DIVISION OF FRACTIONS Dividing a fraction by an integer. 1. If 10 marbles are divided equally between two boys, how many marbles does each boy receive? Then 10 + 2 means that 10 is to be separated into two equal parts, 5 and 5, and that one of these parts is to be taken. 2. If f of a yard of ribbon is divided equally between 2 girls, how many eighths of a yard does each girl receive ? Then f + 2 means that f is divided into 2 equal parts, and g, and that one of these parts is to be taken. 3. If $3 is divided equally among four boys, what part of the money does each boy receive? Then if = 4 means that it is to be separated into 4 equal parts, 24, 25, 26, and on, and that one of these parts is to be taken. 4. What term of the fraction f do you divide by 2 to get ? 5. What term of the fraction do you divide by 4 to get ? 6. Show that the fractions , ld, if, and if each can be divided by 2 without changing the size of the fractional unit. Observe, then, that a fraction can be divided by an integer, by dividing the numerator of the fraction by the integer. Divide : 7. by 2 8. Bo by 4 9. if by 3 10. 35 by 5 11. 18 by 6 12.2 by 8 13. 2 by 7 14. by 8 15. 45 by 9 16. 123 by 12 17. 10% by 11 18. 8.6 by 12 19. 64 by 9 20. by 10 21. 131 by 11 22. In + 5, are there 5 equal parts of teach? Can we change to the equivalent fraction 3!? - 5=ır. Since = }, then + 5 = 5 23. In dividing # by 5, what term of the fraction did we multiply by 5? Observe, then, that a fraction can be divided by an integer by multiplying the denominator of the fraction by the integer. Divide : 30. by 3 31. § by 6 26. á by 3 29. by 3 32. by 4 33. If 5 men do 1% of a piece of work in one day, what part of the work is done by one man ? 34. John earns $g in 4 hours. How much does he receive per hour? 35. A real estate agent buys of an acre of land and divides it into 10 lots. What is the size of each lot? 36. When 4 bushels of wheat sell for 3} dollars, what is the price per bushel ? SUGGESTION. First change 3} to an improper fraction. 37. Four newsboys earn $3 by selling papers, and share equally. How much does each boy receive ? 38. A conductor earned $3} in 16 hours. How much per hour? 39. Thirteen carpenters were paid $45] for doing a piece of work. How much did each receive? 40. It cost $ 1} to send a cablegram of 6 words. How much was that per word ? was that • 18 3. Divide 13 by 18. In cases like this it is convenient to 2 indicate the multiplication of the de12 2 noninator by the integer, and cancel. 12 The factor 6 is contained twice in the 13 13 x 1839 numerator and three times in the denoini3 nator. The result is g. NOTE.— When the numerator is exactly divisible by the integer, the method of example 1 is preferable; in all other cases the methods of examples 2 and 3. To divide a fraction by an integer, divide the numerator or multiply the denominator by the integer, canceling when possible. Dividing a small mixed number by an integer. Written Work First change the mixed number to an im135 135 proper fraction. Then divide by multiplying +7= 23 the denominator. The result is , which may 8 56 be reduced to the mixed number 24. Find the quotients : 2. 224 = 13 5. 417 - 22 8. 51= 20 3. 351 - 16 6. 374 - 10 9. 29-41 - 9 4. 17} = 12 7. 181 = 32 10. 46} = 15 11. A train travels 99% miles in 4 hours. What is its rate per hour ? 12. When a man earns $243 in 6 days, how much does he earn per day ? 13. A ten-story building is 112 feet high. What is the average height of each floor? 14. In 28 days a hotel used 3614 pounds of butter. How many pounds did it use a day? Dividing a large mixed number by an integer. Written Work 1. Divide 15702 by 8. 8) 15703 Divide as in whole numbers. The quotient is 196 1962 and the remainder 21. of 21 = } of \, or ft. The result is 19631. Find the value of : 2. 2687] = 9 5. 4267* = 12 8. 1977 = 5 3. 1365 * = 8 6. 58313 - 11 9. 31644 =10 4. 38535 : 7 7. 4783} = 6 10. 17907 +12 Dividing any number by a fraction by changing both numbers to similar fractions. 1. What kind of whole units can be added ? What kind can be subtracted ? Illustrate by examples. 2. What change must be made in 10 ft. + 2 in. before the numbers can be divided ? 3. Observe that only concrete numbers of the same kind can be divided. Thus $20 - $10, 100 ft. • 10 ft., etc. 4. What name is given to fractions having the same denominator? Change and i to 20ths. 5. How often is 15 twentieths contained in 16 twentieths ? 16 twentieths 15 twentieths 115. Test: 15 twentieths x 115 = 16 twentieths. Then + f= - 18 = 16 + 15=11: 6. 8+4= 4 + 4 = 4 + 4 = ? NOTE. - Observe that 8 can be written as an improper fraction f and then both fractions can be changed to similar fractions. 7. How, then, can a fraction be divided by a fraction ? NOTE. — Mixed numbers should first be changed to improper fractions. 5. 6. 5 1 Written Work Find quotients : 1. } + 9. 13 2. 15-15 5 + 1 10. 54 - 25 3. 6 + 7. + 11. 34 - 4 12. 57:10 13. Compare 1 = 1 and 1+4. 14. Compare 8+1 and 8. 15. How many times are 24 contained in 84 ? Divide 81 by 24. 4. 12 12 |