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43. Multiply 7} by 84.

Ans. 6036 44. Multiply 47 by 91.

Ans. 453.. 45. Multiply 114 by 8.

Ans. 9915. 46. Multiply 125 by 11g.

Ans. 1471 47. What cost 78 cords of wood at $ 5% per cord ?

Ans. $4131 48. What cost 73yds. of cloth at $34 per yard ?

Ans. $ 2512 49. What cost 64 gallons molasses at 23 cents per gallon ?

Ans. $ 15225 50. If a man travels 34 miles in one hour, how far will he travel in 97 hours ?

Ans. 34. 51. What cost 36111 acres of land at $ 25% per acre ?

Ans. $ 9167113. 52. If şof of a dollar buy one bushel of corn, what

will 7 of of a bushel cost ? Ans. 7 of a dollar. 53. How many square rods of land in a garden, which is 9716 rods long, and 494 rods wide ?

Ans. 481036 rods. 54. If ; of 4 of i of an acre of land cost one dollar, how much may be bought with of $ 18 ?

Ans. 167 acres. Note. The following questions are to exercise the foregoing rules. 55. What are the contents of a field 76,35 rods in length

and 18 rods in breadth ? Ans. 8A, 3R. 304p. 56. What are the contents of 10 boxes which are 7 feet long, li wide, and 14 feet in height ?

Ans. 16917 cubic feet. 57. From 11 of an acre of land there were sold 20 poles and 200 square feet. What quantity remained ?

Ans. 2R. 1p. 223ft. 58. What cost 1 of an acre at $ 1.75 per square rod ?

Ans. $ 236.9243. 59. What cost is of a ton at $ 15% per cwt. ?

Ans. $ 49.7315. 60. What is the continued product of the following numbers 143, 114, 54, and 104?

Ans. 9184. 61. From is of a cwt. of sugar there was sold , of it; what is the value of the remainder at $ 0.123 per Ib. ?

Ans. $ 3.57.

83

per acre ?

per lb. ?

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62. What cost 19 barrels of flour at $7% per barrel ?

Ans. $ 1434. 63. What cost 13 quintals of fish at $3% per quintal?

Ans. $ 5131 64. I have two parcels of land, one containing 770 acres, and the other 912 acres. What is their value at $ 783

Ans. $ 1380.705. 65. From a quarter of beef weighing 1753 lbs. I gave John Snow of it ; of the remainder I sold to John Cloon. What is the value of the remainder at ofcents

Ans. $ 2.0413 66. Alexander Green bought of John Fortune a box of sugar containing 475 lbs. for $ 30.00. He sold of it at 8 cents per lb., and of the remainder at 10 cents per lb. What is the value of what still remains at 124 cents per lb., and what does Green make on his bargain ?

Ans. Green's bargain, $ 16.973.

Value of what remains $ 13.19%. 67. What cost 114 of an acre at $ 144 per acre ?

Ans. $2.00. 68. D. Sanborn's garden is 234 rods long and 134 rods wide, and is surrounded by a good fence 7 feet high. Now if he shall make a walk around his garden within the fence 7 feet wide, how much will remain for cultivation ?

Ans. 1A. 3R. 7p. 8513&_ft. 69. On of my field, I plant corn ; on of the remainder I sow wheat ; potatoes are planted on 4 of what still remains, and I have left two small pieces, one of which is 3 rods square, and the other contains 3 square rods. How large is

my
field ?

Ans. 1A. OR. 29p. 70. Multiply z of 4 of 11 by of 1} of zß. Ans. to.

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12

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Section 24.

DIVISION OF VULGAR FRACTIONS.

1. To divide a fraction by a whole number. 1. How many times will contain 9 ?

To understand this question, +x= Ans. we will suppose of an apple

OPERATION.

were to be divided equally among 9 persons. Now, if we divide 4 of an apple into 9 equal parts, there would be 63 parts, and each person would receive 6s; but there being 4, each man will receive 5 times = 6 Ans. Hence we see the propriety of the following

RULE,

Multiply the whole number by the denominator of the fraction, and write the product under the numerator. 2. Divide / by 12.

Ans. 12 3. Divide 11 by 8.

Ans. 6. 4. Divide y by 12.

Ans. Tās 5. John Jones owns of a share in a railroad, valued at $ 117 ; this he bequeaths to his five children. What part of a share will each receive ?

Ans. 4. 6. Divide by 15.

Ans. Tỉs. 7. Divide by 28.

Ans. Is 8. James Page's estate is valued at $ 10,000, and he has given 4 of it to the Seamen's Society ; of the remainder he gave to his good minister ; and the remainder he divided equally among his 4 sons and 3 daughters. What sum will each of his children receive ?

Ans. $ 68048 II. To divide a whole number by a fraction. 9. How many times will 13 contain ?

Ans. 304.

It is evident, that 13 1 X}== 304 Ans.

will contain 4, as many

times as there are sevenths in 13, which are 7 x 13 = 91 times. Again, if 13 contain 1 seventh 91 times, it will contain 3 sevenths as many times as 91 will contain 3 = 301 Ans. Hence the following

OPERATION.

RULE.

Multiply the whole number by the denominator of the fraction, and divide the product by the numerator. 10. Divide 18 by }.

Ans. 204. 11. Divide 27 by 13.

Ans. 291

12. Divide 23 by 1.

Ans. 92. 13. Divide 5 by }.

Ans. 25. 14. Divide 12 by .

Ans. 16. 15. Divide 16 by 1.

Ans. 32. 16. Divide 100 by 17.

Ans. 11111. 17. I have 50 square yards of cloth, how many yards, of a yard wide, will be sufficient to line it ?

Ans. 83} yards. 18. A. Poor can walk 31 miles in 60 minutes ; Benjamin can walk is as fast as Poor. How long will it take Benjamin to walk the same distance ?

Ans. 73} minutes.

OPERATION.

III. To divide a mixed number by an integer. 19. Divide 173 by 6.

Ans. 24%. We divide 17 by 6, and find it is con6) 173 tained 2 times, which we write under the 243

17, and we have 5 remaining, which we

multiply by 8, the denominator of the fraction ; and to the product we add the numerator, 3,

; and the amount is 43, this we write over the product of 6, the divisor, multiplied by the denominator, 8, = 48. The rationale of the above question is the same as of those in Rule I. of this section. Hence the following

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RULE.

Divide the integers as in whole numbers, and if any thing remains, multiply it by the denominator of the fraction, and to the product add the numerator of the fraction, and write it over the product of the divisor, multiplied by the denominator. 20. Divide 173 by 7.

Ans. 236. 21. Divide 187 by 8.

Ans. 217. 22. Divide 2711 by 9.

Ans. 3105. 23. Divide 31 ) by 11.

Ans. 2016 24. Divide 784 by 12.

Ans. 617. 25. Divide 1891} by 4.

Ans. 4718. 26. Divide 10714 by 3.

Ans. 3536

27. Divide $ 174 among

ny men.

Ans. $234. 28. Divide $ 1067 among 8 boys. Ans. $ 1343. 29. What is the value of of a dollar ?

Ans. $0.3415. 30. Divide $ 10711 among 4 boys and 3 girls, and give the girls twice as much as the boys.

Ans. boy's share $ 10%. Girl's share $213.. 31. If $ 14 will purchase 37 of a ton of copperas, what quantity will $ 1 purchase ? Ans. lcwt. Oqr. 24lbs.

IV. To divide one fraction by another. 32. Divided by .

Ans. 131

To understand the ra{ x==131 Ans.

tionale of this process, we

find the two factors of $, which are * and ; for * multiplied by } are $, as is evident from a preceding rule. We now divide ž by 1, which, by case I. of this section, will be } X = 5. Again, we wish to divide 32 by š. It is evident, that 3 will contain f nine times as often, as it will a unit, and it contains a unit 3 times, therefore it contains į nine times 7=i X 2=3= 131 Ans. In performing this question, it will be perceived, that the numerator of the dividend has been multiplied by the denominator of the divisor, and the denominator of the dividend by the numerator of the divisor. Hence the following

OPERATION

RULE.

Invert the divisor and proceed as in multiplication. If, however, there be mixed numbers in the question, they must be reduced to improper fractions, and compound fractions must be reduced to simple fractions. 33. Divide 7 by 4.

OPERATION.

} x1==11. Ans. 34. Divide 74 by 34.

OPERATION

=

74= 4,34 = 2*, 41 X=41 = 236 Ans. 35. Divide [ by 1.

Ans. 31.

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