11. At of a dollar a pound, how much coffee can be bought for $12? Ans. 64 pounds. 12. If it takes of a yard of cloth to make a vest, how many vests can be made from 6 yards? Ans. 9 vests. 126. When the divisor is a mixed number, reduce it to an improper fraction, before dividing. 18. At 64 cents a pound, how many pounds of rice can be bought for $1.50? Ans. 24 pounds. 19. How many bushels of wheat, at $24 a bushel, can be bought for $39? Ans. 18 bushels. When the divisor is a mixed number, how do you proceed? Explain the operation. Case III. A Fraction by a Fraction. 127. 1. Let it be required to divide by 2. which is times, or 12; or, by reducing, 13. quotient of divided by & is 1. Therefore, the Rule.-Divide by the numerator of the divisor, and multiply by its denominator; or, Invert the divisor, and proceed as in multiplication. If there are mixed numbers, reduce them to improper fractions. 12. How many pounds of tea, at 4 of a dollar a pound, can be bought for $71? Ans. 30 pounds. 13. When for of a dollar 34 bushels of apples can be bought, what is the cost of 1 bushel? 14. At 3 of a dollar for 2 of a yard of cloth, what is the price per yard? Ans. 117 dollars. What is a Prime Num What is an Integer? (84.) 15. At of a dollar a gallon, how many gallons of kerosene can be bought for $51? 16. How many bottles, of 11 pints each, can be filled 3. Change $31 to sixths of a dollar. 4. Reduce 193 to an improper fraction. 5. Change 22 to a fractional form. Ans. . Ans. $186. Ans. 136. 6. Change 22 to a fraction whose denominator is 3. 7. Reduce and to fractions having a common de. nominator. Ans. 1. 22. What is the value of 14 ÷ ÷? REVIEW. What is Analysis? (94.) What is a Fraction? A Common Fraction? (142.) The Terms of a Fraction? (96.) 23. A merchant owning of a ship, bought more; Ans. 1. how much did he then own of it? 24. A farmer divided some hay into 20 equal parts, and gave 16 parts to his cows, and the rest to his sheep; what fraction of the whole did the sheep get? Ans. Ans. 99731. 25. What number is that to which if you add 3ğ, the sum will be 16? Ans. 123. 26. If of a mill is worth $3740, what is the value of the whole? 27. When 13 tons of coal are sold for $712, what is the price per ton? Ans. 5. 28. Paid $10 for tea, at the rate of 7 of a dollar a pound; how many pounds did I buy? 29. If the divisor is, and the quotient the dividend? 30. How many bushels of corn, at bushel, must be given for 1g of a ton of ton? 21, what is Ans. 5. of a dollar a coal, at $41⁄2 a Ans. 8. 31. When broadcloth is 48 dollars a yard, how many yards can be bought for 3 cords of wood, at 7 dollars a cord? Ans. 4 yards. QUESTIONS FOR ANALYSIS. 1. If 1 barrel of flour cost $9, how much will ₫ of a barrel cost? SOLUTION. - If 1 barrel cost $9, of a barrel will cost of $9, or $2.25; and will cost 3 times $2.25, or $6.75. Therefore, if 1 barrel of flour cost $9, of a barrel will cost $6.75. 2. If 1 ton of coal be worth $5.25, what is of a ton worth? Ans. $4.20. 3. When $8.80 is paid for doing a certain amount of work, how much must be paid for doing as much? 4. If an acre of land produce 36% hundred weight of hay, how much will of an acre produce? 5. If in a lot there are 1527 acres, what is the extent of of it? Ans. 11 acres. 6. If of a barrel of flour cost $6.75, what will 1 barrel cost? SOLUTION. If of a barrel cost $6.75, 4 of a barrel will cost of $6.75, or $2.25, and 4, or 1 barrel, will cost 4 times $2.25, or $9. Therefore, if of a barrel of flour cost $6.75, 1 barrel will cost $9. 7. If of a yard of cloth cost $3.78, what will a whole yard cost? Ans. $4.32. 8. Paid $156 for a horse, which was as much as I paid for a wagon; how much did I pay for the wagon? Ans. $180. 9. A farmer sold 311 bushels of grain, which was of all he had; how much had he? Ans. 36 bushels. 10. If 11 acres is of a certain field, what is its entire extent? Ans. 151 acres. 11. If 4 tons of hay cost $52, what will 3 tons cost? SOLUTION. - If 4 tons cost $52, 1 ton will cost $13. 3 tons are 1 tons; and if 1 ton cost $13, of $52, or will cost 12. When $60 are paid for 12 yards of broadcloth, how much must be paid for 9 yards? Ans. $49.37. 13. If 3 tons of hay cost $41, what will 4 tons cost? |