33. What is the value of 3 of of 10 of of 15? 34. What is the value of of 34 of 34 of 29? DIVISION. CASE I. 185. To divide a fraction by an integer. 1. Mr. Allen divided 3 fourths of a dollar equally between 3 boys. How much did each receive? 2. A man divided of an acre into 3 equal lots. How large were they? 3. If 7 yards of cloth were bought for $3, what was the cost per yard? 4. If 4 books cost $13, what is the cost of each? 5. Mr. Hurd put of his crop of wheat on 3 wagons. What part of his crop was on each wagon? How much is ÷3? 6. In dividing a fraction, what part of the fraction is divided? 7. A gentleman divided a barrel of flour equally between 2 people. What part of a barrel did each receive? How much is ÷÷2? 8. 3 boys spent altogether $1. If each spent the same amount, what part of a dollar did each spend? How much is 13? 9. Mr. Smith divided of his farm into 3 equal fields. What part of his farm did each field contain? How much is 3? How is the result obtained from the fraction ? 10. In what other way, then, besides dividing the numerator may a fraction be divided? 11. When a number is divided by 3 what part of it is found? 12. When a fraction is divided by 7 what part of it is found? 6 13. What is of 4? 3? of? F÷5? 14. What is the value of 2? Of ÷3? Of ÷ 9? 186. PRINCIPLE.—Dividing the numerator or multiplying the denominator of a fraction by any number, divides the fraction by that number. WRITTEN EXERCISES. 1. Divide 12 by 6. PROCESS. = Or, = ANALYSIS. Since dividing the numerator of a fraction divides the fraction, the fraction may be divided by. 6 by dividing the numerator by 6. Or, Since multiplying the denominater divides the fraction, the fraction may be divided by 6 by multiplying the denominator by 6. The result by both processes is 17. RULE.-Divide the numerator or multiply the denominator by 21. A man gave each of his 5 sons an equal share of ğ of his estate. What part of the whole did each receive? 22. 8 men built of a mile of wall in 10 days. What part of a mile did each man build daily? 23. Mr. B. earned $351 by working 8 days. How much did he earn per day? 24. I paid $10 for 27 pounds of butter. What did I pay a pound? 25. A farmer realized $233 for 21 bushels of clover seed. How much did he get per bushel? 26. Three men who have been partners in business gain $32163. If they share equally, what will be each one's part of the gain? CASE II 187. To divide an integer by a fraction. 1. How many fourths are there in an apple? In 2 apples? 2. How many apples, at cent each, can be bought for 2 cents? For 3 cents? For 10 cents? 3. At $1 a yard, how many yards of cloth can be bought for $1? For $2? For $3? For $10? 4. At $1 an ounce, how many ounces of nutmegs can be bought for $2? How many at $3 an ounce can be bought for $2? 5. If a man can mow of a field per day, how long will it take him to mow the entire field? How long if he can mow per day? 6. At $ a bushel, how many bushels of lime can be bought for $5? At $ a bushel how many bushels can be bought for $5? 7. When apples are worth of a cent apiece, how many can be bought for 12 cents? How many times is contained in 12? 8. How many pieces of cloth of a yard long can be cut from a piece 9 yards long? How many times is in 9? contained 9. How many times is contained in 8? in 9? X WRITTEN EXERCISES. 1. Divide 12 by 9. PROCESS. 2 12÷- 127-14 Or, 12=84; 84÷G=14 ANALYSIS. is contained in 12 7 times 12, or 84 times; and, onesixth of 84 times, or 14 times. Or, Reducing 12 to sevenths, we have 84 sevenths. 6 sevenths are contained in 84 sevenths 14 times. RULE.—Multiply the integer by the denominator of the fraction and divide the product by the numerator. x Or, Reduce the dividend and the divisor to similar fractions, and divide the numerator of the dividend by the numerator of the divisor. 26. Divide 24 by 31. PROCESS. 31=1 ANALYSIS.-When the divisor is a mixed number we reduce it to an improper fraction and proceed according 24324x2=64 to the rule. Thus, 31: ; and 24 divided by 48, and by or 69. Or, = =} of 48, We may reduce 3 to halves, and 24 to halves, and divide the numerator of the dividend by the numerator of the divisor. Divide the following by both processes: 27. 15 by 31. 28. 23 by 63. 29. 26 by 73. 31. 39 by 83. 32. 46 by 75. 33. At $3 a yard, how many yards of cloth can be bought for $15? 34. When corn is worth $ a bushel, how many bushels must a man sell to get money enough to pay $18 taxes? 35. A man invested $32 in peaches at $13 per basket. How many baskets did he purchase? 36. What is the price of hay, when 3 tons sell for $37? 37. Mr. Shaw paid $6 for 143 pounds of Java coffee. What did it cost him per pound? 38. It requires 656 pounds of meat to supply 34 soldiers 3 weeks. How much does each soldier eat daily? CASE III. 188. To divide a fraction by a fraction. 1. How many fourths are there in 1? How many fifths? eighths? tenths? fifteenths? twentieths? 2. How many pieces of cloth of a yard long, can be cut from a yard? |