Divide in the most convenient way: 3. 6 by .3 11. 70 by .0056 19. 1 by .001 4. 9 by .06 12. 154 by .28 20. 10 by .01 5. 21 by .7 13. 78 by .052 21. 17 by .68 6. 10 by .01 14. 190 by .0076 22. 112 by .032 7. 25 by .125 15. 115 by 6.25 23. 324 by .27 8. 80 by .3125 16. 18 by .9375 24. 1904 by .119 9. 36 by .75 17. 4 by .016 25. 114 by .76 10. ` 128 by .032 18. 48 by .1875 26. 896 by .0256 27. If the rainfall in a certain place is, on an average, .01 of an inch a day, in how many days does the rainfall amount to 3 inches? 28. How many layers of gold leaf will be required to form a tablet 5 inches thick, if each layer is .001 of an inch thick ? 29. If one yard of flannel is worth $.625, how many yards can be bought for $575 ? 30. How many pencils can be bought for $324 at $.0075 each ? 31. When slate pencils are worth $.0055 apiece, how many can be purchased for $22 ? Find quotients and prove results: 32. .04 4.002 40..004_.004 48. .728 .13 33. .8: .25 41. .1952 : 16 49. .3136 : .224 34. .125 :.5 42. .00624 :.8 50. .4725 .2 .112 7 43. .0247 • .019 51. 4375 +.125 36. .036 - 4 44. .8799 :.7 52. .17225 - 1325 37. .0001 ;.01 45. .08799 • .007 53. .7665 : .365 38. 0187 .011 46. .15158_ .286 54. .2944 4.512 39. .555.37 47. .408375 ;.135 55. .421875+.1125 35. Find the sum of the quotients: 57. .49;.07 .016 :.04 .6+.8 .216 ;.18 .128.16 .03 •.003= .045 +.15 58. At $.20 a pound, how many pounds of coffee can be bought for $.85? 59. When potatoes are selling at $.125 a peck, how many pecks can be bought for $.75? 60. A mark is $.238. How many marks equal $952? 61. At $.025 each, how many pens can be bought for $.35? Find quotients : 62. .655 • .0131 63. .75 +.0125 64. .3625; .125 65. 1.44 ; .036 66. .9+.015 67. .1; 1.25 68. 10; 2.25 69. .34.03 76. 1.111 + 11.11 REDUCTION OF DECIMALS Reducing a decimal to a common fraction. 1. Express .5 with the denominator tenths; thus, By; then reduce this fraction to its lowest terms. 2. Express in the form of fractions reduced to their lowest terms: .25; 20; .50; .75; .80. Written Work 1. Change .871 to a common fraction in its lowest terms. We express the denominator of the .87=.875 = 875 decimal and reduce the resulting fraction to its lowest terms. 2. Change .66to a common fraction. Since 66} = 2fo, .66} = 200 = 100, or .66} = 280-100 = 388 = 18. This reduced to its lowest terms equals g. 3. Change .075 to a fraction in its lowest terms. We express .075 with its denomina.075= 1/60= tor 1000 and reduce the fraction to its lowest terms, do 4. Change the following decimals to fractions in their lowest terms: .35 .125 .16 .83} .331 .061 Changing a common fraction to a decimal. 1. How can you change to tenths? Express this result decimally. 2. Change ļ to hundredths and express the result decimally. 3. Change to hundredths expressed decimally: }; ; ; ; . 4. Is there any difference in value between 4 and 3• 4? between $ and 5=8? Written Work 1. Change to a decimal. Since a fraction may be regarded as an ex= 34=4)3.00 pression of division, *= 3 + 4. Annexing 0.75 naughts and dividing as on p. 195, we find the answer 0.75. Proof: 0.75 = 16 NOTE.- A decimal point must be placed after an integer before naughts can be annexed. 2. Change pe to a decimal. Proceeding as in example 1, we an+ = 5+ 16 = 16)5.0000 nex four naughts and divide. The 0.3125 result is 0.3125. A common fraction is changed to an equivalent decimal by placing a decimal point after ones' place in the numerator and dividing by the denominator. Change to equivalent decimals and prove: 3. } 6. } 12. 11 13. 11. 16 14.17 In changing * to a decimal, thus, 9)4.000, it is evident that the divi 0.4444' sor is not contained in the dividend an integral number of times. The quotient may be indicated as above, or a + sign may take the place of the fraction to show an undivided remainder. Thus, 9)4.000 0.444+ Change to equivalent decimals : 15. 18. 21. 11 24. 16. i 22. 25. 1 23.4 26. = 16.75. 27. 164 29. 24% 31. 4.1715 33. 2542 28. 123 30. 1126 32. 125 34. 1894 10.25 8. colo 9 19. 13 8 율 REVIEW OF FRACTIONS AND DECIMALS 7. 1. How many books at $2.50 each can be bought for $37.50? 2. Find the value of .06 x.03 divided by 2.5. 3. How many farms, of 804 acres each, can be laid out from a tract of land containing 1211.25 acres ? 4. How many yards of carpet, at $1.15 a yard, can be bought for $29.325 ? 5. Glycerin is 1.265 times as heavy as water. How many pounds of glycerin will equal in weight 4.6875 pounds of water? Find the sum of the quotients : 6. 4.65 +1.55 31.906 $ 1.06 12.5 = 6.25 40.804 ; 1.01 9.03 + 3.01 3.861 ; 3.51 11.75 +2.35 6.012 5.01 25.75 : 5.15 36.542 ; 33.22 8. If a man earns $11 in a day, how much will he earn in 34 days? 9. Find the value of (32 x 43) - 14. 10. If 7.375 yards of cloth cost $29.50, how much will 10.875 yards cost? 11. Change 1, 4, 1, 16 to decimals. 12. Two men bought a store for $6000; one paying .375 of it, and the other .625 of it. How much did each pay? 13. Read 100.01256. |