7. Multiply 23 by 11. 8. Multiply 47 by 15. 9. Multiply 37 by 18. 10. Multiply 67811 by 24. Ans. 16294. 11. What will 233 pounds of lead cost, at 8 cents a pound? 12. What will 15 pound? 13. What will 29 Ans. $1.91. pounds of sugar cost, at 12 cents a Ans. $1.884 cwt. of hay cost, at $1.12 per cwt.? Ans. $32.943. 14. What will 97 yards of broadcloth cost, at $8 per yard? 15. What will 17 Ans. $79.00. tons of potash cost, at $97 per ton? Ans. $1703.561. 16. What will 3 per ton? 17. What will 17 dozen candles cost, at 16 cents a dozen? Ans. $2.783. 18. What will 273 pounds of bar soap cost, at 7 cents a pound? tons of plaster of Paris cost, at $12.75 Ans. $40.18. Ans. $1.918. 11.62 per 19. What will 29 dozen of axes cost, at dozen? Ans. $343.75%. 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. SECTION XV. DIVISION OF VULGAR FRACTIONS. CASE I. To divide one fraction by another. 1. If 2 peaches cost of a cent, what will 1 peach cost? 2. If 1 orange cost 3 apples, what part of an orange will 1 apple buy? 3. If of a yard of cloth cost 1 dollar, what will of a yard cost? yard? 4. A certain teacher divided an orange between 8 of his pupils; what part did each receive? 5. A quarter of a dollar is divided equally between 4 persons, what part does each receive? 6. Among how many boys, must 8 apples be distributed to give each of an apple? 7. Divide by OPERATION. X=1} Ans. By multiplying the numerator of the dividend 4, by the denominator of the divisor 8, the dividend is reduced to eights; and then by multiplying the denominator of the dividend, 7, by 3, the numerator of the divisor, one third of the eights are taken. Hence we deduce the following RULE. Prepare the fractions as in Addition; invert the divisor, and proceed as in Multiplication. 16. Divide Ans. 1. Ans. 118. 16 Ans. 68 173. Ans. 113. Ans. 36 775. Ans. 18 407. 24. Bought of a coal mine for $3675, and having sold of it, I gave of the remainder to a charitable society, and divided the residue between 7 poor persons; what was the share of each? Ans. $50 for each poor person. 25. Of an estate valued at $5000, the widow receives }, the oldest son of the remainder; the residue is equally divided between 7 daughters; what is the share of each daughter? Ans. $158. CASE II. To divide an integer or whole number by a fraction. 1. Divide 17 by 2. OPERATION. 17X468=223 Ans. By multiplying the dividend by 4, it is reduced to fourths; and by dividing the product by 3, the quotient will be threefourths. Hence the following RULE. Multiply the whole number by the denominator of the fraction, and divide the product by the numerator. Multiply the integer by the denominator of the fraction, and write the product under the numerator. OPERATION. 6) 27 We divide the 27 by 6, and find it is contained 4 times, and that 3 remains, which we multiply by the denominator, 418-48 Ans. 5, and to the product we add the numerator, 3, the sum of which is 18; this we write over the product of 6, the divisor, multiplied by the denominator, 5=30. Hence the following RULE. Divide the integer 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. 7. Divide $963 between 11 persons. 8. What is of 1677 cwt. of iron? 180 Ans. $89. Ans. 20 cwt. 9. Divide of a prize, valued at $1723, equally between 12 seamen. Ans. $125.63. 10. What will a barrel of flour cost, if 19 barrels can be purchased for $107? Ans. $5.65 11. If 15 pounds of raisins can be obtained for $33, what will 1 pound cost? Ans. $0.21. 12. If 12 quarts of wine cost $3.752; what will a quart cost? Ans. $0.31. 13. If $19 will buy 375 acres of land; how much can be bought for $1. Ans. 1933 acres. 304 MISCELLANEOUS QUESTIONS. 1. How far will a man walk in 17 hours, provided he goes at the rate of 43 miles an hour? Ans. 82m. 4fur. 8rd. 1ft. 4in. 2. How much land is there in a field, which is 29 rods square? Ans. 5A. 1R. 32p. 141ft. 1091in. 3. How much wood in a pile, which is 172 feet long, 7 feet high, and 43 feet wide? Ans. 4cd. 6617ft. 4. What is the value of 193 barrels of flour, at $ 62 a barrel? Ans. $134.15. 5. What is the value of 376 acres of land, at $75 per acre? Ans. $28387.06. 6. What cost 17 quintals of fish, at $4.75 per quintal? Ans. $81.55. 7. What cost 1670 pounds of coffee, at 122 cents per pound? Ans. $212.99 8. What cost 28 tons of Lackawana coal, at $112 a ton? Ans. $333.27. 9. Bought 37 hogsheads of molasses, at $17.621⁄2 a hhd.; what was the whole cost? Ans. $655.20. 10. What cost of a cord of wood, at $5.75 a cord? Ans. $5.03. 11. What are the contents of a field, which is 139 rods long, and 38 rods wide? Ans. 33A. 3R. 1533p. 12. Bought 15 loads of wood, each containing 113 feet, cord measure. I divide it equally between 9 persons; what Ans. 19 ft. does each receive? 13. If the transportation of 183 tons of iron cost $48.15, what is it per ton? Ans. $2.62 14. If a hhd. of wine cost $983, what is the price of one gallon? Ans. $1.56. 15. If 5 bushels of wheat cost $83; what will a bushel be worth? 16. What will 11 hogsheads and 173 gallons of wine cost, at 192 cents a gallon? Ans. $140.323. Ans. $1.643. 17. How many bottles, each containing 12 pints, are sufficient for bottling a hhd. of cider? Ans. 288 bottles. 18. I have a shed, which is 18 feet long, 10 feet wide, and 7 feet high; how many cords of wood will it contain? Ans. 11cd. 124in. |