DIVISION OF FRACTIONS Dividing a whole number by a fraction. square? 2. How many times is 3. How many times $ $2? in $4? contained in 1? 1/2 are there in $1? in 4. What is the quotient of two halves divided by one half? of ÷? What is the quotient of four halves divided by two halves? of ÷ ? of ÷ } ? 2 § + 5. How many fourths are there in this square? What, then, is the quotient of 1 divided by ? 6. How many $1 are there in $1? in $3? 7. What is the quotient of four fourths divided by one fourth? of? What is the difference between the quotients of 1+ and ÷? of 2+ and ÷ 1? and 12÷? 1÷1 ? of 3÷1 8. Explain how 1+1=1+1; 2+1=1+1; 3+1= ¥÷1; }÷1=121⁄2 ÷ 121⁄2 ; & ÷ } = 35 ÷ 38%· 33. Change 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 each to 4ths; to 6ths; to 8ths; to 10ths. Thus, 1==== 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÷before we divided 1 by ? 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, 840 ÷ 40 ÷ 4 = 10. = 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 1, 1, 8, J. 6 A proper fraction is a fraction whose numerator is less than its denominator; as, 4, 4, 8. 2 6 Change 41, 51, 23, 5, 71, to improper fractions. 14. 17÷ 2 6 ÷ 12. 6 ÷ 13. 1/308 17. 31÷ 1 19. 84÷23 6. 2층- 글 7. 31÷1 20. How much are eggs per dozen when 36 cents are paid for 21 dozen? 21. A man's wages amounted to 46 dollars for 9 days' work. How much did he receive per day if he earned this amount in 9 days? 22. A sum of money yielded 71 dollars interest. How many years was the money at interest if it yielded 71 dollars each year? 23. A merchant sold 81 cents' worth of ribbon. If he sold 6 yards, what was the price per yard? 20. At 2ğ dollars each, how many vests can be bought for $42? 21. At $1 apiece, how many pictures can be bought for $101? a yard. How many 22. I paid $28 for cloth at $1 a yard. yards did I buy? 23. I spent $17 for molasses at $1, 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 3 bushels of apples cost $27, how much will one bushel cost? 27. A man earns $161 in 5 days. How much is this per day? 28. At $2 per 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. of of the square of the square. = { 5. In dividing by 2, we separate into two equal parts; thus, 4, 4, and take one of these equal parts. Observe that taking of and dividing by 2 gives the same result. 6. of of the square of the square; then ÷ 4 = }. 7. In dividing by 4, we separate into 4 equal parts; thus,,,,, and take one of these equal parts. Then +4. Observe that taking of and dividing by 4 gives the same result. = = 8. of 18 of the square of the square; then 18+8 ? 16 Observe that taking gives the same result. 9. 18816 = of 18 and dividing 18 by 8 13. 18+9=2% ? ? ? ? 11. 28+5=20 12. 18+4=15 16. 14÷8=24 20. 18+5=28 15. 18+4=18 19. 12÷6= 30 ? ? 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. |