22. If } of a square is divided into 2 equal parts, what fraction of the square is each part? Then } + 2 = 23. If į of a square is divided into 2 equal parts, what fraction of the square is each part? Then • 2=1 24. If of a square is divided into 8 equal parts, what fraction of the square is each part? Then } +8= . 25. Since 1 + 2 = 1, 1 = 2 = }, and } = 8=1d, 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 • 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; } by 2; } by 7; g by 4; 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: 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+ = Dividing any number by a fraction by inverting the terms of the divisor. 1. 1+1 +1= 1+1= 2. 1à 11 Observe that in each of the examples given above the quotient equals 1 x the denominator, or 1xį, 1x 4,1 xí, 1x 4,1 x 1, 1 x 1. 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= 4 will the quotient of 1+ 4 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. 4. 1+1 = 1, and 1= = 1 of 1 = ž. 1+1 = f, and 1+ = } of I =. Find the quotients of 1+4;1+3; 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+ 4 = 3 = = 34. 5. 1:1 12. 19. • } 26. 15 + 6. 1+1 13. 3+1 20. 16+ 27. 16+ 7. 1+3 14. 4+4 21. 24+ 28. ,10 + 8. 1; } 15. 22. 20 + 4 29. 9. 1+ $ 16. 6+5 }} 23. 15+ 30. 7+1 10. 1: 17. 31. 6+ 5 11. 1:6 18. 10+ 0 25. 12+ 32. 9+] 5+5 8:12 Noo Written Work 1. Divide 128 by it. 8 Since it is contained in 1, t& times, 16 25 128 x = 200 is contained in 128, 128 x 1 or 200 25 16 times. Any number may be divided by a fraction by inverting the terms of the divisor and multiplying. 128 ; Divide : 2. 18 by 3. 25 by g 4. 28 by } 5. 21 by s 6. 36 by 1% 7. 42 by 1 8. 54 by 9. 63 by } 10.72 by s 11. 84 by 31 12. 90 by 16 13. 108 by 13 14. 84 by z 15. 16. 288 by 24 17. 400 by 16 18. 285 by love 19. 546 by it 20. 425 by 45 21. 378 by 14 22. 324 by 14 96 by s 23. Divide 36 by 33. Divide: 36. 780 by 74 25. 33 by 3 31. 75 by 27 37. 355 by 87 26. 44 by 43 32. 90 by 34 38. 295 by 69 27. 60 by 3 33. 92 by 23 39.748 by 3 28. 76 by 44 34. 85 by 13 40. 549 by 8 29. 60 by 6 35. 245 by 56 41. 620 by 78 Divide : 42. 113 by 3 43. 63 by 13 44. 109 by 21 45. 45 by 112 48. 104 by 24 49. 15ę by 27 50. 124 by 5 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. |