OPERATION. ¥ × ==224 Ans. It is evident that 17 will contain as many times as there are fourths in 17, which are 4 X 17 =68 times. Again, if 17 contain 1 fourth 68 times, it will contain 3 fourths as many times as 68 will contain 3=223 Ans. RULE. Multiply the whole number by the denominator of the frac tion, and divide the product by the numerator. To divide a mixed number by an integer or whole number. 1. Divide 27 by 6. OPERATION. 6)273 418-48 Ans. We divide 27 by 6, and find that it is contained 4 times, which we write under the 27, and we have 3 remaining, which we multiply by 5, the denominator of the fraction, and to the product we add the numerator 3, and the amount is 18. This we write over the product of 6, the divisor, multiplied by the denominator, 5, then reduce the fraction. 6 x 530. We RULE.-Divide the integers as in whole numbers, and if any thing remains multiply it by the denominator of the fraction, and to the prod uct add the numerator of the fraction, and write it over the product of the divisor, multiplied by the denominator. 2. Divide 293 by 9. 3. Divide 14 by 7. 4. Divide 13 by 8. 5. Divide 14 by 6. 6. Divide $373 among 9 men. Ans. 34. Ans. 28. Ans. $48. Ans. $838. *Ans. 20 cwt. 9. Divide of a prize, valued at $1723, equally between 12 seamen. Ans. 125.6312. 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 $34, what will 1 pound cost? Ans. $0.211. 12. If 12 quarts of wine cost $3.752, what will a quart Ans. $0.31. cost? 13. If $19 will buy 3751 acres of land, how much can be bought for $1? Ans. 1933 acres. CASE IV. To divide one fraction by another, whether the fractions be simple, compound, mixed, or complex. 1. Divide by . OPERATION. Ans. 1. To understand the rationale of 4× = −1 Ans. this process, we find the two factors of, which are and; multiplied by make, as is evident from a preceding rule. We now divide by f, which by Case I of this section will be X= Again, we wish to divide by . It is evident that will contain eight times as often as it will a unit, and it contains an unit times, therefore it contains eight times +=+X+==14 Ans. It will be perceived, that in perforining this question 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. RULE.-Invert the divisor, and proceed as in multiplication. If, however, there be mixed numbers in the question, they must first be reduced to improper fractions, and compound and complex fractions must be reduced to simple fractions. OPERATION. x=; } } = 0. 3×4=33018 Ans. 5. Divide of 7 by of 11. Ans. . 187×77-51526118 Ans. 7. Divide of 91 by of 87. Ans. 478. Ans. Ans. 18. Ans. 1. Ans. Ans. 11 49 1241 20. Divide 161 by 148. 21. Divide of by of fr Ans. 1. 22. Divide of 7 23. Divide of 15 by 7 of 22. Ans. 24. Bought of a coal-mine for $3675, and having sold of my share, I gave of the remainder to a charitable society, and divided the residue among 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 among 7 daughters; what is the share of each daughter? Ans. $158. SECTION XXI. QUESTIONS TO BE PERFORMED BY ANALYSIS. 1. If of a bushel of corn cost 63 cents, what cost a bushel? what cost 15 bushels ? Ans. $10.80. Illustration. If 7 eighths of a bushel cost 63 cents, 1 eighth will cost 1 seventh of 63 cents = 9 cents; and 8 eighths will cost 8 times 9 cents 72 cents, and 15 bushels will cost 15 times 72 cents = $10.80. 2. If 47lb. of pepper cost $2.15, what cost one pound? what cost 30lb. ? Ans. $13.50. Illustration. In 47lb. there are 43lb. Then, if 43 ninths lb. cost $2.15, 1 ninth will cost 1 forty-third of $2.15 $0.05, and 9 ninths or 1lb. will cost 9 times $ 0.05 = $ 0.45, and 30lb. will cost 30 times $0.45 = $13.50. 3. When $1728 are paid for 30 tons of iron, what cost 1 ton? what cost 717 tons? Ans. $432. 4. When $432 are paid for 77 tons of iron, what quantity should be received for $1728 ? Ans. 5. For 77 tons of iron there were paid $432; what sum will it require to pay for 30 tons? Ans. Ans. 6. For 30 tons of iron $1728 were paid; what quantity should be received for $432? 7. Gave 7 bushels of rye for a barrel of flour; how much rye will it then require to purchase 6 barrels of flour? Ans. 492 bushels. 8. Divide $1728 among 17 boys and 15 girls, and give each as much as a girl; what sum does each receive? Ans. each girl $669; each boy $ 4247. 9. If of a ton of hay cost $14.49, what cost 4 tons ? boy Ans. 10. If 4 tons of hay cost $82.50%, what part of a ton will $14.49 buy? Ans. 11. If $14.49 will buy 3 of a ton of hay, how much hay can be obtained for $82.50%? Ans. 12. When $82.504 are paid for 4 tons of hay, what will be the cost of of a ton ? Ans. 13. When 147 tons of copperas are sold for $ 500, what is the value of 1 ton? what is the value of 911 tons? Ans. 14. When 91 tons of copperas are sold for $333.331, what is the value of 147 tons? Ans. 15. Gave $333.331 for 911 tons of copperas; what quantity of copperas should be received for $500? Ans. 16. For 147 tons of copperas $500 were paid; how much might be purchased for $333.33 ? Ans. 17. Purchased 973 gallons of molasses for $31.32; what cost 1 gallon? what cost 7633 gallons? Ans. 18. Sold 7633 gallons of molasses for $244.36; what should I receive for 977 gallons? Ans. 19. If $244.36 will buy 7633 gallons of molasses, what quantity can be obtained for $31.32? Ans. 20. Gave 1975lb. of flax for 40 barrels of flour; how many pounds were given for 1 barrel? how many pounds would it require to buy 144 barrels ? Ans. 7110lb. 21. If 17 bushels of rye cost $15.75, what cost 1 bushel ? what cost 94 bushels ? Ans. $8.5683. 22. If 9 barrels of flour cost $ 504, what cost 1 barrel ? what cost 87 barrels ? Ans. $492. Ans. 50 23. If 13 boarders consume a barrel of pork in 78 days, how long would it last, if 7 more boarders were added to their number? days. 24. If a man by laboring 10 hours a day can, in 9 days, perform a certain piece of work, how many days would it require to do the same work, were he to labor 15 hours a day? 25. If a man, by laboring 15 hours a day, in 6 days can perform a certain piece of work, how many days would it require to do the same work by laboring 10 hours a day? Ans. 26. If a man, by laboring 10 hours a day, can in 9 days perform a certain piece of work, how many hours must he labor each day to perform the same work in 6 days? Ans. 27. Sold 17 bushels of corn for $54; what was received for 1 bushel? what should I have charged for 973 bushels ? Ans. $303. 28. Bought 93 tons of hay at $197 per ton; for what must it be sold per cwt. to gain $7 on my bargain? Ans. $18. |