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6. From A of an acre take of a rod.

? Ans. IR. 17p. 22yd. 2ft. 108in. 7. From is of a cord take it of a cord.

Ans. 91ft. 1602 in. 8. From 7 of a hhd. of wine there leaked out of it; what remained ?

Ans. 6gal. 3qt. Opt. 175gi. 9. From Boston to Concord, N. H., the distance is 72 miles ; having travelled of this distance, how much remains ?

Ans. 30m. 6fur. 34rd. 4ft. 8in. 15 bar. 10. From & of a year take of a week.

Ans. 101da. 5h. 54m. 174sec. 11. From # of an acre take 4 of a foot.

Ans. 1R, 18p. 5yd. 4ft. Oin.

SECTION XIX.

MULTIPLICATION OF VULGAR FRACTIONS.

CASE I. To multiply a simple fraction by a simple fraction. 1. Multiply } by s.

OPERATION. This process may be understood by supš x =41 Ans. posing a man to have found ß of a dollar,

and that he gave of it to his wife, and that he wished to ascertain what part of a dollar his wife received. If I of a dollar be divided into 5 equal parts, one of these parts will be of a dollar. And, if į of į of a dollar best of a dollar, of will be 7 times as much, and 7 times ay are o If then, ļ of } be to, of will be 3 times as much, and 3 times I are it. The wife will therefore receive at of a dollar.

RULE. — Multiply the numerators together for a new numerator, and the denominators for a new denominator. The fraction should then be reduced to its lowest terms. 2. Multiply A by s.

Ans. 3. Multiply by 18.

Ans. The 4. Multiply by fi.

Ans. 5. Multiply by 16.

Ans. 192 6. Multiply | by .

Ans. 2. 7. Multiply by .

Ans. * 8. Multiply 14 by .

Ans. 4.

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The operation of the following questions may be abridged by cancelling. 10. Multiply 14 by 12.

Ans. 5. 11. Multiply I by 4.

Ans. 5. 12. Multiply by is.

Ans. ing 13. Multiply i's by is.

Ans. s. 14. Multiply 7 by it:

Ans. 7. 15. Multiply go by 1980.

Ans.Tdo CASE II. To multiply a whole number by a fraction, or a fraction by a whole number.

1. If a man earn of a dollar in one day, how much will he earn it. y days? OPERATION.

To analyze this question, we say, s XI = 603 = $7] Ans. if he earn 7 eighths of a dollar in 1

day, in 9 days he will earn 9 times as much, and 9 times 7 eighths are 63 eighths = 63 = $77 Ans.

RULE. — Multiply the whole number by the numerator of the fraction, and divide the product by the denominator, and the quotient is the answer required. 2. Multiply 12 by .

Ans. 84. 3. Multiply 15 by it.

Ans. 821 4. Multiply 4 by 11.

Ans. 49. 5. Multiply z by 12.

Ans. 3. 6. Multiply : by 19.

Ans. 165. 7. Multiply by 14.

Ans. 12. 8. Multiply 13 by 4.

· Ans. 73. 9. Multiply 16 by js.

Ans. 215. · 10. Multiply 11 by .

Ans. 64. NOTE. - If any of the fractions are compound, they must be reduced to simple fractions by Case VI., Sect. XVI." 11. Multiply of 3 of 1 by 12.

Ans. 24. OPERATION. of X X}= = 36 36 X ** = = 21 Ans.

12. Multiply of 11 of 1 by 100.

Ans. 121. 13. Multiply 4 of of } by 11.

Ans. 3, 14. What cost iz of a ton of hay, at $ 17 per ton?

Ans. $911. 15. What cost of an acre of land, at $37 per acre ?

Ans. $161%. + 16. At of a dollar per foot, what cost 7 cords of wood ?

Ans. $ 35.

CASE III. To multiply a mixed number by a whole number, or a whole number by a mixed number.

1. Multiply 73 by 9. OPERATION. In performing this question, we say 9 times 5

7 eighths are 45 eighths, and 45 eighths are equal to

9 59. We write down the sand carry the 5 to the 68.5 product of 9 times 7 = 68.

RULE. — Multiply the numerator of the mixed number by the whole number, and divide the product by the denominator of the fraction, and as many times as it contains the denominator, so many units must be carried to the product of the integers. If, after division, any thing remains, let it be a numerator and the divisor a denominator to a fraction to be affixed to the product. 2. Multiply 8.by 7.

Ans. 601. 3. Multiply 9% by 8.

Ans. 753. 4. Multiply 117 by 7.

Ans. 824. 5. Multiply 150 by 7.

Ans. 108 %. 6. Multiply 143 by 9.

Ans. 1312. 7. Multiply 235 by 11.

Ans. 2575. 8. Multiply 473 by 15.

Ans. 7091. 9. Multiply 37by 18.

Ans. 6791. 10. Multiply 67811 by 24.

Ans. 16294. 11. What will 237 pounds of lead cost, at 8 cents a pound ?

Ans. $1.91. 12. What will 1511 pounds of sugar cost, at 12 cents a pound ?

Ans. $1.881 13. What will 29 cwt. of hay cost, at $ 1.12 per cwt. ?

Ans. $ 32.949. 14. What will 97 yards of broadcloth cost, at $8 per yard ?

Ans. $79.00. 15. What will 17. tons of potash cost, at $97 per ton ?

Ans. $ 1703.561.

16. What will 315 tons of plaster of Paris cost, at $12.75 per ton ?

Ans. $ 40.1859. 17. What will 173 dozen candles cost, at 16 cents a dozen ?

Ans. $2.781. 18. What will 27% pounds of bar soap cost, at 9 cents a pound?

Ans. $ 1.914. 19. What will 297 dozen of axes cost, at $11.62 per dozen ?

Ans. $ 343.752. 20. Bought 28 bales of cotton cloth, each bale containing 31% yards; what will be the cost, at 16 cents per yard ?

Ans. $ 140.56.

Note. - If both numbers be mixed, or either of them be a complex fraction, they must first be reduced to simple ones.

21. Multiply 87 by 11%.

OPERATION.
87=7t; 113=91.

4 X = 6461 = 10084 Ans. 22. Multiply 16171 by 1945.

Ans. 31369%. 23. Multiply by Ban

Ans. 34. 24. Multiply in by 17 ft.

Ans. 156. 25. Multiply by 71

Ans. 6337. 26. Multiply of 94 by of 17.

Ans. 786. 27. Multiply % of 7 by it of 8711. Ans. 403ž. 28. Multiply 7 by 31.

Ans. 261 29. Multiply 8 by :

Ans. 6. 30. Multiply 12 by 4.

Ans. 84. 31. Multiply 15 by ft.

Ans. 84: 32. A merchant owns } of a ship, he sells of his share to A. What part is that of the whole ship?

Ans. zzz. 33. Multiply 37 by 104.

Ans. 3921. 34. Multiply of 77 by [ of 111.

Ans. 4913. 35. Multiply of 9 by of 17.

Ans. 2685 36. Multiply 5 of 836 by 4 of 91.

Ans. 25,175. 37. Multiply 18g by 15%.'

Ans. 29911 38. Multiply 1 of 1 by # of

Ans. 28885. 39. What cost 7 barrels of flour, at $5% per barrel ?

Ans. $ 3941 40. What cost 94 acres of land, at $27% per acre ?

Ans. $25694.

41. What cost 87 bushels of apples, at $14 per bushel ?

Ans. $117. 42. Bought 117 bushels of corn, at $1% per bushel, and sold

of it for $ 15 per bushel, and the remainder at $17 per bushel ; what is gained on the sale of the corn? Ans. $ 3.

43. What is the continued product of the following numbers : 27 874 o 816, 374 981 27 and 128?

Ans. site

Section XX.
DIVISION OF VULGAR FRACTIONS.

CASE I.
To divide a fraction by an integer or whole number.
1. How many times will contain 8?

OPERATION. To illustrate this question we will supà Xš= 6 Ans. pose of an orange to be divided equally

among 8 persons. Now, if we divide of an orange into 8 equal parts, one of these parts will be equal to of a whole orange, but as there are to be divided among 8 persons, each person will receive 5 times zó = Ans.

RULE. — Multiply the whole number by the denominator of the fraction, and write the product under the numerator. Or, divide the numerator of the fraction by the whole number, if it can be done without a remainder, and write the quotient over the denominator. 2. Divide 1 by 18.

Ans. Tys: 3. Divide 15 by 28.

Ans. 1 4. Divide by 27.

Ans. 255 5. Divide 2 by 128.

Ans. oto 6. Divide H by 98.

Ans. Tot 7. Divide it by 19.

Ans. 14. 8. Divide by 167.

Ans. Toz. 9. Divide 16 by 49.

Ans. TAS 10. Divide I's by 15.

Ans. 225.

CASE II.

To divide a whole number by a fraction. 1. How many times will 17 contain ?

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