OPERATION It is evident that 17 will contain Y X = 8 = 22 Ans. I 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=22 Ans. Rule. - Multiply the whole number by the denominator of the fraction, and divide the product by the numerator. 2. Divide 18 by It. Ans. 284. 3. Divide 28 by Ans. 415. 4. Divide 27 by L. Ans. 459. 5. Divide 128 by Zs. Ans. 960. 6. Divide 98 by 17. Ans. 1511 7. Divide 19 by . Ans. 312 8. Divide 167 by 15. Ans. 2005 9. Divide 49 by zs. Ans. 8818. 10. Divide 15 by 15. Ans. 225. CASE III. To divide a mixed number by an integer or whole number. 1. Divide 273 by 6. OPERATION. We divide 27 by 6, and find that it is 6)273 contained 4 times, which we write under 418 — 43 Ans. 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,= 6 x 5=30. We then reduce the fraction. 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. 2. Divide 293 by 9. Ans. 343. 3. Divide 141 by 7. Ans. 21. 4. Divide 137 by 8. Ans. 142. 5. Divide 143 by 6. Ans. 213. 6. Divide $ 373 among 9 men. Ans. $ 415 7. Divide $ 96% among 11 persons. Ans. $ 83. 8. What is of 16711 cwt. of iron ? Ans. 2031 cwt. 9. Divide ţ of a prize, valued at $ 1723, equally between 12 seamen. Ans. $ 125.631.1. 10. What will a barrel of flour cost, if 19 barrels can be purchased for $ 1073? Ans. $ 5.6535. 11. If 15 pounds of raisins can be obtained for $ 34, what will 1 pound cost ? Ans. $ 0.21.11. 12. If 12 quarts of wine cost $ 3.75%, what will a quart cost? Ans. $ 0.31 : 13. If $ 19 will buy 37514 acres of land, how much can be bought for $17 Ans. 19384 acres. CASE IV. To divide one fraction by another, whether the fractions be simple, compound, mixed, or complex. 1. Divide 6 by ft. Ans. 14. OPERATION. To understand the rationale of 4 x = -111 Ans. this process, we find the two factors of , which are į and }; multiplied by f make, as is evident from a preceding rule. We now divide 4 by , which by Case I of this section will be XI=4. Again, we wish to divide a bys. It is evident that I will contain f eight times as often as it will a unit, and it contains an unit times, therefore it contains f eight times =iX = =121 Ans. It will be perceived, that in performing 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. 45 1985 X =5459 = 648 Ans. 7. Divide of 91 by io of 87. Ans. 2649. OPERATION. #x9 = 364; 1 X 2=192. 364 x 75=4844 Ans. 8. Divide by . 15 x = = ft Ans. 9. Divide it by. Ans. 15. 10. Divide by 19. Ans. 133. 11. Divide by s. Ans. It 12. Divide is by 11. Ans. 116 13. Divide by 14. Ans. He 14. Divide 1ě by ts. 15. Divide by 73. Ans. ** 16. Divide Å by 16%. Ans. L. 17. Divide 114 by 4. Ans. 20. 18. Divide 214 by 184. Ans. 1113. 19. Divide 173 by 284. Ans. Afts. 20. Divide 1613 by 14. Ans. 1111 21. Divide 11 of by of it. Ans. 11. 22. Divide 5 of 74 by A of 17%. Ans. It 23. Divide 4 of 15 by 1 of 22. Ans. 183765 24. Bought į of a coal-mine for $ 3675, and having sold Ans. 113. 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. $15846. 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 4 lb. there are 4,31b. Then, if 43 ninths lb. cost $ 2.15, 1 ninth will cost 1 forty-third of $ 2.15 = $ 0.05, and 9 ninths or llb. will cost 9 times $ 0.05 = $ 0.45, and 301b. will cost 30 times $ 0.45 = $13.50. 3. When $1728 are paid for 304 tons of iron, what cost 1 ton ? what cost 777 tons ? Ans. $ 432. 4. When $ 432 are paid for 737 tons of iron, what quantity should be received for $1728 ? Ans. 5. For 737 tons of iron there were paid $432; what sum will it require to pay for 3045 tons ? Ans. ' 6. For 3045 tons of iron $1728 were paid ; what quantity should be received for $ 432?. Ans. 7. Gave 770 bushels of rye for a barrel of flour; how much rye will it then require to purchase 6 barrels of flour ? Ans. 49%; bushels. 8. Divide $1728 among 17 boys and 15 girls, and give each boy It as much as a girl ; what sum does each receive ? Ans. each girl $ 6691 ; each boy $ 4241. 9. If 7 of a ton of hay cost $14.49, what cost 44 tons ? Ans. 10. If 43 tons of hay cost $ 82.50%, what part of a ton will $14.49 buy ? Ans. 7 " 11. If $14.49 will buy of a ton of hay, how much hay can be obtained for $ 82.503 ? Ans. harga 12. When $ 82.50% are paid for 4 tons of hay, what will be the cost of of a ton ? Ans. 13. When 14; tons of copperas are sold for $ 500, what is the value of 1 ton ? what is the value of 91 tons ? Ans. 14. When 911 tons of copperas are sold for $ 333.33}, what is the value of 14% tons ? Ans. 15. Gave $ 333.33} 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 977 gallons of molasses for $ 31.32; what cost 1 gallon ? what cost 7635 gallons ? Ans. 18. Sold 7635 gallons of molasses for $244.36; what should I receive for 977 gallons ? Ans. 19. If $ 244.36 will buy 763} 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 91 bushels ? Ans. $ 8.56%}. 22. If 9 barrels of flour cost $ 50%, what cost 1 barrel ? what cost 873 barrels ? Ans. $ 49238. 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? Ans. 50-7 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. j. 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 17-3 bushels of corn for $54 ; what was received for 1 bushel ? what should I have charged for 973 bushels ? Ans. $ 3031. 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. $1.eu |