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tion in arithmetic is carried on by means of abstract numbers. It is just as impossible to multiply 23 dollars by 169 as to multiply 169 by 23 dollars. In the process of multiplication, the multiplicand and multiplier are both abstract. If the reasoning shows that it is admissible to regard the multiplicand as concrete, the name applied to it must also be given to the product.

44. If 1 copy of Webster's Dictionary costs $15, how much will 135 copies cost? Ans. $2025. 45. Suppose a book to contain 235 pages, with 45 lines on each page, how many lines are there in the book? Ans. 10575.

46. Suppose a book to contain 10575 lines, with 43 letters in each line, how many letters are there in the book? Ans. 454725. 47. At one time a gentleman bought 123 acres of land at $9 per acre; at another time he bought 123 acres at $20 per acre. How much did he pay for both Ans. $3567.

farms?

48. If I buy 123 acres of land, and give $29 per acre, how much do I pay for the land?

Ans. $3567. 49. If a cask contains 63 gallons, how many gallons in 304 casks? Ans. 19152 gallons. 50. A train of 21 cars has 51 barrels of oil on each car. How many barrels are on the train?

Ans. 1071 barrels.

51. Since there are 60 minutes in an hour, how many minutes in 24 hours? 48 hours? 72 hours? 96 hours? 120 hours? First Ans. 1440 minutes.

52. How many seconds in 1440 minutes?

Ans. 86400 seconds.

53. How many inches in 247 yards?

Ans. 8892 inches.

54. How many quarts in 529 bushels?

Ans. 16928 quarts.

55. A farmer bought 327 sheep at $2 apiece, 37 cows at $25 each, 3 horses at $125 each, a cart for $37, and a plow for $7.20. He now buys a new whip, and finds that he has expended in all exactly $2000. What did the whip cost? Ans. $1.80

DECIMALS.

38. To multiply a number involving decimal fractions by a whole number.

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(1) PROBLEM.-What is the product of 3.125 multiplied by 9?

(2) MULTIPLICATION.-9 times 5 are 45 (thousandths); 9 times 2 are 18, 18 and 4 are 22 (hundredths); 9 times 1 are 9, 9 and 2 are 11 (tenths); 9 times 3 are 27, 27 and 1 are 28 (units).

(3) RESULT.-Hence, the product of 3.125 multiplied by 9 is 28.125; that is, twenty-eight (units) and one hundred and twenty-five thousandths.

RULE.

Multiply exactly as in 37. The decimal point in the PRODUCT must have the same number of figures on the right of it as is found on the right of the point in the MULTIPLI

CAND.

2. Find the value of 7.125 × 8. 3. Find the value of 23.725 × 4.

Ans. 57.000

Ans. 95.000

4. Find the value of 7.009 × 9.

5. Find the value of 15.25 x 4.
6. Find the value of 19.137 x 5.

Ans. 63.081

Ans. 61.00

Ans. 95.685

7. Multiply 125.375 by 9; 8; 7; 6; 5; 4; 3; 2. Ans. 1128.375; 1003.000, etc.

8. Copy upon your slates and recite the following:

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14. Copy, upon your slates and recite the following:

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15. If you can buy a slate for $0.25, how much will 2 slates cost at the same rate? 3 slates? 4 slates? 5 slates? 6 slates? 7 slates? 8 slates? 9 slates? 10 slates? 37 slates? Ans. $0.50 ... $9.25 16. What will 12 yards of calico cost at $0.20 per yard? What will 13 yards cost? 14 yards? 15 yards? 17 yards? 20 yards? Ans. $2.40 ... $4.00

17. If a Primary Arithmetic costs $0.375, what will 2 books cost? 3 books? 11 books? 10 books? 21 books? 37 books? Ans. $0.75 ... $13.875. 18. If strawberries sell at $0.125 per quart, how much will 8 quarts cost? 16 quarts? 24 quarts? 32 quarts? 40 quarts? 192 quarts? First Ans. $1.00

19. If an orange is worth $0.0625 (six cents two mills and five tenths of a mill, or six and a quarter cents), what are 16 oranges worth? 32 oranges? 128 oranges? 144 oranges? Last Ans. $9.00

20. If a quart of milk is worth $0.06, what are 16 quarts worth? 24 quarts? 32 quarts? 48 quarts? 144 quarts? Last Ans. $8.64

21. If I buy 19 cows at $21 each, and sell them at $28 each, how much do I make in the trade?

Ans. $133 22. A man bought 23 watermelons for $0.125 each, and sold them for $0.25 each. How much did he make in the trade? Ans. $2.875 23. What is the value of 23 pounds of rice at $0.16 per pound? 46 pounds? 69 pounds? 92 pounds? 115 pounds? First Ans. $3.68 24. What is the value of 19 dozen eggs at $0.12 per dozen? 38 dozen? 57 dozen? 76 dozen?

First Ans. $2.28

25. A grocer buys 29 dozen eggs at $0.07 per dozen, and sells them at $0.12 per dozen. How much does he make clear? Ans. $1.45

26. What is the value of 37 pounds of raisins at $0.25 per pound? 74 pounds? 111 pounds? 148 pounds? First Ans. $9.25. 27. What is the value of 17 bushels of potatoes at $0.375 per bushel? 34 bushels? 51 bushels? 68 bushels? 85 bushels? First Ans. $6.375 28. What is the value of 137 bushels of corn at $0.875 per bushel? 374 bushels? 411 bushels? 548 bushels?

29. What is the value of 125 $0.93 per bushel? 250 bushels?

First Ans. $119.875 bushels of wheat at First Ans. $116.25

DIVISION.

39. DIVISION is the operation of finding how many times one number is contained in another.

EXAMPLES.

1. Copy upon your slates and read the following: 2)2 2)4 2)6 2)8 2)10 2)12 2)14 2)16 2)18

5

6

1 2 3 4 7 8 9 Read thus: 2 in 2, once; 2 in 4, 2 times, etc. 2. Copy upon your slates and read the following: 3)3 3)6 3)9 3)12 3)15 3)18 3)21 3)24 3)27

1

4

5

6

7

8 9

2 3 Read thus: 3 in 3, once; 3 in 6, 2 times, etc. 3. Copy upon your slates and read the following: 4)4 4)8 4)12 4)16 4)20 4)24 4)28 4)32 4)36

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Read thus: 4 in 4, once; 4 in 8, 2 times, etc. 4. Copy upon your slates and read the following: 5)5 5)10 5)15 5)20 5)25 5)30 5)35 5)40 5)45

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Read thus: 5 in 5, once; 5 in 10, 2 times, etc. 5. Copy upon your slates and read the following: 6)6 6)12 6)18 6)24 6)30 6)36 6)42 6)48 6)54 6 7 8 9

1

2

3 4 5

Read thus: 6 in 6, once; 6 in 12, 2 times, etc.

6. Copy upon your slates and read the following: 7)7 7)147)21 7)28 7)35 7)42 7)28 735 742 7)49 7)56 7)63

3

1 2 4 5 6 7 8 9 Read thus: 7 in 7, once; 7 in 14, 2 times, etc.

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