary gave a poor man six cents, and Kate 
 gave him five; how much did he receive from 
 l3oth ? How much are 6 and 5 ? 
 
 7. If six horses are in the stable, and I put in 
 eight more, how many will be there then ? 
 
 8. Six goats and .one goat make how many ? 
 
 9. Six shoes in one drawer, and six in another, 
 make how many in all ? 
 
 Do these sums in addition on your slate : 
 
 (10) (11) (12) (13) (14) (15) 
 
 80 92 43 66 730 80 
 31 25 653 42 10 605 
 26 41 203 11 256 113 
 
 137 
 
24 
 
 ADDITION. 
 
 LESSON XXI. 
 
 How many are 1 and 7 ? 
 How many are 7 and 1 ? 
 How many are 2 and 7 ? 
 How many are 3 and 7? 
 How many are 4 and 7 ? 
 How many are 5 and 7 ? 
 How many are 6 and 7 ? 
 
 7 and 2 ? 
 
 7 and 3? 
 
 7 and 4? 
 
 7 and 5 ? 
 
 7 and 6? 
 
 Mary has a bunch of seven 
 cherries, and buys seven more ; 
 how many has she then ? Count 
 and see. 
 
 Seven boys and eight girls make how many 
 children in all ? How many are 7 and 8 ? 
 
 Seven wine glasses in one 
 row and nine in another 
 make how many in all? 
 How many are 7 and 9 ? 
 How many are 7 and 10? 1MI1M II II 111 II I 
 
 7 and 1 are 8. 
 7 and 2 are 9. 
 7 and 3 are 10. 
 7 and 4 are 11. 
 7 and 5 are 12. 
 
 and 
 and 
 and 
 and 
 
 6 are 13. 
 
 7 are 14. 
 
 8 are 15. 
 
 9 are 16. 
 
 7 and 10 are 17. 
 
SUMS IN ADDITION. 25 
 
 LESSON XXII. 
 
 1. To get home, I shall have to go seven miles 
 by steamboat, and five by stage; how far will I 
 have to travel ? What is the sum of 7 and 5 ? 
 
 2. A farmer had seven rooms in his house, and 
 built a wing with three rooms more ; how many 
 rooms had he then ? How many are 7 and 3 ? 
 
 3. A gardener set out three lilacs, four roses, 
 and ten verbenas ; how many plants did he set 
 out in all? Add 3, 4, and 10. 
 
 4. Mary dressed five dolls for the fair, Augusta 
 two, and Helen seven ; how many did all three 
 dress ? How many are 5, 2, and 7 ? 
 
 5. If my black hen has seven chickens, and 
 my white hen nine, how many have both ? 
 
 6. How far will a horse go in 2 hours, if he 
 travels Y miles the first hour, and 6 the second ? 
 
 7. How many are 6 and 4 ? 5 and 9 ? 4 and 
 7? 7 and 4? 7 and 2? 3 and 10? 2 and 8? 
 1, 6, and 1 ? 4, 3, and 8 ? 6, 1, and 6 ? 1 and 
 7 ? 6 and 3 ? 
 
 Here are more sums for your slate. Make 
 your figures neatly. Eead each number, and tell 
 whether the upper or lower one is the greater. 
 
 (8) (9) (10) (11) (12) (13) 
 
 163 329 48 856 775 507 
 425 670 731 132 11 182 
 
ADDITION. 
 
 LESSON XXIII. 
 
 How many are 1 and 8 ? ->(- wwwww 
 How many are 8 and 1 ? -X >HHHHH 
 How many are 2 and 8 ? 8 and 2 ? 
 How many are 3 and 8 ? 
 How many are 4 and 8 ? 
 How many are 5 and 8 ? 
 How many are 6 and 8 ? 
 How many are 7 and 8 ? 
 
 *8 and 3 ? 
 8 and 4 ? 
 8 and 5 ? 
 8 and 6 ? 
 8 and 7 ? 
 
 Eight doves in one group, and eight in another, 
 make how many in all ? How many are 8 and 8 ? 
 Eight rounds in one ladder, and 
 nine rounds in another, make how 
 many rounds in all ? What is the 
 sum of 8 and 9 ? 
 Eight spokes are in one 
 wheel, and ten in another ; how 
 many are in both ? 8 and 10 
 are . 
 
 8 
 
 and 
 
 1 
 
 are 
 
 9. 
 
 8 
 
 and 
 
 ' 6 
 
 are 
 
 14. 
 
 8 
 
 and 
 
 2 
 
 are 
 
 10. 
 
 8 
 
 and 
 
 7 
 
 are 
 
 15. 
 
 8 
 
 and 
 
 3 
 
 are 
 
 11. 
 
 8 
 
 and 
 
 8 
 
 are 
 
 16. 
 
 8 
 
 and 
 
 4 
 
 are 
 
 12. 8 
 
 and 
 
 9 
 
 are 
 
 17. 
 
 8 
 
 and 
 
 5 
 
 are 
 
 13. ! 8 
 
 and 
 
 10 
 
 are 
 
 18. 
 
SUMS IN ADDITION. 27 
 
 LESSON XXIV. 
 
 1. A lady bought eight cents' worth of needles, 
 and six cents' worth of thread ; how much did she 
 lay out ? How many are 8 and 6 ? 
 
 2. Eight birds are sitting on a bush ; if ten 
 more alight b$ their side, how many will there 
 be ? What is the sum of 8 and 10 ? 
 
 3. If I spend six dollars for clothes, two dol- 
 lars for books, and three dollars for groceries, how 
 much do I spend in all ? 6, 2, and 3, are . 
 
 4. Sarah has three rabbits, Ruth five, and 
 Herman seven. If Sarah and Ruth give theirs 
 to Herman, how many will he have ? Add 3 3 
 5, and 7. 
 
 5. If a dairy-maid makes eight pounds of 
 butter one day, and four the next, how many 
 does she make in all ? How many are 8 and 4 ? 
 
 6. How many boys will two benches hold, 
 if one holds eight and the other nine ? Add 
 8 and 9. 
 
 7. Add on your slate seventeen and eighty. 
 
 8. Add twenty to two hundred and twelve. 
 
 Read these numbers ; add them. 
 
 (9) (10) (11) (12) (13) (14) (15) 
 
 63 57 91 40 21 35 72 
 
 82 81 88 88 85 84 85 
 
 "145 157 
 
28 
 
 ADDITION. 
 
 How 
 How 
 How 
 How 
 How 
 How 
 How 
 How 
 How 
 
 LESSON XXV. 
 
 many are one and nine ? f ttttttttt 
 many are nine and one ? ttttttttt t 
 many are 2 and 9 ? 9 and 2 ? 
 
 9 and 3 ? 
 
 9 and 4 ? 
 
 9 and 5 ? 
 
 9 and 6 ? 
 
 many are 3 and 9 ? 
 many are 4 and 9 ? 
 many are 5 and 9 ? 
 many are 6 and 9 ? 
 many are 7 and 9 ? 
 many are 8 and 9 ? 
 
 9 and 7 ? 
 
 9 and 8 ? 
 
 stars in all ? 
 
 ^ ^ Nine stars in one 
 
 ^k^kf^i. group, and nine in an- 
 other, make how many 
 Count and see. 
 
 If there are nine cannon- 
 balls in one pile, and ten in 
 another, how many balls are 
 there in both ? What is the sum of 9 and 10 ? 
 
 A jeweller has nine watches in his safe, and 
 five on his counter ; how many has he in all ? 
 
 9 and 1 are 10. 
 9 and 2 are 11. 
 9 and 3 are 12. 
 9 and 4 are 13. 
 9 and 5 are 14. 
 
 9 and 6 are 15. 
 
 9 and 7 are 16. 
 
 9 and 8 are 17. 
 
 9 and 9 are 18. 
 
 9 and 10 are 19. 
 
SUMS IN ADDITION. 29 
 
 LESSON XXVI. 
 
 1. If Harry has nine dollars in the bank, and 
 four in his pocket, how much has he in all ? 
 
 2. A milkman sold one customer three quarts 
 of milk, another six quarts, and a third seven ; 
 how many quarts did he sell all three? What is 
 the sum of 3, 6, and 7 ? 
 
 3. Blanche has two canary birds, Rose seven, 
 and Alice three ; if Eose and Alice give theirs 
 to Blanche, how many will she then have ? 
 
 4. If one field yields nine bushels of potatoes, 
 and aixother ten, how much do both yield ? 
 
 5. If Frank gets nine good marks in the morn- 
 ing, and five in the afternoon, how many does he 
 get during the day ? How many are 9 and 5 ? 
 
 6. Nine currants on one string, and nine on 
 another, make how many currants in all ? 9 and 
 9 are how many ? 
 
 7. There are nine eggs in one hen's nest, and 
 six in another ; if we put the eggs together, how 
 many will there be ? What is the sum of 9 and 6 ? 
 
 8. What is the sum of 1, 8, and 2 ? 
 
 Read the following numbers. Add them. 
 
 (9) (10) (11) (12) (13) (14) 
 
 510 601 17 82 140 91 
 
 67 95 700 33 806 45 
 
 412 203 41 62 42 52 
 
30 ADDITION. 
 
 LESSON XXVII. 
 
 How many are one and ten ? 
 
 How many are ten and one ? 
 
 How many are 2 and 10 ? 10 and 2 ? 
 
 How many are 3 and 10 ? 10 and 3 ? 
 
 How many are 4 and 10 ? 10 and 4 ? 
 
 How many are 5 and 10 ? 10 and 5 ? 
 
 How many are 6 and 10 ? 10 and 6 ? 
 
 How many are 7 and 10 ? 10 and 7 ? 
 
 How many are 8 and 10 ? 10 and 8 ? 
 
 How many are 9 and 10 ? 10 and 9 ? 
 
 How many are two tens ? Ans. Twenty. 10 
 
 How many are ten and ten ? 
 
 You have eight fingers and two thumbs ; I 
 have the same. How .many fingers and thumbs 
 have we together? What is the sum of 8, 2, 
 and 10 ? 
 
 A dime is worth ten cents ; a half-dime is 
 worth five cents. How many cents are both 
 together worth ? How many are 10 and 5 ? 
 
 What is the sum of 7, 3, 'and 8 ? 
 
 What is the sum of 6, 4, and 3 ? 
 
 10 and 1 are 11. 
 
 10 and 2 are 12. 
 
 10 and 3 are 13. 
 
 10 and 4 are 14. 
 
 10 and 5 are 15. 
 
 10 and 6 are 16 
 10 and 7 are 17. 
 10 and 8 are 18. 
 10 and 9 are 19 
 10 and 10 are 20. 
 
THE EVEN THOUSANDS. 31 
 
 LESSON XXVIII. 
 
 What is the greatest number that can be 
 expressed with one figure ? 
 
 Ans. Nine (9). 
 
 If you add 1 to 9, what do you get ? 
 
 Ans. Ten (10). 
 
 What is the greatest number that can be 
 expressed with two figures ? 
 
 Ans. Ninety-nine (99). 
 
 If you add 1 to 99, what do you get ? 
 
 Ans. One hundred (100). 
 
 What is the greatest number that can be 
 expressed with three figures ? 
 
 Ans. Nine hundred and ninety-nine (999). 
 
 If you add 1 to 999, what do you get ? 
 
 Ans. One thousand (1000). 
 
 How many figures are used in writing 1000? 
 
 What figure shows the number of thousands ? 
 
 Ans. The fourth figure 1. 
 
 How, then, do we write two thousand? 
 
 Ans. By putting a 2 in the fourth place 
 
 Learn the even thousands : 
 
 One thousand 1000 
 
 Two thousand 2000 
 
 Three thousand 3000 
 
 Four thousand 4000 
 
 Five thousand 5000 
 
 Six thousand 6000 
 
 Seven thousand 7000 
 
 Eight thousand 8000 
 
 Nine thousand . . . 9000 
 
32 EXERCISE IN NOTATION. 
 
 LESSON XXIX. 
 
 Learn the even hundreds between 1000 and 
 2000 : 
 
 1100, one thousand one hundred, or eleven hundred. 
 1200, one thousand two hundred, or twelve hundred. 
 1300, one thousand three hundred, or thirteen hundred. 
 1400, one thousand four hundred, or fourteen hundred. 
 1500, one thousand five hundred, or fifteen hundred. 
 1600, one thousand six hundred, or sixteen hundred. 
 1700, one thousand seven hundred, or seventeen hundred. 
 1800, one thousand eight hundred, or eighteen hundred. 
 1900, one thousand nine hundred, or nineteen hundred. 
 2000, two thousand. 
 
 Write on your slate the numbers between 1000 
 and 1100, and then read them. Thus : 
 
 1001, one thousand and one. 
 
 1002, one thousand and two, &c 
 Write one thousand and ten. 1010. 
 Write two thousand and ten. 2010. 
 Write 1 thousand 2 hundred and ten. 1210. 
 Write 8 thousand 2 hundred and ten. 8210. 
 Write one thousand four hundred. 1400. 
 Write six thousand four hundred. 6400. 
 Name the places, going from right to left. 
 Ans. UNITS, TENS, HUNDREDS, THOUSANDS. 
 Read and then add the following numbers : 
 
 1024 1031 1059 1400 1099 
 2024 3031 4000 5000 1600 
 
NOTATION, NUMERATION. 33 
 
 LESSON XXX. 
 
 What place denotes thousands ? 
 Ans. The fourth place. 
 
 How do you write five thousands, nine hun- 
 dreds, seven tens, one unit ? 
 
 Ans. 5 in the fourth place denotes five thou- 
 sands ; 9 in the third place, nine hundreds ; 7 
 in the second place, seven tens ; 1 in the first 
 place, one unit. Thus we get 5971. 
 
 Read this number. 
 
 Ans. Five thousand nine hundred and seventy- 
 one. 
 
 Write the following, placing units under units, 
 tens under tens, &c. : Four thousands, 8 hun- 
 dreds, 6 tens, 2 units ; five thousands, 3 hun- 
 dreds, 1 ten, 1 unit ; nine thousands, 2 hundreds, 
 8 tens, 7 units ; seven thousands, 4 hundreds. 
 
 Eead the numbers just written. 
 
 Mention the thousands, hundreds, tens, and 
 units, in the following numbers : 4629 ; 9780 ; 
 5111 ; 1236 ; 7405 ; 2293 ; 529 ; 18. 
 
 When a naught stands in the third or second 
 place, must you say no hundreds, no tens f 
 
 Ans. No ; it is passed over in reading. Thus, 
 9007 is read nine thousand and seven. 
 
 Kead 7012 ; 6099 ; 3003 ; 8064; 1011; 5002. 
 
34: NOTATION, NUMERATION, COUNTING. 
 
 LESSON XXXI. 
 
 Write the following numbers with figures : 
 One thousand six hundred and fifty-three. 
 Five thousand nine hundred and eighteen. 
 Seven thousand eight hundred and ninety. 
 Three thousand five hundred and seven. 
 Eight thousand and forty-nine. 
 Eead the following numbers : 4321 ; 2906 ; 
 6870 ; 5012 ; 1864 ; 9990 ; 1007 ; 8700 ; 3401. 
 
 When we count, one, two, three, four, &c. 5 
 how do we get each number ? 
 
 Ans. By adding 1 to the number going before. 
 Now in stead of adding 1, add 2 each time : 
 
 1 7 13 19 25 31 37 
 
 3 9 15 21 27 33 39 
 
 5 11 17 23 29 35 41 
 
 and so on to 99. 
 
 In adding units, if the sum is 9, what do we do ? 
 
 Ans. We set down the 9 in the units' place. 
 
 If the sum is 10, what do we do ? 
 
 Ans. 10 consists of units, 1 ten. 6 
 Hence we set in the first or units' place, _^ 
 and 1 in the second or tens' place. 
 
 Whenever the sum consists of two figures, how 
 must we place them ? 
 
 Ans. Set the right-hand figure in the units' 
 place, the left-hand figure in the tens' place. 
 
CARRYING IN ADDITION. 35 
 
 LESSON XXXII. 
 
 Add the following numbers : 
 
 (1) (2) (3) ' (4) (5) (6) (7) 
 
 4: 5 8 7 9 4 9 
 3 4 1 31 11 
 2342211 
 
 1 2 3 4 5 6 7 
 
 26 Now look at this sum. Begin to add at 
 17 the right. 7. and 6 are 13 three units and 
 43 1 ten. "We set down 3 in the units' place, 
 and as there are other tens we add our 1 ten 
 in with them, making 4, which we set down in 
 the tens' place. Answer, 43. 
 
 What is this process called ? 
 
 Ans. Carrying. In the given sum, we carried 1. 
 
 When must we carry in addition ? 
 
 Ans. Whenever, in adding a column of fig- 
 ures, we find their sum is over 9. 
 
 What is the rule for carrying ? 
 
 Ans. Set down the right-hand figure, and 
 carry the left-hand figure to the next column. 
 
 If the sum of a column is 34, which figure 
 must be set down, and which carried ? 
 
 Ans. Set down 4, and carry 3. 
 
 What do you set down, and what do 
 carry, if the figures added make 96? If they 
 make 71; 80 ; 52 ; 11 ; 48 ; 84 ; 17/ 
 
36 ADDING COLUMNS ALOUD. 
 
 LESSON XXXIII. 
 
 Look at this sum. Learn to add each column 
 aloud, in the following manner : 
 
 1959 IST COLUMN. Two, five, six, eight, seven- 
 <j own 7 an d carry 1. 
 
 7 * 
 
 2o COLUMN. One, five, seven, ten, fif- 
 
 1342 ^ een se ^ down 5> an d Can 7 1- 
 rr^z 3o COLUMN. One, four, six, nine, 
 eighteen set down 8, and carry 1. 
 
 4'ra COLUMN. One, two, four, seven, eight, 
 nine set it down. 
 
 Answer, nine thousand eight hundred and 
 fifty-seven. 
 
 Add the following in the same way, not on 
 the slate, but aloud. 
 
 (1) (2) (3) (4) (5) 
 
 112 1270 1492 1666 374 
 
 22 321 2101 1022 311 
 
 332 2011 2121 232 1002 
 
 232 3322 1060 2432 2123 
 
 211 1346 2714 4212 5463 
 
 909 8270 9488 9564 9273 
 
 Commencing with 2, give the numbers formed 
 by adding 2 each time, up to 100. Thus : 
 
 2 6 10 14 18 22 26 
 
 4 8 12 16 20 24 28, &c. 
 
ADDING THREE. 37 
 
 LESSON XXXIV. 
 
 Do the following sums on your slate. Set 
 down the figure carried, beneath each column, 
 in the space left. 
 
 (1) (2) (3) (4) 
 
 1228 3222 1252 2122 
 
 1654 222 2202 1422 
 
 2343 2222 1942 1465 
 
 3421 3965 2749 4358 
 
 Carried 
 
 How much are 3 and 3 ? 3 and 13 ? 
 
 How much are 3 and 4 ? 3 and 34 ? 
 
 How much are 3 and 5 ? 3 and 45 ? 
 
 How much are 3 and 6 ? 3 and 66 ? 
 
 How much are 3 and 7? 3 and 87? 
 
 Which is greater, 900 or 700 ? 900 or 1000 ? 
 
 Which is greater, 1 hundred or 1 thousand ? 
 
 Commencing with 3, give the numbers formed 
 by adding 3 each time : 
 
 3 18 33 48 63 78 93 
 
 6 21 36 51 66 81 96 
 
 9 24 39 54 69 84 99 
 
 12 27 42 57 72 87 102 
 
 15 30 45 60 75 90 105 
 
 If I have 27 roses, and buy 3 more, how many 
 will I then have ? If some one gives me three 
 more, and I raise 3 from slips, how many will I 
 then have in all ? 
 
38 
 
 ADDING FOUR. 
 
 LESSON XXXV. 
 
 How many are 4 and 4 ? 4 and 14 ? 4 and 
 4and34? 4and44? 4and54? 4and64? 
 How many are 4 and 5 ? 4 and 75 ? 4 and 85 ? 
 How many are 4 and 6 ? 4 and 86 ? 4 and 96 ? 
 How many are 4 and 7 ? 4 and 47? 4 and 57? 
 
 
 Robert has 8 fish in his basket and 4 on the 
 grass ; how many has he in all ? How many 
 are 8 and 4 ? 18 and 4 ? 28 and 4 ? 48 and 4,? 
 
 How many are 4 and 9 ? 4 and 89 ? 34 and 9 ? 
 
 Commencing with 4, give the numbers formed 
 Thus : 
 
 by adding 4 each time. 
 
 4 
 8 
 
 12 
 16 
 
 20 
 24 
 
 28 
 32 
 
 36 
 40 
 44 
 
 48 
 
 52 
 56 
 60 
 64 
 
 68 
 72 
 76 
 80 
 
 84 
 88 
 92 
 96 
 
ADDING FIVE. 39 
 
 LESSON XXXVI. 
 
 How many are 5 and 5 ? 5 and 15 ? 5 and 
 25 ? 5 and 45 ? 
 
 How many are 5 and 6 ? 5 and 26 ? 5 and 
 
 36 ? 5 and 46 ? 5 and 56 ? 55 and 6 ? 5 and 
 66 ? 65 and 6 ? 
 
 How many are 5 and 7 ? 5 and 77 ? 
 
 How many are 5 and 8 ? 5 and 88 ? 
 
 How many are 5 and 9 ? 5 and 29 ? 25 and 
 
 9 ? 5 and 49 ? 45 and 9 ? 5 and 59 ? 5 and 69 ? 
 
 Commencing with 5, give the numbers formed 
 by adding 5 each time. Thus : 
 
 5 20 35 50 65 80 95 
 10 25 40 55 70 85 100 
 15 30 45 60 75 90 105 
 
 What do these numbers end in ? 
 
 1. John had twenty cents ; his mother gave 
 him five, and his father five more. How many 
 had he then? How many are 20, 5, and 5 ? 
 
 2. Forty-eight apples in one basket, and five 
 in another, make how many apples in all ? 
 
 3. A traveller rode thirty-nine miles one day, 
 and five miles the next. How far did he ride 
 both days ? Add 39 and 5. 
 
 4. I have just found five pins, said Eli, and I 
 had seventeen before. How many have I now ? 
 
40 ADDITION. 
 
 LESSON XXXVII. 
 
 How many are 6 and 6 ? 6 and 16 ? 46 and 6 ? 
 How many are 6 and 7 ? 6 and 27 ? 27 and 6 ? 
 
 How many are 6 and 8 ? 6 and 88 ? 38 and 
 6 ? 58 and 6 ? How many are 6 and 9 ? 6 and 
 99 ? 29 and 6 ? 
 
 How many are 7 and 7 ? 7 and 47 ? 87 and 
 7? How many are 7 and 8? 7 and 58? 28 
 and 7 ? How many are 7 and 9 ? 69 and 7 ? 
 
 How many are 8 and 8 ? 8 and 78 ? 18 and 
 8? How many are 8 and 9 ? 8 and 99? 68 
 and 9? 69 and 8 ? 
 
 How many are 9 and 9 ? 9 and 59 ? 79 and 9 ? 
 
 How many are 10 and 2 ? 40 and 2 ? 6 and 
 10 ? 6 and 60 ? 10 and 8 ? 90 and 8 ? 10 and 
 9 ? 9 and 100 ? 30 and 3 ? 
 
 1. There are twenty-nine girls in one class, 
 and eight in another ; how many in both ? 
 
 2. How many apple-trees have I on my farm, 
 if there are 27 in one field and 6 in another ? 
 
 3. A half dollar is worth fifty cents, and a 
 dime ten cents. How much are both worth ? 
 
 4. Nine pigeons join a flock of thirty-eight. 
 How many does the flock then contain ? 
 
 5. Sixteen roses in one bouquet, and eight in 
 another, make how many in both ? 
 
SUMS IN ADDITION. 41 
 
 LESSON XXXVIII. 
 
 Read the following numbers in turn. Add 
 aloud (not on the slate), as shown on page 36. 
 
 (1) (2) (3) (4) 
 
 546 145 834 689 
 
 3063 2083 1045 1989 
 
 789 1978 626 3754 
 
 4261 939 3997 1965 
 
 825 1987 1698 876 
 
 9484 7132 8200 9273 
 
 Now you have some sums for the slate. Be 
 sure to set units under units, tens under tens, &c. 
 
 1. Add ninety-nine; eighty-seven; fifty-six; 
 twenty-four ; and one hundred and eight. 
 
 2. Add four hundred and fifty ; nineteen ; 
 eight thousand six hundred and nine ; seven hun- 
 dred and twenty-three ; and eighty -four. 
 
 3. Add two thousand four hundred and 
 twenty-one ; nine hundred and eighty-seven ; 
 eighteen hundred and ninety-nine ; three thou- 
 sand and sixteen ; nine hundred and ninety-nine. 
 
 4. Add three thousand and eight ; nine hun- 
 dred and ninety ; seventeen hundred and fifty-six ; 
 five hundred and ninety-seven; two thousand 
 eight hundred and eighty-eight. 
 
 What is Numeration? What is Notation? 
 What is Addition? 
 
SUBTRACTION. 
 
 LESSON XXXIX. 
 
 the 
 away ; 
 
 Two pigeons were on 
 ground. One has flown 
 how many are left ? 
 
 Two cows were standing 
 near a pond. One of them has 
 gone into the water ; how 
 many are left on the bank ? 
 
 Take 1 from 2, and what is left \ 
 
 What is this process called ? 
 
 Ans. Subtraction. 
 
 What is Subtraction ? 
 
 Ans. Subtraction is the process of taking one 
 number from another. 
 
 When we count one, two, three, four, &c., 
 how do we get each number ? 
 
 Ans. By adding 1 to the number going before. 
 
 When we count backward, ten, nine, eight, 
 &c., how do we get each number ? 
 
 Ans. By subtracting 1 each time from the 
 number going before. 
 
 Count backward from 100 to 1. 
 
 1 from 1 leaves 0. 
 1 from 2 leaves 1. 
 1 from 3 leaves 2. 
 1 from 4 leaves 3. 
 1 from 5 leaves 4. 
 
 1 from 6 leaves 5. 
 1 from 7 leaves 6. 
 1 from 8 leaves 7. 
 1 from 9 leaves 8. 
 1 from 10 leaves 9. 
 
SUBTRACTION. 
 
 LESSON XL. 
 
 What is Subtraction ? 
 
 When we take one number from another, 
 what is the result called ? 
 Ans. The Remainder. 
 
 Three boys were riding. Two got out to 
 gather berries ; how many were left in the wagon ? 
 
 Four dogs ran barking after the wagon. Two 
 have turned back ; how many are left there ? 
 
 Five cows were standing in afield. Two have 
 lain down ; how many remain standing ? 
 
 2 from 2 leaves 0. 
 2 from 3 leaves 1. 
 2 from 4 leaves 2. 
 2 from 5 leaves 3. 
 2 from 6 leaves 4. 
 
 2 from 7 leaves 5. 
 
 2 from 8 leaves 6. 
 
 2 from 9 leaves 7. 
 
 2 from 10 leaves 8. 
 
 2 from 11 leaves 9. 
 
44 SUMS IN SUBTRACTION. 
 
 LESSON XLI. 
 
 Which of two numbers must we take from 
 the other, to find their difference ? 
 
 Ans. We must take the less from the greater. 
 
 1. Susan has six apples, and gives away two ; 
 how many has she left ? 
 
 2. If John has ten marbles, and loses one, 
 how many has he then? 
 
 3. A man having five sheep, sold one ; how 
 many remained unsold ? 
 
 4. Mary gives a beggar two cakes. She had 
 nine before ; how many has she left ? 
 
 5. If there are two boys in a class of seven 
 children, how many girls are in the class ? 
 
 6. 2 from 4 leaves how many ? 2 from 24 ? 
 2 from 54 ? 2 from 74 ? 
 
 7. Two from 6, how many ? 2 from 96 ? 
 
 8. Two from 8, how many ? 2 from 48 ? 2 
 from 78 ? 2 from 38 ? 
 
 Commencing with 50, give the numbers ob- 
 tained by subtracting 2 each time. Thus: 50, 
 48, 46, 44, 42, 40, 38, 36, 34, 32, 30, &c. 
 
 SUMS FOE THE SLATE. 
 
 From 
 Take 
 
 Remainder 
 
 (1) 
 
 98 
 12 
 
 (2) 
 
 891 
 120 
 
 (3) 
 
 437 
 121 
 
 (4) 
 
 1652 
 212 
 
 (5) 
 
 7234 
 2112 
 
 
 
 
 
 
SUBTRACTION. 
 
 LESSON XLII. 
 
 What is Subtraction? What is the answer 
 called in a sum in Subtraction ? 
 
 There are 4 panes of glass in this barn win- 
 dow. If 3 are broken, how many are unbroken ? 
 
 There were five sheep in the barn-yard, but 
 three have gone into the field. How many 
 remain ? Count them in the picture. 
 
 Nine chickens were on the ground ; 3 have 
 gone to roost. How many are left on the ground ? 
 
 3 from 3 leaves 0. 
 3 from 4 leaves 1. 
 3 from 5 leaves 2. 
 3 from 6 leaves 3. 
 3 from 7 leaves 4. 
 
 3 from 8 leaves 5. 
 3 from 9 leaves 6. 
 3 from 10 leaves 7. 
 3 from 11 leaves 8. 
 3 from 12 leaves 9. 
 
SUBTRACTION. 
 
 LESSON XLIII. 
 
 Take four oxen from four oxen, 
 and how many are left ? Cover 
 four over, and count the rest. 4 
 from 4 leaves how many ? 
 
 Take four eggs from a nest con- 
 taining five, and how many remain ? 
 Cover 4, and count the rest. 
 
 Here is a knife with six blades. 
 If 4 of them are closed, how many 
 are open ? 4 from 6 leaves how many ? 
 
 Here are seven flowers on one 
 stem, but four are broken ; how many 
 are unbroken ? 
 
 wwww JHHHr From eight stars take 
 four stars ; how many are left ? 
 
 A lady having nine 
 wine glasses, broke four 
 of them ; how many had she left ? 
 
 Four from ten leaves how many ? 
 
 4 from 4 leaves 0. 
 4 from 5 leaves 1. 
 4 from 6 leaves 2. 
 4 from 7 leaves 3. 
 4 from 8 leaves 4. 
 
 4 from 9 leaves 5. 
 
 4 from 10 leaves 6. 
 
 4 from 11 leaves 7. 
 
 4 from 12 leaves 8. 
 
 4 from 13 leaves 9. 
 
SUMS IN SUBTRACTION. 47 
 
 LESSON XLIV. 
 
 _. Three from 7 leaves how many? 3 from 
 17? 3 from 37? 3 from 67? Three from 8 
 leaves how many ? 3 from 88 ? 3 from 98 ? 3 
 from 28 ? 
 
 2. Three from 9 leaves how many ? 3 from 79 ? 
 
 3. Three from ten leaves how many ? Three 
 from twenty ? 3 from 30 ? 3 from 40 ? 3 from 50 ? 
 
 4. Commencing with 60, give the numbers 
 obtained by subtracting 3 each time. Thus : GO, 
 57, 54, 51, 48, 45, 42, 39, &c. 
 
 5. Twelve things make a dozen. If Jane 
 buys a dozen needles, and gives away 3, how 
 many does she keep? If she loses 3 of these, 
 how many has she then ? 
 
 6. A boy spends four cents ; how much has 
 he left, if he had twelve cents at first ? 
 
 7. Amy is four years younger than Lucy, and 
 Lucy is 13 ; how old is Amy ? 
 
 8. If there are eleven persons in an omnibus, 
 and three get out, how many remain ? If four 
 more get out, how many then are left ? 
 
 Eead these numbers. Set them down on 
 your slate. Subtract, and read the remainders. 
 
 (9) . (10) (11) (12) (13) 
 
 From 647 983 1085 4293 7658 
 Tuke 434 423 1043 4131 3343 
 
SUBTRACTION. 
 
 LESSON XLV. 
 
 Is 4 greater or less than 5 ? MM Mil! 
 Can we subtract five from four ? 
 Can we subtract five from five ? 
 
 If we take five dolls away 
 from five dolls, how many are 
 left ? Try and see. 
 
 Whenever we subtract a number from itself, 
 as 5 from 5, what is the remainder ? 
 Ans. Nothing, or naught 0. 
 
 Five marks from ten marks leave 
 how many marks ? Cover five, and 
 count the rest. 
 
 Five marks from twenty marks ^sna 
 leave how many marks ? 
 
 Five from thirty leaves how many ? fjil 
 5 from 40 ? 5 from 50 ? 5 from 60 ? 
 
 James had 6 books on his table ; 
 5 have fallen down. How many 
 are left on the table ? 
 
 ^NJl 
 '"H 
 
 5 from 5 leaves 0. 
 5 from 6 leaves 1. 
 5 from 7 leaves 2. 
 5 from 8 leaves 3. 
 5 from 9 leaves 4. 
 
 5 from 10 leaves 5. 
 5 from 11 leaves 6. 
 5 from 12 leaves 7. 
 5 from 13 leaves 8. 
 5 from 14 leaves 9. 
 
SUMS IN SUBTRACTION. % ^ 49 
 
 LESSON XLVI. 
 
 
 
 1. Thirteen persons were dining together. 
 Four got up and left ; how many remained ? 
 
 2. Maud is seven years old ; her brother is 
 five. Which is the older, and how much ? 
 
 3. A man who had fourteen cents in his 
 pocket, gave away all but five to beggars. How 
 much did he give away ? 
 
 4. Twelve persons were standing near a boiler 
 which burst. Two were killed, and three were 
 injured ; how many were unhurt ? 
 
 5. If I borrow eleven dollars, and payback 
 four, how many do I owe ? 
 
 6. Five from eight leaves how many ? 5 from 
 18 ? 5 from 28 ? 5 from 38 ? 5 from 48 ? 
 
 7. Five from nine leaves how many ? 5 from 
 69 ? 5 from 89 ? 5 from 79 ? 5 from 99 ? 
 
 8. If a boy who has thirty-seven hens, sells 
 four, how many has he left ? 
 
 9. A certain boat holds 19 persons. If five 
 are in it, how many empty seats are there ? 
 
 10. Five from 10 leaves how many ? 5 from 5 ? 
 
 SUMS FOR THE SLATE. 
 
 (1) (2) (3) (4) (5) 
 
 From 937 8165 4397 6028 5984 
 Take 425 5054 2154 4014 5234 
 
50 
 
 SUBTRACTION. 
 
 LESSON XLVII. 
 
 What is the smallest number that we can 
 subtract 6 from ? 
 
 How many does 6 from 6 leave ? 
 
 Look at these seven mice. Six 
 are running away ; how many 
 remain ? 
 
 Six from 7 leaves how many? 6 from 17? 
 6 from 27 ? 6 from 47 ? 6 from 67 ? 
 
 This wheel has eight spokes. Six of 
 them are whole ; how many are broken ? 
 Count and see. | 
 
 Six from 8 leaves how many ? 6 from 38 ? 
 6 from 58 ? 6 from 78 ? 6 from 98 ? 
 
 Take six forks away from nine 
 forks, and how many are left ? 
 
 /HHHc /HHHHHc Six stars from ten 
 stars leave how many stars ? 
 
 1 1 j ! 1 1 I I I I I Six marks from eleven marks 
 leave how many marks ? 
 
 6 from 6 leaves 0. 
 
 6 from 7 leaves 1. 
 
 6 from 8 leaves 2. 
 
 6 from 9 leaves 3. 
 
 6 from 10 leaves 4. 
 
 6 from 11 leaves 5 
 
 6 from 12 leaves 6. 
 
 6 from 13 leaves 7 
 
 6 from 14 leaves 8 
 
 6 from 15 leaves 9. 
 
SUBTRACTION. 51 
 
 LESSON XLVIII. 
 
 What is Subtraction ? What is the answer 
 called in a sum in Subtraction ? 
 
 What is the smallest number that we can 
 subtract 7 from ? 
 
 How many does seven from seven leave ? 7 
 from 27 ? 7 from 97 ? 7 from 57 ? 7 from 37 ? 
 
 Eight fingers on two hands. If 
 seven of them are held up straight, 
 how many will be bent down ? 
 How many does seven from eight leave ? 7 
 from 18 ? 7 from 88 ? 7 from 68 ? 7 from 48 ? 
 7 from 58 ? 
 
 Here we have nine rings 
 on a string. If you cover 
 7 with your hand, how many will you see ? 
 
 Seven from 9 leaves how many ? 7 from 79 ? 
 
 Ten bees are flying round a hive. 
 If 7 are on one side, how many are 
 on the other ? Count and see. 
 Seven from ten leaves how many ? 
 
 7 from 7 leaves 0. 
 
 7 from 8 leaves 1. 
 
 7 from 9 leaves 2. 
 
 7 from 10 leaves 3. 
 
 7 from 11 leaves 4. 
 
 7 from 12 leaves 5. 
 
 7 from 13 leaves 6. 
 
 7 from 14 leaves 7. 
 
 7 from 15 leaves 8. 
 
 7 from 16 leaves 9. 
 
52 SUMS IN SUBTRACTION. 
 
 LESSON XLIX. 
 
 1. There were thirteen lights in a street. Six 
 are blown out ; how many are left burning? 
 
 2. Plenry broke 7 teeth out of a comb. 
 How many teeth were left, if there were 27 at 
 first? 
 
 3. How many sugar-plums would you have 
 to put with nine, in order to make fifteen ? 
 
 4:. If a boy has eleven almonds, and eats all 
 but seven, how many does he eat ? 
 
 5. A blind man received eight cents from one 
 kind boy, and four from another. If he spent 
 six cents on his way home, how many had he 
 left? 
 
 SUMS FOR THE SLATE. 
 
 1. From ninety-seven subtract seventy-six. 
 
 2. Take six thousand and seventeen from 
 eight thousand three hundred and forty-eight ? 
 
 3. From five thousand and seventy -two take 
 three thousand and twenty-two. 
 
 4. A man having ninety-one dollars, bought 
 a coat for twenty dollars ; how much had he left? 
 
 5. A ship with six hundred and sixty-nine 
 passengers on board was wrecked. Four hundred 
 and sixteen escaped ; how many were lost ? 
 
 6. A gale swept over a garden containing 
 eighty-seven bean-poles. Seventy-six were blown 
 down ; how many remained standing ? 
 
SUBTRACTION. 
 
 53 
 
 LESSON L. 
 
 What is the smallest number that we can take 
 8 from ? 
 
 How many does eight from eight leave ? 8 
 from 108 ? 8 from 68 ? 8 from 18 ? 8 from 58 ? 
 Nine marbles were placed in the 
 centre of a ring. The first boy that 
 shot, drove eight away from the cen- 
 tre ; how many were left there ? 
 8 from 9 leaves how many? 8 from 29? . 8 
 from 99 ? 
 
 Ten trees were set out thus. If 
 8 afterwards died, how many re- 
 
 mained ? Cover 8 over, and count o o 
 8 from 10 leaves . 
 
 the rest. 
 
 Eleven spiders were on a wall, 
 but eiht have crawled down. How 
 
 many remain there? 
 
 leaves how many ? 
 Take eight rings away from 
 twelve rings, and how many will 
 be left? 
 
 8 from 11 
 
 oo 
 
 00 
 
 0000 
 0000 
 
 from 8 leaves 0. 
 
 from 9 leaves 1. 
 
 from 10 leaves 2. 
 
 from 11 
 
 from 12 
 
 leaves 3. 
 leaves 4. 
 
 8 from 13 leaves 5. 
 8 from 14 leaves 6. 
 8 from 15 leaves 7. 
 8 from 16 leaves 8. 
 8 from 17 leaves 9. 
 
54 SUBTR ACTION. 
 
 LESSON LI. 
 
 A 
 
 
 
 
 ama 
 
 
 
 
 
 
 
 
 Here is a frame with wires stretched across 
 it, and each wire runs through balls. 
 
 Count the balls on the top wire. How many 
 are there in all ? Now, if from these 10 balls, 
 we push away 9 to the right, how many are left ? 
 
 How many balls on the second wire ? Push 
 away 9, and how many are left ? 
 
 How many balls, on the third wire? Cover 
 9 with your finger, and how many do you see ? 
 
 How many balls on the fourth wire ? Cover 
 9 over, and how many can you count ? 
 
 How many balls on the fifth wire ? Cover 
 9 over, and how many are left ? 
 
 9 from 9 leaves 0. 
 9 from 10 leaves 1. 
 9 from 11 leaves 2. 
 9 from 12 leaves 3. 
 9 from 13 leaves 4. 
 
 9 from 14 leaves 5. 
 
 9 from 15 leaves 6. 
 
 9 from 16 leaves 7. 
 
 9 from 17 leaves 8. 
 
 9 from 18 leaves 9. 
 
SUMS IN SUBTK ACTION. 55 
 
 LESSON LII. 
 
 1. A jar of lard weighed seventeen pounds. 
 If the jar weighed eight pounds, what was the 
 weight of the lard ? 
 
 2. I bought a dozen eggs, but eight of them 
 were bad. How many were good ? 
 
 3. Sixteen boys went a skating. If nine of 
 them fell on the ice, how many escaped falling ? 
 
 4. A farmer had eighteen cows. Four of 
 them died, and he sold five ; how many were left? 
 
 5. Nine lemons fell from a tree on which 
 thirteen were growing. HQW many remained ? 
 
 6. A fisherman who had seventeen lobsters, 
 sold six in the morning and two in the afternoon. 
 How many had he left ? 
 
 7. A boy having fourteen dollars in the bank, 
 drew out all but eight. How much did he draw 
 out? 
 
 SUMS FOE THE SLATE. 
 (1) (2) (3) (4) (5) 
 
 From 18 873 5268 9145 8460 
 Take 9 721 1045 8043 6250 
 
 (6) (7) (8) (9) (10) 
 
 From 17 921 2397 5679 4396 
 Take 8 721 1163 4645 3291 
 
56 CARRYING IN SUBTRACTION. 
 
 LESSON LIU. 
 
 From 652 
 Take 379 
 
 Look at this sum. The lower number is the 
 smaller. Hence it can be taken from the upper. 
 
 Always begin to subtract at the right. 
 
 9 from 2. We can not take 9 from 2, because 
 9 is greater than 2. So we add 10 to the 2, 
 making it 12. 9 from 12 leaves 3. Set down 3 
 for the first figure of the remainder. 
 
 Now, to balance the 10 units just added to 3 
 in the upper line, add 1 ten to the 7 tens in the 
 lower line, making 8. Subtract 8. 
 
 8 from 5. We can not take 8 from 5. So 
 add 10 to the 5, making it 15. 8 from 15 leaves 
 7. Set down 7 for the second figure of the re- 
 mainder. 
 
 To balance the 10 just added to the 5 tens in 
 the upper line, add 1 hundred to the 3 hundreds 
 in the lower line, making 4. Subtract 4. 
 
 4 from 6 leaves 2. Set down 2 for the third 
 figure of the remainder. Answer, 273. 
 
 This process is called Carrying. 
 
 RULE FOR CARRYING IN SUBTRACTION. When 
 
 the lower figure is greater than the one above it, 
 add 10 to the upper figure, subtract, and carry 1 
 to the next lower figure. 
 
SUMS IN SUBTRACTION. 57 
 
 LESSON LIV. 
 
 SUMS FOE* THE SLATE. 
 
 (1) (2) (3) (4) (5) 
 
 From 752 8364: 9017 3429 8560 
 Take 479 2192 4108 3173 6936 
 
 (6) (7) (8) (9) (10) 
 
 From 416 5832 7411 8267 6059 
 Take 273 1988 4143 3179 3421 
 
 11. There were seven hundred and five fish 
 in a net. But, in drawing the net, ninety-six 
 were lost ; how many fish were caught ? 
 
 12. Charles bought some meat for thirty-nine 
 cents. He gave the butcher half a dollar (worth 
 fifty cents). How much change did he get ? 
 
 13. A man who had four thousand and ten 
 dollars, gave his son two thousand seven hundred 
 and eight dollars. How much did he keep ? 
 
 14. A farmer sold eight hundred and twenty- 
 five acres of land. How many had he left, if his 
 farm contained a thousand acres at first ? 
 
 15. Fanny had a present of a box containing 
 144 pens. If she used thirty-nine of them in a 
 month, how many had she left ? 
 
 16. A drover sold 87 head of cattle out of a 
 drove of 250. How many had he left? 
 
58 SUMS IN SUBTRACTION. 
 
 LESSON LV. 
 
 ' 
 MENTAL EXERCISES. 
 
 1. A car started with 40 passengers. At the | 
 first station, 10 passengers got off and 3 got on. 
 How many did it then contain ? 
 
 2. A rose-bush had 82 roses on it. The next 
 day, 6 of these roses fell to pieces, and 9 new ones 
 opened. How many were then on the bush ? 
 
 3. Leaving home with a hundred dollars in 
 my purse, I spent five for a vest, five for a coat, 
 and five for boots. How much had I left ? 
 
 4. Said Dick to Stephen, " Give me your nine 
 chickens, and I shall have seventy-eight." How 
 many chickens had Dick ? 
 
 5. A man rode 90 miles in 4 days. The first 
 day he went 70 miles ; the second day, 10 ; the 
 third day, 5. How far did he go the fourth day ? 
 
 6. Subtract the sum of 70, 10, and 5, from 90. 
 
 7. If Julia is twenty-three years old, and her 
 brother is twenty-nine, what is the difference in 
 their ages ? 
 
 8. Six, and five, and nine, and how many 
 more, make twenty-eight ? 
 
 9. A man who had twenty cents, met five poor 
 boys, and gave them each three cents. How 
 many cents had he left ? 
 
 10. From 20 take the sum of 3, 3, 3, 3, and 3. 
 
MULTIPLICATION. 59 
 
 LESSON LVI. 
 
 One bird, taken once, is one bird. 
 
 If we take one bird twice, we 
 have two birds. 
 
 If we take two birds once, we 
 have two birds. 
 
 If we take two birds 
 twice, how many birds 
 have we ?^ 
 
 What is taking a number one or more times 
 called ? 
 
 Ans. Multiplying. 
 
 Taking a number once is multiplying by 1. 
 Taking a number twice is multiplying by 2. 
 Taking a number 3 times is multiplying by 3. 
 
 Multiplying is a short way of doing what ? 
 Ans. Of adding a number to itself. Thus : 
 
 Twice 1 is 2. 1 and 1 are 2. 
 
 Three times 1 is 3. 1 and 1 and 1 are 3. 
 
 When we multiply, what is the result called ? 
 Ans. The Product. When we say Twice one 
 is two, 2 is the product. 
 
 What is Multiplication ? 
 Ans. Multiplication is the process of taking a 
 number a certain number of times. 
 
60 MULTIPLICATION. 
 
 LESSON LVII. 
 
 What does once mean ? 
 Ans. Once means one time. 
 
 One acorn, taken once, is one acorn. 
 'Once 1 is 1. If 1 is multiplied by 1, the 
 product is 1. 
 
 Two acorns, taken once, are two 
 acorns. Once 2 is 2. If 2 is multi- 
 plied by 1, what is the product ? 
 
 -/HHr How many do three stars, taken once, 
 make ? How much is once 3 ? If 3 is multiplied 
 by 1, what is the product ? 
 
 How many do four eggs, taken 
 once, make ? How much is once 4 ? 
 If 4 is multiplied by 1, what is the 
 product ? 
 
 Then, Once 1 is 1. Once 2 is 2. Once 3 is 
 3. Once 4 is 4. Once any number is the number 
 itself. 
 
 Learn the Table forward and backward. 
 
 Once 
 Once 
 Once 
 Once 
 Once 
 
 1 
 
 2 
 3 
 4 
 
 5 
 
 is 
 is 
 is 
 is 
 is 
 
 1. 
 
 2. 
 
 4:. 
 D. 
 
 Once 
 Once 
 Once 
 Once 
 Once 
 
 6 
 
 7 
 8 
 9 
 10 
 
 is 
 is 
 is 
 is 
 is 
 
 6. 
 7. 
 8. 
 9. 
 10. 
 
MULTIPLICATION. 
 
 61 
 
 LESSON LVIII. 
 SUMS FOK THE SLATE. 
 
 (1) 
 
 Multiply 98 
 By 1 
 
 (2) 
 
 150 
 1 
 
 (3) (4) 
 
 742 3018 
 1 1 
 
 (5) 
 
 6932 
 1 
 
 What does twice mean ? Ans. Two times. 
 If we take one bird twice, how 
 >many birds have we? How much 
 is twice 1 ? 
 If we take two birds 
 twice, how many birds 
 have we ? How much is twice 2 ? 
 
 /HHr If we take three stars twice, how many 
 >HKr stars have we? How much is twice 3 ? 
 
 What is the same as multiplying a number 
 by 2? 
 
 Ans. Adding the number to itself. 
 Twice 1 is 2. 1 and 1 are 2. 
 
 Twice 2 is 4. 2 and 2 are 4. 
 
 Twice 1 is 2. 
 Twice 2 is 4. 
 Twice 3 is 6. 
 Twice 4 is 8. 
 Twice 5 is 10. 
 
 Twice 6 is 12. 
 Twice 7 is 14. 
 Twice 8 is 16. 
 Twice 9 is 18. 
 Twice 10 is 20. 
 
62 MULTIPLICATION. 
 
 LESSON LIX. 
 
 0, taken any number of times, is still 0. 
 Twice is 0. 3 times is 0. 4 times is 0. 
 
 "Now you have some sums for the slate. Read 
 the numbers multiplied, and the products. 
 
 (1) (2) (3) (4) (5) 
 
 Multiply 34 121 520 4213 3004 
 
 By 2 2 2 2 2 
 
 6. How much is twice four hundred and three ? 
 
 7. Multiply two thousand one hundred and 
 eleven by two. 
 
 8. If two thousand three hundred and forty- 
 one is multiplied by two, what is the product ? 
 
 9. How much is once seventy-six ? 
 
 10. Multiply four thousand and thirteen by 2. 
 
 11. What is the product of one and two thou- 
 sand seven hundred ? 
 
 12. How much is twice five hundred and 
 thirty-two ? 
 
 13. Multiply twelve hundred by two. 
 
 3 times 1 is 3. 
 3 times 2 is 6. 
 3 times 3 is 9. 
 3 times 4 is 12. 
 3 times 5 is 15. 
 
 3 times 6 is 18. 
 3 times- 7 is 21. 
 3 times 8 is 24. 
 3 times 9 is 27. 
 3 times 10 is 30. 
 
MULTIPLICATION. 63 
 
 LESSON LX. 
 
 1. If a cord of wood costs five dollars, what 
 will three cords cost ? 
 
 MODEL. If 1 cord costs 5 dollars, 3 cords will cost 3 
 times 5 dollars, or 15 dollars. Answer, 15 dollars. 
 
 Do all the mental suras in Multiplication according to 
 this model. 
 
 2. What will two books cost, at a dollar each ? 
 
 3. How much will a clerk, who gets eight 
 dollars a week, earn in three weeks ? 
 
 4. At 10 dollars each, what will 2 desks cost ? 
 
 5. A man gave two beggars nine cents apiece ; 
 how much did he give them both ? 
 
 6. If one woman can make three dresses in a 
 week, how many dresses can three women make ? 
 
 7. I have two classes, .each containing seven 
 boys ; how many boys do both contain? 
 
 8. If a barrel of flour lasts a family nine weeks, 
 how long will three barrels last them ? 
 
 9. When oranges are worth two cents apiece, 
 and lemons one cent, what will I have to pay for 
 three' oranges and two lemons ? 
 
 4 times 1 is 4. 
 4 times 2 is 8. 
 4 times 3 is 12. 
 4 times 4 is 16. 
 4 times 5 is 20. 
 
 4 times 6 is 24. 
 4 times 7 is 28. 
 4 times 8 is 32. 
 4 times 9 is 36. 
 4 times 10 is 40. 
 
64 
 
 MULTIPLICATION. 
 
 LESSON LSI. 
 
 If one girl can pick five 
 quarts of berries in a morn- 
 ing, how many quarts can 
 four girls pick ? 
 
 MODEL. If 1 girl can pick 5 
 quarts, 4 girls can pick four times 
 quarts, or 20 quarts. Answer, 20 quarts. 
 
 2. There are four fingers on one hand ; how 
 many are there on four hands ? 
 
 3. How many days are there in four weeks, 
 there being seven days in one week ? 
 
 4. "What will 4 combs cost, at 10 cents apiece ? 
 
 5. If one horse eats 8 quarts of oats in a day, 
 how much will 4 horses eat at the same rate ? 
 
 6. A father gave each of his 4 sons 3 dollars ; 
 how much did he give them in all ? 
 
 7. If one stage holds 9 men, how many men 
 will 4 such stages hold ? 
 
 Commencing with 5, give the numbers formed 
 by adding 5 each time. Thus : 5, 10, 15, 20, 25, 
 30, &c. 
 
 5 times 1 is 5. 
 5 times 2 is 10. 
 5 times 3 is 15. 
 5 times 4 is 20. 
 5 times 5 is 25. 
 
 5 times 
 5 times 
 5 times 
 5 times 
 
 6 is 30. 
 
 7 is 35. 
 
 8 is 40. 
 
 9 is 45. 
 
 5 times 10 is 50. 
 
MULTIPLICATION. 65 
 
 LESSON LXII. 
 
 How much is 5 times 4? How much is 4 
 times 5? Which is the greater? 
 
 How much is 5 times 3 ? How much is 3 
 times 5 ? Which is the greater ? 
 
 In finding the product of two numbers, does 
 it matter which we multiply by ? 
 
 1. How many miles will a horse trot in 5 
 hours, if he trots 10 miles an hour ? 
 
 2. If Henry reads 5 books every week, how 
 many will he read in 5 weeks ? 
 
 3. What are 5 pounds of pork worth, at 9 
 cents a pound ? 
 
 4. How many trees are there in 5 rows, con- 
 taining 6 trees each? 
 
 5. Louise writes 2 pages every day ; how 
 many pages does she write in 5 days ? 
 
 6. There are 5 cages in the Museum, with 8 
 monkeys in each ; how many monkeys in all ? 
 
 7. Ned went 5 times to the station, and took 
 1 letter each time ; how many did he take in all ? 
 
 6 times 1 is 6. 
 6 times 2 is 12. 
 6 times 3 is 18. 
 6 times 4 is 24. 
 6 times 5 is 80. 
 
 6 times 6 is 36. 
 6 times 7 is 42. 
 6 times 8 is 48. 
 6 times 9 is 54. 
 6 times 10 is 60. 
 
66 MULTIPLICATION. 
 
 LESSON L2III, 
 
 How much is 6 times 2 ? How much is twice 
 6 ? Which is greater ? 
 
 Which is greater, 6 times 4 or 5 times 5 ? 
 Which is greater, 6 times 2 or 3 times 4 ? 
 
 1. Walking three miles an hour, how far will 
 a man go in six hours ? 
 
 2. If one box of tea lasts a family six months, 
 how long will six boxes last them ? 
 
 3. How many dollars are there in six bags, 
 containing seven dollars each ? 
 
 4. One eagle is worth ten dollars. How many 
 dollars are six eagles worth ? 
 
 5. How far will we get from Albany, sailing 
 6 hours in a boat that goes 9 miles an hour ? 
 
 6. Jane and her five sisters have each a canary 
 bird. How many birds have they all ? 
 
 7. How many flowers are there in 6 nosegays, 
 if each contains 8 flowers ? 
 
 8. Six pin-cushions, with five pins in each, 
 will contain how many pins in all ? 
 
 7 times 1 is 7. 
 7 times 2 is 14. 
 7 times 3 is 21. 
 7 times 4 is 28. 
 7 times 5 is 35. 
 
 7 times 6 is 42. 
 7 times 7 is 49. 
 7 times 8 is 56. 
 7 times 9 is 63. 
 7 times 10 is 70. 
 
MULTIPLICATION. 67 
 
 LESSON LXIV. 
 
 How much is 7 times 6 ? How much is 6 
 times 7 ? Which is the greater ? 
 
 How many times 7 is equal to 7 times 3 ? 
 
 Ans. 3 times 7. Both make 21. 
 
 What is equal to 7 times 5 ? To 7 times 4 ? 
 
 1. How many panes of glass are there in 7 
 windows, containing 8 panes each ? 
 
 MODEL. If there are 8 panes in 1 window, in 7 windows 
 there will be 7 times 8 panes, or 56 panes. Answer, 56 
 panes. 
 
 2. If a boy spends four cents a day, how much 
 will he spend in a week, which contains 7 days? 
 
 3. One fly has two wings ; how many wings 
 have seven flies ? 
 
 4. What will 7 rings cost, at 9 dollars each ? 
 
 5. How many sums will Ella do in seven days, 
 if she does seven every day ? 
 
 6. How many dollars in seven eagles, allow- 
 ing ten dollars to the eagle ? 
 
 7. How many boats pass a draw-bridge in 7 
 days, if five boats go through each day ? 
 
 8 times 1 is 8. 
 8 times 2 is 16. 
 8 times 3 is 24. 
 8 times 4 is 32. 
 8 times 5 is 40. 
 
 8 times 6 is 48. 
 8 times 7 is 56. 
 8 times 8 is 64. 
 8 times 9 is 72. 
 8 times 10 is 80. 
 
68 
 
 MULTIPLICATION. 
 
 LESSON LXV. 
 
 1. If these boys skate four miles an hour, how 
 many miles will they skate in 8 hours ? 
 
 2. Twice every day Fred and Frank come 
 with their sleds, to ride down hill. How many 
 times do they come in eight days ? 
 
 3. If it takes 3 hours to cut a ton of ice from 
 the pond, how long will it take to cut 8 tons ? 
 
 4. One day 8 sleigh-loads, of 9 persons each, 
 came to the pond ; how many persons was that ? 
 
 5. What will eight loads of evergreens cost, 
 at six dollars a load ? 
 
 9 times 1 is 9. 
 
 9 times 2 .is 18. 
 9 times 3 is 27. 
 9 times 4 is 36. 
 9 times 5 is 45. 
 
 9 times 6 is 54. 
 9 times 7 is 63. 
 9 times 8 is 72. 
 9 times 9 is 81. 
 9 times 10 is 90. 
 
MULTIPLICATION. 69 
 
 LESSON LXVI. 
 
 (1) (2) (3) (4) (5) (6) 
 
 Multiply 4:1 21 90 81 70 621 
 
 BJ 567894 
 
 205 2484 
 
 7. Which is greater, 9 times 4 or 7 times 5 ? 
 
 8. How many legs has one chair ? How many 
 legs, then, will nine chairs have ? 
 
 9. How many fingers has one boy? How 
 many fingers, then, will nine boys have ? 
 
 10. Ada's father gives her and her 8 brothers 
 6 cents each. How much does he give them all ? 
 
 11. I have five hens, and each hen has nine 
 chickens. Hens and chickens, how many have I ? 
 
 12. How much will nine turkeys weigh, if 
 their weight is eight pounds apiece ? 
 
 13. There are nine chains, each six feet long. 
 What is the length of the whole nine ? 
 
 14. How many gallons in 9 ten-gallon casks ? 
 
 Eepeat the even tens : 10, 20, 30, 40, 50, &c. 
 
 10 times 1 is 10. 
 10 times 2 is 20. 
 10 times 3 is 30. 
 10 times 4 is 40. 
 10 times 5 is 50. 
 
 10 times 6 is 60. 
 10 times 7 is 70. 
 10 times 8 is 80. 
 10 times 9 is 90. 
 10 times 10 is 100. 
 
70 MULTIPLICATION. 
 
 LESSON LXVII. 
 
 1 2 What is an easy way of multiply- 
 
 10 10 i n g a number by 10 ? 
 10 20 Ans. Placing a naught after it ? 
 
 1. Set down these numbers; multiply them 
 by 10 in the way just shown : 
 
 Eight hundred and forty-seven. 
 Six hundred and seventy-nine. 
 Two hundred and thirteen. 
 Seven hundred and five. 
 Thirty-three. Nineteen. Fifty-one. 
 
 2. Ten cents make a dime ; ten dimes make a 
 dollar. How many cents, then, in a dollar ? 
 How many cents are seven dimes worth ? 
 
 3. If you can buy two apples for a cent, how 
 many can you get for ten cents ? 
 
 4. Ann is five years old. If she lives to be 
 ten times as old, what will be her age? 
 
 5. How many quarts will ten jars contain, if 
 each holds three quarts ? 
 
 6. At 3 cents each, what will 10 oranges cost ? 
 
 7. There are nine inches in a quarter of a 
 yard; how many inches in ten quarters? 
 
 8. If for ten days you get four good marks 
 each day, how many do you get in all ? 
 
 Review all the Tables, from page 60, till you 
 can say them perfectly. 
 
CARRYING IN MULTIPLICATION. 71 
 
 LESSON LXVIII. 
 
 Multiply 734: 
 By 6 
 
 Look at this sum. Always begin to multiply 
 at the right. 
 
 6 times 4 is 24 4 units and 2 tens. Set 
 down the 4 units in the units' place, and carry 
 the 2 tens to the next product. 
 
 6 times 3 is 18, and the 2 tens carried make 
 20 tens or 2 hundreds. Set down in the tens' 
 place, and carry 2 hundreds to the next product. 
 
 & times 7 is 42, and the 2 carried makes 44. 
 Answer, 4404. 
 
 When must we carry in Multiplication ? 
 Ans. Whenever we obtain a product over 9. 
 
 What is the rule for carrying ? 
 
 Ans. Set down the right-hand figure, and 
 carry the left-hand figure to the next product. 
 
 If 36 is your product, which figure do you 
 set down, and which do you carry ? If 63 ? If 72 ? 
 
 Do the following sums aloud, just as the ex- 
 ample at the top of the page is done : 
 
 Multiply 863 638 742 914 
 
 By 4 5 7 9 
 
 3452 3190 5194 8226 
 
72 
 
 MISCELLANEOUS SUMS. 
 
 LESSON LXIX. 
 
 What is Numeration ? "What is Notation ? 
 What is Addition ? What is Subtraction ? 
 What is Multiplication ? 
 
 SUMS FOR THE SLATE. 
 
 (1) 
 
 (2) 
 
 (3) 
 
 (4) 
 
 (5) 
 
 Add 987 
 
 846 
 
 869 
 
 1752 
 
 789 
 
 236 
 
 155 
 
 456 
 
 990 
 
 2789 
 
 795 
 
 383 
 
 978 
 
 2671 
 
 789 
 
 121 
 
 353 
 
 519 
 
 2532 
 
 2789 
 
 143 
 
 625 
 
 780 
 
 898 
 
 1789 
 
 422 
 
 831 
 
 659 
 
 1098 
 
 339 
 
 (6) 
 
 (7) 
 
 (8) 
 
 (9) 
 
 (10) 
 
 From 96 
 
 410 
 
 863 
 
 1002 
 
 3507 
 
 Take 38 
 
 307 
 
 264 
 
 109 
 
 1238 
 
 
 (11) (12) 
 
 (13) 
 
 (14) 
 
 (15) 
 
 Multiply 
 
 81 72 
 
 39 
 
 160 
 
 263 
 
 By 
 
 3 6 
 
 2 
 
 8 
 
 4 
 
 
 (16) (17) 
 
 (18) 
 
 (19) 
 
 (20) 
 
 Multiply 
 
 72 90 
 
 85 
 
 698 
 
 549 
 
 By 
 
 5 10 
 
 7 
 
 10 
 
 9 
 
 
 
 
 
MISCELLANEOUS SUMS. 73 
 
 LESSON LXX 
 
 "What is the result, or answer, called in Ad- 
 dition ? "What, in Subtraction ? What, in Mul- 
 tiplication ? 
 
 1. What is the sum of four hundred and sixty- 
 one, five hundred and eighty-four, and seven 
 hundred and two ? 
 
 2. What is the product of eight hundred and 
 seventy -two, and nine ? 
 
 3. If forty-six is taken from eight thousand 
 and twenty-nine, what is the remainder ? 
 
 4. How many pages in nine books, if each 
 book has two hundred and eighty-eight pages? 
 
 5. One book has four hundred and fifty pages ; 
 another has two hundred and sixty-four. How 
 many pages have both books together? How 
 many more pages has one than the other ? 
 
 6. If a man reads forty -nine books every year, 
 how many will he read in ten years ? 
 
 7. A gardener set out a hundred and nineteen 
 trees every week for five weeks. If 95 out of 
 the whole number died, how many lived ? 
 
 8. Maud's uncle left his whole property to 
 her and her five brothers, giving them each one 
 thousand and fifty dollars. What was he worth 
 in all? 
 
 9. Multiply a thousand and twelve by eight. 
 
74 MULTIPLYING BY TWO FIGURES. 
 
 LESSON LXXI. 
 
 Multiply 509 by 18. Let us see how 
 509 we are to multiply by two figures. 
 
 Set down 18 under 509, units under 
 
 4072 units, tens under tens. 
 509 Begin at the right. 
 
 9162 8 times 9 is 72. Set down 2, and 
 
 carry 7. 
 
 8 times is 0, and 7 is 7. Set it down. 
 
 8 times 5 is 40. Set it down. The first 
 product, as you see in the sum, is 4072. 
 
 Now multiply by 1. 
 
 Once 9 is 9. Set it down in the same column 
 with the 1 by which you are multiplying. Once 
 is 0. Once 5 is 5. The second product is 509. 
 
 Now add the two products. Answer, 9162. 
 
 Always set the first figure of each product in 
 the same column with the figure by which you are 
 multiplying. 
 
 In finding the product of two numbers, multi- 
 ply by the one that has the fewer figures. 
 
 Do these sums aloud, like the one above : 
 
 Multiply 87 260 159 
 
 By 24 38 56 
 
 348 2080 954 
 
 174 780 795 
 
 Product 2088 9880 8904 
 
MULTIPLICATION. 75 
 
 LESSON LXXII. 
 
 When occurs in the number you multiply 
 by, how do you proceed ? 
 
 Ans. Bring down the 0, and go on multiply- 
 ing by the next figure, all in the same line. 
 
 Multiply 97 by 30. 97 
 
 Bring down the 0. Then multiply ^0 
 by 3, setting the result in the same line. 2910 
 
 3 times 7 is 21. Set down 1 under 
 the 3, and carry 2. 3 times 9 is 27, and 2 is 
 29. Answer, 2910. 
 
 What is an easy way of multiplying a number 
 by 100? 
 
 Ans. Placing two naughts after it. 
 
 How much does 57 multiplied by 100 make ? 
 
 Multiply 19 by 100. Multiply 100 by 19. 
 Which is the greater ? 
 
 What is the product of 65 and 100 ? 
 
 SUMS FOR THE SLATE. 
 (1) (2) (3) (4) (5) 
 
 Multiply 27 81 90 98 190 
 By 16 37 24: 95 26 
 
 (6) (7) (8) (9) (10) 
 
 Multiply 34: 57 68 90 43 
 By 20 89 50 100 100 
 
76 
 
 DIVISION. 
 
 LESSON LXXIII. 
 
 Two oxen make a yoke. How 
 many yoke will 4 oxen make ? 
 
 Ans. As many yoke as 2 is contained times 
 in 4, or 2. Answer, 2 yoke. 
 
 How many yoke will 6 
 oxen make ? 
 Ans. As many yoke as 2 is contained times 
 in 6, or 3. Answer, 3 yoke. 
 
 "What is finding how many times one number 
 is contained in another called ? 
 
 Ans. Dividing. Finding how many times 2 
 is contained in 6, is dividing 6 by 2. 
 
 What is meant by dividing 9 by 3 ? 
 
 Ans. Finding how many times 3 is contained 
 in 9. 
 
 "When we divide, what is the result called ? 
 
 Ans. The Quotient. Two is contained in 6 
 three times ; 3 is the quotient. 
 
 When we divide by 1, what is the quotient. 
 
 Ans. The same as the number divided. 
 Thus : 
 
 1 in 1, once. 
 1 in 2, twice. 
 1 in 3, 3 times. 
 1 in 4, 4 times. 
 1 in 5, 5 times. 
 
 in 
 in 
 in 
 in 
 
 9, 
 
 6 times, 
 
 7 times. 
 
 8 times. 
 
 9 times. 
 
 I 1 in 10, 10 times. 
 
DIVISION. 
 
 77 
 
 LESSON LXXIV. 
 
 What is Division ? 
 
 Ans. Division is the process of finding how 
 many times one number is contained in another. 
 
 What is the result called in Division ? 
 
 How many times is one apple contained in 
 one apple ? In five apples ? In ten ? In four- 
 teen? In a hundred apples? In a thousand 
 apples ? 
 
 How many times will 1 go into 3 ? Into 27 ? 
 
 Divide 415 by 1, and what is the quotient ? 
 
 How many times is 2 contained in 4 ? In 6 ? 
 Two make a pair. How many pair will 8 
 rabbits make ? Count and see. 
 
 How many pair will ten horses make 
 
 2 in 
 2 in 
 2 in 
 2 in 
 
 2, once. 
 4, twice. 
 
 3 times. 
 
 4 times. 
 
 6, 
 8, 
 
 2 in 10, 5 times. 
 
 2 in 12, '6 times. 
 2 in 14, 7 times. 
 2 in 16, 8 times. 
 2 in 18, 9 times. 
 2 in 20, 10 times. 
 
78 DIVISION. 
 
 LESSON LXXV. 
 
 1. Two make a brace. If a sportsman shoots 
 20 pheasants, how many brace does that make ? 
 
 MODEL. It makes as many brace as 2 is contained times 
 in 20, or 10. Answer, 10 brace. 
 
 Follow this model in the mental sums in Division. 
 
 2. Two make a couple. If a group of 16 
 boys pair off, how many couples will they make? 
 
 3. How many pair will twelve gloves make ? 
 
 4. If 16 cents are divided equally between 
 two poor men, how many cents will each get? 
 
 5. Amy and her sister divided 14 chestnuts 
 equally between them. How many did Amy 
 have ? 
 
 ^^rt!L*x When a thing is divided into 
 two equal parts, each part is called 
 
 What is the half of 14 ? Of 18 '? 
 
 How many times is 1 contained in 1 ? 2 in 2 ? 
 When we divide any number by itself, what is 
 the quotient? Ans. 1. 
 
 How many times is 3 contained in 3 ? 
 
 3 in 3, once. 
 3 in 6, twice. 
 3 in 9, 3 times. 
 3 in 12, 4 times. 
 3 in 15, 5 times. 
 
 3 in 18, 6 times. 
 3 in 21, 7 times. 
 3 in 24, 8 times. 
 3 in 27, 9 times. 
 3 in 30, 10 times. 
 
DIVISION. 
 
 LESSON LXXVI. 
 
 How much is 3 times 2 ? 
 
 How many times is 3 contained in 6 ? 2 in 6 ? 
 
 /\ 1. It takes three lines to form a 
 
 triangle. How many triangles will 
 
 twenty-one lines form ? 
 
 2. How many cents will 15 apples cost, at the 
 rate of 3 for a cent ? 
 
 3. If we walk three miles an hour, how many 
 hours will it take us to walk twelve miles? 
 
 4.~lf 3 pounds of butter last a family a week, 
 how many weeks will thirty pounds last them ? 
 
 5. Twenty-four is how many times three ? 
 
 6. How much is half of 18? How many 
 times 3 is 9 ? 
 
 One half of 18 is how many times 3 ? 
 
 7. One half of 6 is how many times 3 ? 
 
 8. If it takes 3 feet to make a yard, how 
 many yards are there in 27 feet of ribbon ? 
 
 9. Thomas divided eighteen almonds equally 
 among his three sisters ; how many did he give 
 each ? How often will 6 go into 18 ? 
 
 4 in 4, once. 
 4 in 8, twice. 
 4 in 12, 3 times. 
 4 in 16, 4 times. 
 4 in 20, 5 times. 
 
 4 in 24, 6 times. 
 
 4 in 28, 7 times. 
 
 4 in 32, 8 times. 
 
 4 in 36, 9 times. 
 
 4 in 40, 10 times. 
 
80 DIVISION. 
 
 LESSON LXXVII. 
 
 Any number is contained in 0, times. 
 
 1 in 0, times. 2 in 0, times. 3 in 0, 
 times, &c. 
 
 Divide 1208 by 4, on your slate. 
 
 Set down 4, the number you divide 
 by, at the left of the other number 
 with a line between. 
 
 In dividing, always commence at the left. 
 
 As you find the quotient, write it under the 
 number divided ? 
 
 4 is not contained in 1. See, then, how often 
 it will go into 12, the first two figures. 
 
 4 in 12, 3 times. Set down 3 under the 2. 
 
 4 in 0, times. Set it down. 4) 1208 
 
 4 in 8, twice. Set down 2. Ans. 302 
 
 Do these sums in Division on your slate : 
 
 (1) (2) (3) (4) (5) 
 
 4)204 4)808 2)682 2^1020 3) 9630 
 
 (6) (7) (8) (9) (10) 
 
 1)768 2)168 3)186 3)2109 3) 3009 
 
 5 in 5, once. 
 5 in 10, twice. 
 5 in 15, 3 times. 
 5 in 20, 4 times. 
 5 in 25, 5 times. 
 
 5 in 30, 6 times. 
 
 5 in 35, 7 times. 
 
 5 in 40, 8 times. 
 
 5 in 45, 9 times. 
 
 5 in 50, 10 times. 
 
DIVISION. 81 
 
 LESSON 
 
 1. If four wheels are needed for one car, how 
 many cars will twenty-eight wheels suj^ly ? 
 
 MODEL. If 4 wheels are needed for one car, 28 wheels 
 will supply as many cars as 4 is contained times in 28, or 
 7 cars. Answer, 7 cars. 
 
 2. A farmer distributes 40 pigs equally in 
 four pens. How many does he put in each ? 
 
 3. A man who earns 4 dollars a week, is paid 
 24 dollars. For how many weeks is he paid ? 
 
 4. If I place four boys on a bench, how many 
 benches shall I need for thirty-six boys ? 
 
 5. If 5 oranges are worth as much as 15 
 apples, how many apples is one orange worth ? 
 
 6. If five rocking-horses cost forty-five dollars, 
 how much do they cost apiece ? 
 
 7. How many dresses will 12 yards of ribbon 
 trim, if it takes 4 yards to trim one dress ? 
 
 8. Four pecks make a bushel; how many 
 bushels will 16 pecks make ? 
 
 9. If one pew holds five persons, how many 
 pews will it take to hold thirty persons? 
 
 6 in 6, once. 
 
 6 in 12, twice. 
 
 6 in 18, 3 times. 
 
 6 in 24, 4 times. 
 
 6 in 30, 5 times. 
 
 6 in 36, 6 times. 
 6 in 42, 7 times. 
 6 in 48, 8 times. 
 6 in 54, 9 times. 
 6 in 60, 10 times. 
 
82 DIVISION. 
 
 LESSON LXXIX. 
 
 SUMS FOR THE SLATE. 
 * t 
 
 1. Divide twelve hundred by 4. Divide it 
 by 6. Divide it by 3. 
 
 2. Divide two thousand five hundred and five 
 by five. 
 
 3. Divide four thousand eight hundred and 
 sixty by six. Divide it by two. 
 
 4. How many times is five contained in thirty- 
 five hundred and fifty-five ? 
 
 5. How many times is six contained in three 
 thousand six hundred and six ? 
 
 6. If two thousand dollars be divided equally 
 among five persons, how much will each get ? 
 
 7. If four hundred and twenty books are 
 distributed equally on six shelves, how many 
 will there be on each shelf? 
 
 8. If four hundred soldiers are divided into 
 5 companies, how many will there be in each ? 
 
 9. If four partners together make two thou- 
 sand dollars in one year, how much is that 
 apiece ? 
 
 7 in 7, once. 
 
 7 in 14, twice. 
 
 7 in 21, 3 times. 
 
 7 in 28, 4 times. 
 
 7 in 35, 5 times. 
 
 7 in 42, 6 times. 
 7 in 49, 7 times. 
 7 in 56, 8 times. 
 7 in 63, 9 times. 
 7 in 70, 10 times. 
 
DIVISION. 83 
 
 LESSON LXXX. 
 
 1. Kuth is sent to divide 18 cakes equally 
 among her 6 sisters. How many must she give 
 each? 
 
 2. How many classes of six scholars each can 
 be formed out of fifty-four scholars ? 
 
 3. Allowing six candles to the pound, how 
 many pounds are there in thirty- six candles ? 
 
 4. How many books can be made out of 60 
 sheets of paper, if it takes 6 sheets to make one 
 book? 
 
 5. Paul has 4 cents, and Kose has 20. They 
 put their money together, and divide it equally 
 among 6 poor girls. How much does each girl 
 get? 
 
 6. If one horse can draw as much as 7 men, 
 how many horses will draw as much as 56 men ? 
 
 7. How many weeks of 7 days each are there 
 in 49 days ? 
 
 8. I am 63 years old, and am just 7 times the 
 age of my son. How old is my son ? 
 
 9. Seven times two is how many times seven ? 
 
 8 in 8, once. 
 
 8 in 16, twice. 
 
 8 in 24, 3 times. 
 
 8 in 32, 4 times. 
 
 8 in 40, 5 times. 
 
 8 in 48, 6 times. 
 
 8 in 56, 7 times. 
 
 8 in 64, 8 times. 
 
 8 in 72, 9 times. 
 
 8 in 80, 10 times. 
 
84 
 
 DIVISION. 
 
 LESSON LXXXI. 
 
 These eight boys are having a fine sail. 
 
 If they are charged 40 cents for the boat, how 
 much will each have to pay ? 
 
 If they catch 24 fish and divide them equally, 
 how many will each get ? 
 
 If they have 16 apples along, how many will 
 there be for each boy ? 
 
 How many times eight is the half of 16 ? 
 
 9 in 9, once. 
 9 in 18, twice. 
 9 in 27, 3 times. 
 9 in 36, 4 times. 
 9 in 45, 5 times. 
 
 9 in 54, 6 times. 
 
 9 in 63, 7 times. 
 
 9 in 72, 8 times. 
 
 9 in 81, 9 times. 
 
 9 in 90, 10 times. 
 
DIVISION. 85 
 
 LESSON LXXXII. 
 SUMS FOE THE SLATE. 
 
 1. If one stage-coacli will hold 9 passengers, 
 how many such coaches will it take to hold 
 ninety-nine passengers ? 
 
 2. How many nine-gallon jars will it take to 
 hold two hundred and seventy gallons? 
 
 3. If a family use nine pounds of coffee in a 
 month, how long will one hundred and eighty- 
 nine pounds last them ? 
 
 4. How many sets of 9 volumes each can be 
 made up out of nine thousand and ninety volumes ? 
 
 5. If three thousand two hundred and eight 
 dollars be divided among eight heirs, how many 
 dollars will each receive ? 
 
 6. If there are eight panes of glass in one 
 window, how many windows will four hundred 
 and eighty-eight panes supply ? 
 
 7. Divide eight thousand one hundred by 9. 
 Write down the even tens up to 100 : 10, 
 
 20, 30, &c. 
 
 10 in 10, once. 
 
 10 in 20, twice. 
 
 10 in 30, 3 times. 
 
 10 in 40, 4 times. 
 
 10 in 50, 5 times. 
 
 10 in 60, 6 times. 
 10 in 70, 7 times. 
 10 in" 80, 8 times. 
 10 in 90, 9 tirnes. 
 10 in 100, 10 times. 
 
SUMS IN DIVISION. 
 
 LESSON LXXXIII. 
 
 What is Numeration ? What is Notation ? 
 
 What is Addition ? What is Subtraction ? 
 
 What is Multiplication ? What is Division ? 
 
 What is the result, or answer, called in Ad- 
 dition? What in Subtraction? What in Mul- 
 tiplication ? What in Division ? 
 
 1. Ten cents make a dime. How many dimes 
 in fifty cents ? 
 
 2. Ten dimes make a dollar. How many 
 dollars in eighty dimes ? 
 
 3. Ten dollars make an eagle. How many 
 eagles in thirty dollars ? 
 
 4. How many companies of ten men each can 
 be formed out of ninety men ? 
 
 5. Charles has 7 dollars, and Robert 3. They 
 put their money together, and buy ten turkeys. 
 What do the turkeys cost apiece ? 
 
 6. A man riding 10 miles an hour, travels 20 
 miles. How many hours is he on the way ? 
 
 7. If ten omnibus tickets cost 60 cents, what 
 does one ticket cost ? 
 
 Do the following sums on your slate : 
 
 (1) (2) (3) (4) 
 
 8)7208 9) 7290 9) 3699 10) 7000 
 
DIVISION. 87 
 
 LESSON LXXXIV. 
 
 How often is 6 contained in 7 ? 
 
 Ans. It is contained once for 6 in 6, once. 
 
 It is not contained twice ; for twice 6 is 12. 
 
 Is 6 contained in 7 once exactly ? 
 
 Ans. No; 6 is contained once exactly in 6. 
 As 7 is one more than 6, we say that 6 goes into 
 7 once, and one over. 
 
 How often is 6 contained in 20 ? 
 Ans. 6 in 18, 3 times ; 18 from 20 leaves 2. 
 Hence 6 goes into 20 three times, and two over. 
 
 How often will 3 go into 26 ? 4 into 38 ? 7 
 into 50 ? 2 into 21 ? 8 into 55 ? 5 into 44 ? 
 
 What is that which is left over called ? 
 Ans. The Remainder. 
 
 If we come to a figure too small to contain 
 the one we are dividing by, what do we do ? 
 
 Ans. If it is not the first figure, we set down 
 in the quotient. 
 
 Divide 3604 by 6. 
 
 6) 3604 
 
 Quotient 600, and 4 remainder. 
 
 Divide, as above, on your slate : (1.) 635 by 9. 
 (2.) 563 by 8. (3.) 4089 by 4. (4.) 621 by 2. 
 (5.) 6308 by 3. (6.) 499 by 7. (7.) 4009 by 5. 
 
88 CARRYING IN DIVISION. 
 
 LESSON LXXXV. 
 
 3 2 
 
 Look at this sum. Commence 
 4) 3901 at the left. 4 is not contained in 
 
 975, i rem. 3. See, then, how often it will go 
 
 into 39, the first two figures. 
 4 in 39, 9 times and 3 over. Set down 9 
 under the 9, and prefix the remainder 3, in your 
 mind, to the next figure making 30. 
 
 1 4 in 30, 7 times and 2 over. Set down 7 
 under the 0, and prefix 2 to the next figure- 
 making 21. 
 
 4 in 21, 5 times and 1 over. Set down 5, and 
 the remainder 1 to the right. Answer : quotient 
 975, and 1 remainder. 
 
 This prefixing of the remainder to the next 
 figure is called Carrying. 
 
 When must we carry in Division ? 
 Ans. Whenever, before reaching the end of 
 the sum, we have a remainder. 
 
 Do these sums aloud, like the above example : 
 
 (1) (2) (3) 
 
 2)1349 3)2_904 4)JL762 
 
 Quo. 674, 1 rein. Quo. 968 Quo. 440, 2 rem. 
 
 (4) (5) (6) (7) 
 
 5) 2564 6) 6702 8) 9679 9)4235 
 
DIVIDING BY TEN. 89 
 
 LESSON LXXXVI. 
 
 Divide 4017 by 10. 10)4017 
 
 10 in 40, 4 times. Set down 
 
 A J 4.1. f\ 401. Trem. 
 
 4 under the 0. 
 
 10 in 1, times and 1 over. Set down 0, and 
 carry 1. 10 in 17, once and 7 over. Set down 
 1, and 7 for the remainder. Answer, 401 and 
 7 remainder. 
 
 Now compare this answer with the number 
 to be divided 4017. It is the same as if we had 
 cut off the right hand figure for the remainder, 
 and taken the rest for the quotient 401 1 7. 
 
 Give, then, an easy rule for dividing by 10. 
 
 Ans. Cut off the right-hand figure of the 
 number to be divided for the remainder, and take 
 the other figures for the quotient. 
 
 Set down the following numbers. Divide 
 them by 10 in the way just shown. 
 
 1. Five thousand two hundred and nineteen. 
 
 2. Eighteen hundred and sixty-three. 
 
 3. Nine thousand and seventy-eight. 
 
 4. Eleven hundred and eleven. 
 
 5. Four thousand one hundred and forty. 
 
 6. Seven thousand two hundred and six. 
 
 7. Nine hundred and ninety-four. 
 
 8. Eight thousand and one. 
 
 9. Nineteen hundred and five. 
 
90 SUMS IN ADDITION. 
 
 LESSON LXXXVII. 
 
 What sign is used to denote Addition ? 
 Ans. This sign + , called plus, 
 
 What does 4 + 5 mean ? 
 
 Ans. It is read, four plus five. It means 4 
 added to 5, and is equal to 9. 
 
 When numbers are to be added or subtracted, 
 how must we be sure to set them down ? 
 
 Ans. So as to bring units under units, tens 
 under tens, &c. 
 
 Eead the following sums. Set down the 
 numbers properly, and add them on your slate. 
 
 1. 987 + 764-3665 + 544-2443. Ans. 7225. 
 
 2. 752 + 3953 + 414+6 + 1745. Ans. 6870. 
 
 3. 306 + 1032 + 89 + 567 + 765. 
 
 4. 4 + 455 + 2260 + 1476 + 7+3488. 
 
 5. 8 + 859 + 4954+483 + 1891 + 10 + 705. 
 
 6. 10 + 758 + 655 + 950 + 62 + 969 + 863 + 737. 
 
 7. 1659 + 2 + 2348 + 9 + 3299 + 1028 + 79 + 17. 
 
 8. 1728 + 756 + 1699 + 789 + 1967+539 + 154. 
 How many tens must we add together, to pro- 
 duce 80 ? Set them down, and add them. 
 
 How many one hundreds must we add, in 
 order to get 1000 ? Set them down, and add 
 them. 
 
 What is the sum of 8 times 10, and 10 times 
 100? 
 
SUMS IN SUBTRACTION. 
 
 91 
 
 LESSON LXXXVIII. 
 
 What sign is used to denote Subtraction ? 
 Ans. This sign , called minus. 
 
 What does 5 4 mean ? 
 Ans. It is read five minus four. It means 4 
 subtracted from 5, and is equal to 1. 
 
 When minus is used, which is the number to 
 be subtracted ? 
 
 Ans. The one that stands after the minus. 
 
 Read the following. 
 
 1. 1829 304. 
 
 2. 4506 2702. 
 
 3. 1234 899. 
 
 4. 4108 1053. 
 
 5. 2738 1374. 
 
 6. 2345 1779. 
 
 7. 2301 126. 
 
 8. 6456 1679. 
 
 Find the remainders. 
 
 9. 3647 1753. 
 
 10. 4567 2679. 
 
 11. 7091 5132. 
 
 12. 5678 1679. 
 
 13. 9000 7889. 
 
 14. 6789 3289. 
 
 15. 7890 4719. 
 
 16. 2006 1018. 
 
 17. Mr. W. has 2500 d9llars in one bank, and 
 5000 in another. He buys a house for 6000 dol- 
 lars. If he draws out money enough to pay for 
 it, how much will he have left in bank ? 
 
 18. How much is 2500 + 5000 6000 ? 
 
 19. How much is 1422 + 2578 1510 ? 
 
 20. How much is 3761 + 5239 999? 
 
92 SUMS IN MULTIPLICATION. 
 
 LESSON 
 
 LXXXIZ. 
 
 What sign is used to 
 Ans. This sign x . 
 
 denote Multiplication ? 
 
 "What does 4x5 mean ? 
 
 Ans. It means/bw multiplied lyfive, and is 
 equal to 20. 
 
 Which is greater, 4x5 or 5x4? 
 What is an easy way of multiplying by 10 ? 
 What easy way of multiplying by 100 ? 
 
 What is the number to be multiplied called ? 
 Ans. The Multiplicand, 
 
 What is the number 
 Ans. The Multiplier. 
 
 you multiply by called ? 
 
 When the multiplier contains 0, how were 
 you told to proceed ? 
 
 Head the following sums. Find the products. 
 
 1. 1605 x 6. 
 
 10. 62 x 100. 
 
 2. 4198 x 2. 
 
 11. 396 x 19. 
 
 3. 973 x 9. 
 
 12. 57 x 80. 
 
 4. 861 x 10.' 
 
 13. 403 x 17. 
 
 5. 1284 x 7. 
 
 14. 189 x 20. 
 
 6. 1066 x 5. 
 
 15. 148 x 63. 
 
 7. 851 x 8. 
 
 16. 82 x 95. 
 
 8. 2396 x 4. 
 
 17. 25 x 204. 
 
 9. 271 x 36. 
 
 18. 65 x 90. 
 
SUMS IN" DIVISION. 93 
 
 LESSON SO. 
 
 What sign is used to 
 Ans. This sign -7-. 
 
 denote Division ? 
 
 What does 14-7-7 mean ? 
 
 Ans. It means fourteen divided y seven, and 
 is equal to 2. 
 
 When the sign for division stands between 
 two numbers, which is to be divided ? 
 Ans. The one before it is to be divided by 
 the one after it. 
 
 What is the number 
 
 to be divided called ? 
 
 Ans. The Dividend. 
 
 
 What is the number 
 Ans. The Divisor. 
 
 you divide by called ? 
 
 What easy rule was given for dividing by 10 ? 
 
 Eead the following sums. Find the quotient 
 and remainder. 
 
 1. 8064 4. 
 
 10. 4713 5. 
 
 2. 9193 3. 
 
 11. 6565 - 9. 
 
 3. 2709 - 9. 
 
 12. 3709 - 8. 
 
 4. 4004 - 5. 
 
 13. 2723 - 4. 
 
 5. 7777 - 2. 
 
 14. 3379 - 6. 
 
 6. 1941 - 10. 
 
 15. 6055 - 3. 
 
 7. 1468 - 1. 
 
 16. 7327 - 8. 
 
 8. 2496 - 7. 
 
 17. 5403 - 7. 
 
 9. 5684 6. 
 
 18. 2670 - 10. 
 
94 MISCELLANEOUS ST7MS. 
 
 LESSON XCI. 
 PROMISCUOUS MENTAL SUMS. 
 
 1. If a man earns 15 dollars a week, and 
 spends 9, how much will he save in 4 weeks ? 
 How much iff. 6 weeks ? 
 
 First find how much he will save in 1 week, then in 4. 
 
 2. Ellen puts aside 3 cents every day for the 
 poor, and James puts aside 5 cents. 'How much 
 will they both have for the poor in a week ? 
 
 3. We collect 10 dollars for the poor one day, 
 and 6 the next. If we divide the whole among 
 4 poor families, how much will each get ? 
 
 4. Mary reads 2 pages every morning, and 7 
 every afternoon ; how many pages does she read 
 in a week ? 
 
 5. If 10 peaches fill a quart measure, how 
 many quart measures will 80 peaches fill ? 
 
 6. A farmer has 3 white hens and 4 black 
 ones. If each hen hatches 4 chickens, how many 
 chickens will the farmer have ? 
 
 7. If 8 pounds of butter are used out of a jar 
 that contains 17, how many pounds will remain ? 
 
 8. If 7 pears cost 21 cents, how much is that 
 apiece ? What will 10 such pears cost ? 
 
 9. A lawn contains 19 trees ; 2 are oaks, 7 
 firs, and the rest elms. How many elms are 
 there ? 
 
HALVES, THIRDS, FOURTHS. 
 
 95 
 
 LESSON XOII. 
 
 When a thing is divided into 2 
 equal parts, what is each part called ? 
 Ans. A Half. 
 
 How many halves in a whole pear ? Count 
 and see. 
 
 When a thing is divided into 3 
 equal parts, what is each part called ? 
 
 Ana. A Third. 
 How many thirds in a whole pear ? 
 
 When a thing is divided into 
 equal parts, what is each part called ? 
 Ans. A Fourth, or Quarter. 
 
 How many fourths, or quarters, in a whole 
 pear ? Count and see. 
 
 What is this line divided into ? 
 What is this line divided into ? 
 What is this line divided into ? 
 
 Which is greater, a half, a third, or a fourth ? 
 Look at the lines divided above, and see. 
 
96 FRACTIONS. 
 
 LESSON XCIII. 
 
 If a whole is divided into 5 equal parts, each 
 part is called one Fifth. 
 
 If a whole is divided into 6 equal parts, each 
 part is called one Sixth. 
 
 If a whole is divided into 7 equal parts, each 
 part is called one Seventh. 
 
 If a whole is divided into 8 equal parts, each 
 part is called one Eighth. 
 * . 
 
 If a whole is divided into 9 equal parts, each 
 part is called one Ninth. 
 
 If a whole is divided into 10 equal parts, each 
 part is called one Tenth. 
 
 What are such equal parts of a whole called ? 
 Ans. Fractions. 
 
 Learn how to write these fractions : 
 
 One half 
 One third 
 One fourth 
 
 One fifth i 
 One sixth | 
 One seventh |. 
 
 One eighth 
 One ninth 
 One tenth 
 
FRACTIONS. 97 
 
 LESSON XCIV. 
 
 Learn this table : 
 
 2 halves, one whole. 
 
 3 thirds, one whole. 
 
 4 fourths, one whole. 
 
 5 fifths, one whole. 
 
 6 sixths, one whole. 
 
 7 sevenths, one whole. 
 
 8 eighths, one whole. 
 
 9 ninths, one whole. 
 
 10 tenths, one whole. 
 
 Since 2 halves make a whole, to find one half 
 cut the whole into 2 equal parts. 
 
 To find half of a number, divide it by 2. 
 
 To find i, divide by 3. 
 To find , divide by 4. 
 To find ], divide by 5. 
 To find , divide by 6. 
 
 To find -i, divide by 7. 
 To find J, divide by 8. 
 To find i, divide by 9. 
 To find T V, divide by 10. 
 
 SUMS FOE THE SLATE. 
 
 1. What is i of 6184 ? Of 298 ? Of 336 ? 
 
 2. What is 1 of 369 ? Of 1482 ? Of 1578 ? 
 
 3. Find one tenth of 8970. Of 2310. Of 80. 
 4.' What is 1 of 2548? Of 332? Of 380? 
 
 5. Find one sixth of 1812. Of 924. Of 342. 
 
 6. Find j of 2808. Of 6534. Of 4851. 
 
 7. Find 1 of 4060. Of 3750. Of 4005. 
 
 8. Take | of 1752. Of 7008. Of 3224. 
 
 9. Take 1 of 5810. Of 3325. Of 693. 
 
 i 
 
98 
 
 FEDERAL MONEY. 
 
 LESSON SOV. 
 
 Now we must learn about money, weights, &c. 
 money of the United States 
 
 What is 
 called ? 
 
 the 
 
 Ans. Federal Money. 
 
 Cent 
 
 TABLE OF FEDERAL MONEY. 
 
 10 mills make 1 cent. 
 10 cents, 1 dime. 
 
 10 dimes, 1 dollar. 
 1 eagle. 
 
 Dime. 
 
 Eagle. 
 
 Besides these, we have other coins : 
 fThe three cent piece, worth 3 cents. 
 
 The half-dime, worth 5 cents. 
 
 f> ^ 
 
 [g The quarter-dollar, worth 25 cents. 
 
 [The half-dollar, worth 50 cents. 
 
 . fThe quarter-eagle, worth 2| dollars. 
 
 'I -1 The half-eagle, worth 5 dollars. 
 
 (The double eagle, worth 20 dollars. 
 
FEDERAL MONEY. 99 
 
 I 
 
 LESSON XCVI. 
 
 What mark is used to denote dollars ? 
 
 Ans. This mark $, placed lefore the number. 
 
 Twenty dollars is written $20. 
 
 Twenty dollars, six cents, is written $20.06 
 
 Twenty dollars, thirteen cents, $20.13 
 
 Twenty dollars, twelve cents, 1 mill, $20.121 
 
 Twenty dollars, one mill, $20.001 
 
 The first two figures after the period denote 
 cents. The third figure denotes mills. 
 
 $60.019 is read sixty dollars, one cent, 9 mills. 
 $4.502, four dollars, fifty cents, two mills. 
 
 Read and add the following. In setting them 
 down, let the periods all range in line. 
 
 1. $103.24 + $47.91 + $3008.008 + $546.356. 
 
 2. $6000.009 4- $652.88 + $1267 + $987.765. 
 
 3. $800.81 + $6793.054 + $21.421 +$1896. 
 
 4. $9.428 + $4200.919 + $87.75 + $365.56. 
 
 5. From eighty-seven dollars, forty $87.405 
 cents, five mills, take ten dollars, ninety- 
 one cents. Ans. $ 
 
 6. From nine hundred dollars, take thirty-two 
 dollars, seventy-three cents, five mills. 
 
 7. From fifty dollars, seventy cents, take 
 nineteen dollars, one cent, six mills. 
 
100 EXERCISES IN FEDERAL MONEY. 
 
 LESSON XOVII. 
 
 1. A lady buys 7 pounds of meat at 10 cents 
 a pound ; how much must she give for it ? 
 
 If she hands the butcher a dollar bill, how 
 much change must he give her ? 
 
 2. Robert buys a slate for 10 cents, and a 
 book for 40 cents. He gives the store-keeper half 
 a dollar. How much change must he receive ? 
 
 3. John buys half of a six cent pie, and hands 
 the baker a dime. How much change will he get ? 
 
 4. How many cents make a dime ? How many 
 cents are 5 dimes worth ? 9 dimes ? 10 dimes ? 
 
 1 dollar? 
 
 5. How many dollars make an eagle ? How 
 many eagles in 40 dollars ? In 80 dollars ? 
 
 6. How many dollars is a half-eagle worth ? 
 
 2 half-eagles ? 5 half-eagles ? 10 half-eagles ? 
 
 7. How many half-dimes are equal to 10 
 cents ? To 30 cents ? To 60 cents ? To a dollar? 
 
 8. I leave home with an eagle in my pocket. 
 I spend $4 in market, and on my way home give 
 10 beggars a dime each. How much have I left ? 
 
 9. If a man deposits an eagle in the savings 
 bank every week, how many dollars will he have 
 there in ten weeks ? 
 
 10. How many dimes in one eagle ? 
 
 11. If a boy gives a store-keeper a dollar, and 
 gets 25 cents change, how much has he spent ? 
 
STERLING MONEY. 
 
 101 
 
 LESSON XCVIII. 
 
 What is the money of Great Britain called ? 
 Ans. English or Sterling Money. 
 
 Sovereign. 
 
 TABLE OF STEELING MONEY. 
 
 . 4 farthings make 1 penny. 
 12 pence, 1 shilling. 
 
 20 shillings, 1 pound. 
 
 21 shillings, 1 guinea. 
 What mark is used to denote pounds ? 
 
 Ans. This mark , placed before the number. 
 
 Wh.at coin represents 1 pound? 
 Ans. The sovereign, a gold coin. 
 
 How many shillings is 1 sovereign worth? 
 Ans. Twenty shillings. 
 
 Which is worth more, a sovereign or a guinea ? 
 
 1. How many farthings in 1 penny ? In 8 
 pence? In 10 pence? 
 
 2. What part of a penny is a farthing ? 
 
 3. How many farthings in a half-penny ? 
 
 4. If I pay 9 shillings for a map, and 1 for 
 a book, which costs the more ? How much more ? 
 
 5. If a boy who has 2 spends half of it, how 
 many shillings has he left ? 
 
 6. Five beggars received 8 farthings each, 
 How many pence did that make for all five ? 
 
102 
 
 LESSON SCIX. 
 
 TROY WEIGHT. 
 
 What is Troy weight used in weighing ? 
 Ans. Gold, silver, and precious stones. 
 
 TABLE. 
 
 24 grains make 1 pennyweight. 
 20 pennyweights, 1 ounce. 
 12 ounces, 1 pound. 
 
 APOTHECARIES' WEIGHT. 
 
 By whom is Apothecaries' weight used ? 
 Ans. By apothecaries, in mixing medicines. 
 
 TABLE. 
 20 grains make 1 scruple. 
 
 3 scruples, 1 dram. 
 
 8 drachms, 1 ounce. 
 12 ounces, 1 pound. 
 
 1. A person who has a pound of gold dust, sells 
 4 ounces of it. How many ounces has he left ? 
 
 2. How many spoons weighing 10 penny- 
 weights each will it take to make an ounce ? 
 
 3. How many powders of 5 grains each can a 
 druggist make out of 1 scruple of calomel ? 
 
 4. How many drams in 2 ounces ? In 8 
 ounces ? In 11 ounces ? 
 
AVOIRDUPOIS WEIGHT. 103 
 
 LESSON C. 
 
 AVOIRDUPOIS WEIGHT. 
 
 What is Avoirdupois Weight used for ? 
 Ans. For weighing the metals except gold 
 and silver, groceries, and all coarse goods. 
 
 TABLE. 
 
 16 drams make 1 ounce. 
 16 ounces, 1 pound. 
 
 25 pounds, 1 quarter. 
 
 4 quarters, 1 hundred-weight. 
 
 20 hundred-weight, 1 ton. 
 
 1. How many cornucopias holding 4 ounces 
 each can be filled with a pound of candy ? 
 
 2. How many pounds in a quarter ? In a 
 hundred-weight ? In 20 hundred-weight ? In a 
 ton? 
 
 3. How many pounds in 2 tons of coal ? 
 
 4. Emma weighs just half as much as Charles, 
 and he weighs 80 pounds. What is Emma's 
 weight ? 
 
 5. If a grocer sells two boys half . a pound of 
 cheese each, how many ounces is that in all ? 
 
 6. If 5 pounds are used out of a quarter of 
 flour, how many pounds are left ? 
 
 7. If a hundred-weight of pork is divided 
 among 10 men, how many pounds will each have ? 
 
104: LONG MEASURE. 
 
 LESSON 01. 
 LONG MEASURE. 
 
 For what is Long Measure used ? 
 
 Ans. For measuring length and distance. 
 
 One inch. 
 
 Make a line one inch long on your slate. 
 
 TABLE. 
 
 12 inches make 1 foot. 
 
 3 feet, 1 yard. 
 
 5 J yards, 1 rod or pole. 
 
 40 rods, 1 furlong. 
 
 8 furlongs, 1 mile. 
 
 1. How many inches long is a yard-stick ? 
 
 2. A boy who has to walk a mile to town, 
 has gone half the way. How many furlongs has 
 he yet to go ? 
 
 3. A tall man is 6 feet high. How many 
 yards is that ? 
 
 4. Allowing a yard to each step, how many 
 feet will a man go in 10 steps ? 
 
 5. How many rods in a furlong? In 8 fur- 
 longs? In a mile? 
 
 6. About how many inches wide is this page ? 
 
 7. How many inches in a quarter of a yard ? 
 
LIQUID MEASURE. 105 
 
 LESSON Oil. 
 LIQUID MEASURE. 
 
 For what is Liquid Measure used ? 
 Ans. For measuring liquids; such as milk, 
 oil, vinegar, molasses, liquors, &c. 
 
 TABLE. 
 
 4 gills make 1 pint. 
 
 2 pints, 1 quart. 
 
 4 quarts, 1 gallon. 
 
 31^ gallons, 1 barrel. 
 
 2 barrels, 1 hogshead. 
 
 2 hogsheads, 1 pipe. 
 
 2 pipes, 1 tun. 
 
 1. A tumbler holds about half a pint ; how 
 many tumblerfuls in a quart ? 
 
 2. How many pints will fill a quart measure ? 
 
 3. If a milkman mixes 2 pints of water with 
 4 quarts of milk, how much will he have in all ? 
 
 4. Suppose half a gallon leaks out of a barrel 
 of oil ; how many gallons remain in it ? 
 
 5. How many quart pitchers can be filled 
 from a two-gallon pail ? 
 
 6. How many barrels will a pipe of wine fill ? 
 
 7. If I have 8 quarts of cider, and give half 
 of it away, how many gallons have I left ? 
 
106 DRY MEASURE. 
 
 LESSON CHI. 
 DRY MEASURE. 
 
 For what is Dry Measure used ? 
 Ans. For measuring fruit, vegetables, coal, 
 salt, grain, &c. 
 
 TABLE. 
 
 2 pints make 1 quart. 
 8 quarts, 1 peek. 
 4 pecks, 1 bushel. 
 
 36 bushels, 1 chaldron. 
 
 The dry quart measure is of wood ; the liquid 
 quart measure is of tin. 
 
 A small measure contains 2 quarts. 
 
 1. A man bought a bushel of apples ; if one 
 peck was rotten, how many pecks were good ? 
 
 2. How many quarts in a half peck ? 
 
 3. If a horse eats 8 quarts of oats a day, how 
 long will it take him to eat a bushel ? 
 
 4. If a pint of chestnuts costs 6 cents, what 
 will a quart cost ? 
 
 5. If 5 girls go a berrying, and each girl picks 
 a quart, how many pints will they have in all ? 
 
 6. Which are cheaper, potatoes at a dollar a 
 bushel, or 30 cents a peck ? 
 
 7. What is a peck of corn worth, at 80 cents 
 a bushel ? 
 
TIME MEASURE. 107 
 
 LESSON CIV. 
 
 TIME MEASURE. 
 
 60 seconds make 1 minute. 
 60 minutes, 1 hour. 
 
 24 hours, 1 day. 
 
 7 days, 1 week. 
 
 4 weeks, 1 lunar month. 
 
 13 lunar naonths, 1 year. 
 
 How many days in a lunar month ? 
 What other kind of months is there ? 
 Ans. Calendar months. 
 Name the calendar months of the year in order, 
 and the number of days in each. / 
 
 1st month, January, 31. 
 
 2d month, February, 28. 
 
 3d month, March, 31. 
 
 4th month, April, 30. 
 
 5th month, May, 31. 
 
 6th month, June, 30. 
 
 7th mo., July, 31. 
 
 8th mo., August, 31. 
 
 9th mo., September, 30. 
 
 10th mo., October, 31. 
 
 llth mo., November, 30. 
 
 12th mo., December, 31. 
 
 These days added together make 365 days in 
 the year. Every fourth year is a Leap Year ; 
 then February has 29 days, and the year 366. 
 
 There are four seasons in the year : 
 SPRING, consisting of March, April, May ; 
 SUMMER, June, July, August ; 
 AUTUMN or FALL,^3eptember, October, November ; 
 WINTER, December, January, February. 
 
108 MISCELLANEOUS TABLE. 
 
 LESSON CV. 
 
 MISCELLANEOUS TABLE. 
 
 j 12 things make 1 dozen. 
 
 ( 12 dozen, 1 gross. 
 
 20 things, 1 score. 
 
 ( 24 sheets, 1 quire of paper. 
 
 \ 20 quires, 1 ream. 
 
 56 pounds, 1 firkin of butter. 
 
 100 pounds, 1 quintal of fish. 
 
 196 pounds, 1 barrel of flour. 
 
 200 pounds, 1 barrel of pork. 
 
 "Which weighs more, a barrel of flour or a 
 barrel of pork, and how much ? 
 
 2. If a man lives to be u three score years and 
 ten," how old is he ? 
 
 3. A box of pens holds a gross ; how many 
 dozen in a box ? How many pens in a box ? 
 
 4. How many sheets in one fourth of a quire 
 of paper ? 
 
 5. If five pounds of butter are taken out of a 
 full firkin, how many pounds will remain ? 
 
 6. How many pounds in 5 quintals of codfish ? 
 
 7. "Which month is the shortest in the year ? 
 
 8. John was to st.a^iii:tli^city a week. He 
 has been there 5 days ; how imucli longer is he 
 to stay ? 
 
 . 
 
Ql\io 
 Ql 
 
 UNIVERSITY OF CALIFORNIA LIBRARY 
 
 
 
APPLETONS' ARITHMETICAL SERIES. 
 JEty Gr. P. QTT^OKEWBOS, A. ML. 
 
 UHOK TIIE BASIS OF THE WORKS OF 
 
 GEO. R. PERKINS, LL.D. 
 
 THIS Kt-w Series of Arithmetics viil be as perfect in all 
 respc-t- . thought, and labor can make it. All the ex- 
 
 tended -experience ol' the author and hi.s peculiar faculty for 
 impaHing instruction to the young, aideu by suggestions from 
 our best teachers, will be brought to bear, to produce a clear, 
 comprehensive, philosophical, and practical svstem. 
 
 Our books will be found perfectly graded, oar defink 
 simple, our analyses unencumbered with verbiage, our ar- 
 rangement the most natural, our methods the shortest possi- 
 ble. Every device will be resorted to, to prevent the mere 
 mechanical doing of sums; the pupil's mind will be con- 
 stantly kept on the alert, and his Arithmetic lesson will thus 
 be made an invaluable mental discipline. 
 
 The Series will consist of the following Books: 
 
 I. A PRIMARY ARITHMETIC. Beautifully 
 Illustrated ; carries the beginner through the first four Rul< 
 
 the simple Tables. Now ready. 
 
 II. Alt EUEJIE^TARY ARITHMETIC. 
 Reviews the subjects of the Primary; also embraces Frsictions, 
 Federal Money, Reduction, and the Compound Rul cady. 
 
 III. A PRACTICAL ARITHMETIC. Full, 
 clear, condensed. Prepared with direct reference to the wants of 
 Common Schools. In preparation. 
 
 IV. JL HIGHER ARITHMETIC. Designed to 
 prepare pupils for th business of life: its inptliods will be those 
 actually used by business men. In preparation, 
 
 V. A MENTAL ARITHMETIC. For imparting 
 readiness in mental calculations. Introduces many new and beauti- 
 ful processes. In preparation. 
 
 Teachers that want the best books should examine the above.