22. If } of a square is divided into 2 equal parts, what fraction of the square is each part? Then +2= 1 = 1 23. If į of a square is divided into 2 equal parts, what fraction of the square is each part? Then I +2= 24. If } of a square is divided into 8 equal parts, what fraction of the square is each part? Then 1 +8= }, 25. Since 1 +2=1, 1+2= }, and } +8=16, how may we divide a fraction by a whole number without dividing the numerator by the whole number? A fraction may be divided by a whole number by multiplying the denominator by the whole number. 26. In q = 3 is it easier to divide the numerator or to multiply the denominator ? in g = 5? 27. State the easier method of dividing: 4 by 3; f by 2; 3 by 2; } by 7; g by 4; s by 5. 28. Under what conditions is it easier to divide the numerator? when is it easier to multiply the denominator ? Observing the two methods, divide the following fractions, using the method best adapted to the problem: 4 45. 37 = 9 30. 1} = 4 38. 46. 4. - 6 }=4 32. 1 - 3 2 2 2 48. * +5 go 49. 1-3 34. 2 6 42. 16 = 7 50. 13 + 6 3 유 51. 13:5 36. 12 2 52. 16 + 4 29. 37. • 4 31. 39. 47. 40. 33. • 10 41. •10 35. 43. 44. 1= 5 3. If 8 yards of ribbon cost $16, find the cost of 1 yard. 4. I bought 6 gallons of oil for $1. What was the price per gallon ? 5. A boy earns $£ in a day by working 9 hours. How much does he earn in an hour ? 6. If 5 dozen bananas cost $4, how much does 1 dozen cost ? 7. Eight men in a day complete iš of a piece of work. How much of the work could one man complete in a day? 8. It takes of a thousand feet of lumber to make 12 boxes. How many feet are there in each box? 9. If 12 panes of glass cost $3, how much does one pane cost? 10. If 17 handkerchiefs cost $17, how many cents does each cost ? 11. In id of a day a man earns $9. How long does it take him to earn $1 ? 12. In 11 of an hour an oil well produces 33 barrels of oil. How long does it take it to produce one barrel ? 1+1= 1+1 Dividing any number by a fraction by inverting the terms of the divisor. 1. 1+1= 2. 1+1 1+3= Observe that in each of the examples given above the quotient equals 1 x the denominator, or 1x, 1x4, 1x1, 1x4, 1 x 1, 1x1 3. Divide 12 successively by 2, 3, 4, 6. The quotients, 6, 4, 3, 2 respectively, become smaller as the divisors become larger. Then if 1=1= 1 will the quotient of 1+1 be larger or smaller than 4 ? Since is 3 times as large as 1, the quotient of 1+ will be } of the quotient of 1: 1; } of 4 = $. 4. 1:= , and 1= = 1 of 1 = 1. 1+1 = f, and 1= 5 = } of ( = g. Find the quotients of 1-4; 1= }; 1+%; 1+$. Notice that in every case the quotient equals the divisor with its terms inverted. The number of times a fraction is contained in 1 equals the denominator of the fraction divided by the numerator, or the fraction inverted. Find quotients by inverting the divisor and multiplying: Thus: 3+ = 3x = ” = 31. 5. 1:1 12. 2 19. 8+} 26. 15+ 6. 1+ 4 13. 20. 16 = 1 27. 16 = } 7. 1: s 14. & A 21. 24 - 4 28. ,10; 1 $ 8. 1; } 15. 22. 20.= 29. 8-12 9. 1+3 16. 23. 15 = 3 30. 7+% 10. 1: 17. 31. 6+ 11. 1: 18. 10+ 0 25. 12-5 32. 9+) 3+ Written Work 1. Divide 128 by 1s 8 Since it is contained in 1, i times, 16 25 = 128 x = 200 lf is contained in 128, 128 x H or 200 25 16 times. Any number may be divided by a fraction by inverting the terms of the divisor and multiplying. 128 ; 23. Divide 36 by 3%. Divide: 24. 27 by 21 30. 84 by 47 36. 780 by 74 25. 33 by 33 31. 75 by 27 37. 355 by 87 26. 44 by 42 32. 90 by 3 38. 295 by 66 27. 60 by 34 33. 92 by 2-3 39.748 by 3 28. 76 by 44 34. 85 by 18 40.549 by 89 29. 60 by 63 35. 245 by 55 41. 620 by 73 Divide : 42. 11by 3 45. 48 by 1.12 48. 104 by 24 43. 63 by 1 46.712 by 14 49. 155 by 27 44. 109 by 2 1 47.7 by 23 50. 124 by 5f HAM, INT. ARITH, -5 COMPARISON – WHOLE NUMBERS AND FRACTIONS 8 16. 1. 1 = š; = ģ. Then how do į and į compare? 2. If a unit is first divided into halves and then each half into halves, into how many parts is the unit divided ? Is į of a unit larger or smaller than ] of a unit ? 3. Divide a unit into halves, fourths, eighths, and sixteenths, and show how many sixteenths of a unit it takes to make of the unit ; f of the unit ; f of the unit ; of the unit. 4. Draw equal squares to show that 1 = 4 or 5. Compare and 4 ; 4 and 1; and g. 6. How does 4 of 20 compare with 1 of 20 ? of 16 with of 16 ? of 50 with of 20 ? 7. A has 40 acres of land, and B 60 acres. How does A's farm compare in size with B's ? 8. 8 is what part of 12, 16, 24, 32, 48, 72? SUGGESTION.- Make 8 the numerator in each case and the other numbers the denominators and reduce the fractions to their lowest terms. Thus 1 = 1; i = 1; 2= }, etc. 9. If 5 quarts of milk cost 45 cents, how much will 12 quarts cost ? 18 quarts ? 24 quarts ? 10. Elizabeth buys 31 yards of ribbon for 35 cents. At the same rate, how much would she pay for 107 yards ? SUGGESTION. - How many times 31 is 101? 11. A woodsman cuts 15 cords of wood in 6 days. How many cords, at the same rate, could he cut in 48 days ? 12. Compare 8 and 2; 6 and 4; 2 and 8; 5 and 10. |