33. What is the value of of i of li of of 15? 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 $%, 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 } :32 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 1 : 2? 8. 3 boys spent altogether $1. If each spent the same amount, what part of a dollar did each spend? How much is į : 32 9. Mr. Smith divided 1 of his farm into 3 equal fields. What part of his farm did each field contain? How much is 1 :-3? How is the result obtained from the fraction 1? 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? 13. What is { of 1? 4:3? } of ? = 5? 14. What is the value of $ = 2? Of 5 -- 3? Of 1 +9? 186. PRINCIPLE.—Dividing the numerator or multiplying the denominator of a fraction by any number, divides the fraction by that number. WRITTEN EXERCISES. PROCESS. 1. Divide 14 by 6. ANALYSIS.—Since dividing the nu14 =-6=146 = 1 옮 merator of a fraction divides the frac tion, the fraction 14 may be divided by. Or, 6 by dividing the numerator by 6. Or, • 13 - 6=i= 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 1. RULE.—Divide the numerator or multiply the denominator by the given integer. Divide: Divide: 15. 173 by 6. Divide: 17. 38.5 by 8. 19. 361 by 10. 20. 251 by 7. 21. A man gave each of his 5 sons an equal share of 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 $35} by working 8 days. How much did he earn per day? 24. I paid $104 for 27 pounds of butter. · What did I pay a pound? 25. A farmer realized $2331 for 21 bushels of clover seed. How much did he get per bushel? 26. Three men who have been partners in business gain $3216. If they share equally, what will be each one's part of the gain? CASE 11. 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 cach, can be bought for 2 cents ? For 3 cents? For 10 cents? 3. At $f a yard, how many yards of cloth can be bought for $1? For $2? For $3? For $10? 4. At $} an ounce, how many ounces of nutmegs can be bought for $2? How many at $z an ounce can be bought for $2? 5. If a man can mow 4 of a field per day, how long will it take him to mow the entire field? How long if he can mową per day? 6. At $j a bushel, how many bushels of lime can be bought for $5? At $3 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 contained in 9? 9. How many times is a contained in 8? in 9? WRITTEN EXERCISES. PROCESS. 12: 1. Divide 12 by g. ANALYSIS.— is contained in 12 7 times 12, or 84 times; and q, one. 유 i sixth of 84 times, or 14 times. Or, Or, Reducing 12 to sevenths, we have 84 sevenths. 6 sevenths are contained 12=84; 84:- =14 in 84 sevenths 14 times. X RULE.—Multiply the integer by the denominator of the fraction and divide the product by the numerator. 01, X Reduce the dividend and the divisor to similar fractions, and divide the numerator of the dividend by the numerator of the divisor. Divide: Divide: 2. 18 by 4. Divide: 10. 72 by 18. 51 by 27. 19. 69 by 4. 20. 70 by 11 21. 65 by 23. 22. 90 by 41 23. 36 by 13. 24. 39 by 1 25. 24 by 13 9. 39 by Ó. 33. At $1 a yard, how many yards of cloth can be bought for $15? 34. When corn is worth $5 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 $1% per basket. How many baskets did he purchase ? 36. What is the price of hay, when 34 tons sell for $37? 37. Mr. Shaw paid $6 for 14ş pounds of Java coffee. What did it cost him per pound? - 38. It requires 656 pounds of meat to supply 34 soldiers 31 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? |