DIVISION OF FRACTIONS Dividing a whole number by a fraction. 1. How many halves are there in this square ? 2. How many times is j contained in 1 ? / 3. How many times $1 are there in $1? in $2? in $4? 1 - 12=2 4. What is the quotient of two halves divided by one half ? of į. What is the quotient of four halves divided by two halves ? 14 of 1 + 1 ? of g = ? 5. How many fourths are there in this square ? What, then, is the quotient of 1 divided by 1 ? K 14 = 4 6. How many $4 are there in $1? in $3? 7. What is the quotient of four fourths divided by one fourth ? of 4+1? What is the difference between the quotients of 1+1 and 4 +1? of 2= 1 and f = 12 of 3+1 and 14 +1? 8. Explain how 1 + 1 = 4 + 1; 2 + 1 = 1 = 1; 3+1= +1; $1= 12 + 1' ; = =*+ 3%. 28. Give quotients: 9. 2+1 15. 5+ } 10. 4:1 16. 6+ 1 11. 5=1 17. 6 = 1 12. 2+1 18. 8+1 13. 4+1 19. 5+1 14. 3+ } 20. 4+1 21. 12 = 1 9 = 1 27. 15 = 1 2+1 4+ 5:} 31. 16 = 1 32. 10 + 1 30. 33. Change 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 each to 4ths; to 6ths ; to 8ths ; to 10ths. Thus, 1 = 4 = = = 18. 34. What change must be made in and before they can be added or their difference taken ? 35. What change did we make in the problem 1: 1 before we divided 1 by 1? 36. What change did we make in the fractions in example 8 before one fraction was divided by another fraction ? This is the first step. 37. When the fractions have been made similar what is the second step in dividing the fractions ? the third step ? Any number may be divided by a fraction by changing both numbers to similar fractions and then dividing the numerators. Thus, 8= * = 40 = $ = 40 + 4 = 10. ☆ : }= }= = 15 = 8= 13. Dividing a whole number or a mixed number by a fraction. An improper fraction is a fraction whose numerator is equal to or greater than its denominator; as 4, 5, 6, 7. A proper fraction is a fraction whose numerator is less than its denominator; as, 4, 4, é Change 41, 51, 23, 51, 73, to improper fractions. Written Work 41 = g Change 41 to the improper fraction . i= 4, *=,= 18 + 3, or 6. *=*=6 = c. d. 9 14. 6 ; 12. 6 18. Divide: 13 = 1 9. 10 15. 21 = 1 10. 8 ; 3/ 16. 19. 89 = 23 20. How much are eggs per dozen when 36 cents are paid for 24 dozen ? 21. A man's wages amounted to 46 dollars for 97 days' work. How much did he receive per day if he earned this amount in 91 days? 22. A sum of money yielded 71 dollars interest. How many years was the money at interest if it yielded 7 dollars each year ? 23. A merchant sold 81 cents' worth of ribbon. If he sold 6 yards, what was the price per yard ? 12. Dividing a mixed number by a mixed number. Written Work 1. Divide 1ị by 11 First change the mixed numbers 6 = c.d. to improper fractions, then make the fractions similar, and di de the nu11 = 11 merator of the dividend by the nu& = !=9+8, 9 or 1} merator of the divisor. 2. 71 = 21 8. 123 - 61 14. 3] + 93 3. 6z = 1 9. 144 + 24 15. 33 +31 4. 51-14 10. 31 +21 16. 8f +61 5. 83 - 2 11. 53 = } 17. 9] + 3} 6. 71-13 61 - 74 18. 31% = 2% 7. 3} = 21 13. 83 - 92 19. 61 -47 20. At 2g dollars each, how many vests can be bought for $42 ? 21. At $1] apiece, how many pictures can be bought for $101? 22. I paid $284 for cloth at $1} a yard. How many yards did I buy? 23. I spent $17} for molasses at $1b a gallon. How many gallons did I buy? 24. At $1} each, how many straw hats can be bought for $143 ? 25. A merchant purchases $50% worth of gas lamps at $4} a piece. Find the number purchased. 26. When 31 bushels of apples cost $216, how much will one bushel cost? 27. A man earns $ 163 in 52 days. How much is this per day? 28. At $2per pair, how many pairs of shoes can be bought for $171? 1. How many fourths of a square are there in one square ? 2. How many eighths of a square are there in one square ? 3. How many sixteenths of a square are there in one square? 4. 1 of 4 of the square = { of the square. 5. In dividing 4 by 2, we separate 4 into two equal parts ; thus, į, 4, and take one of these equal parts. Observe that taking 1 of 4 and dividing 4 by 2 gives the same result. 6. I of of the square = of the square; then f +4= 7. In dividing | by 4, we separate into 4 equal parts; thus, j, , k, k, and take one of these equal parts. Then f+4= g. Observe that taking of f and dividing f by 4 gives the same result. 8. 5 of 18 of the square = 1a of the square; then 18 + 8 1&. Observe that taking } of 18 and dividing 18 by 8 gives the same result. 9. 18 +8= 1 13. = 9= 25 17. 3} = 7= } 10. 11 + 3= 1 14. ff +6= 315 18. 14 + 2 = 11. 18 +5= 20 15. 13 + 4= 18 19. 16 = 6= 30 12. 18 +4= 16 16. 14+8= 21 20. 3+5= 21. How may a fraction be divided by a whole number? A fraction may be divided by a whole number by dividing the numerator of the fraction by the whole number. 28 |