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: 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? Reducing a decimal to a common fraction. 1. Express .5 with the denominator tenths; thus, ; 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. = Since 663 20o, .667 = 2oo ÷ 100, or .663202÷100=388 88. This reduced to its lowest terms = equals 3. 3. Change .075 to a fraction in its lowest terms. Changing a common fraction to a decimal. 1. How can you change to tenths? Express this result decimally. 2. Change to hundredths and express the result decimally. 3. Change to hundredths expressed decimally: ; 4. Is there any difference in value between and 3÷4? between and 5+ 8? Written Work 1. Change to a decimal. q=3+4=4)3.00 0.75 = Since a fraction may be regarded as an expression of division, 3 ÷ 4. Annexing naughts and dividing as on p. 195, we find the answer 0.75. Proof: 0.75 = 7% = NOTE.- A decimal point must be placed after an integer before naughts can be annexed. 2. Change to a decimal. =5÷16 = 16)5.0000 0.3125 Proceeding as in example 1, we annex four naughts and divide. The 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: 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 REVIEW OF FRACTIONS AND DECIMALS 1. How many books at $2.50 each can be bought for $37.50? 2. Find the value of .06 × .03 divided by 2.5. 3. How many farms, of 80 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: 8. If a man earns $12 in a day, how much will he earn in 34 days? 9. Find the value of (31 × 43) ÷ 13. 10. If 7.375 yards of cloth cost $29.50, how much will 10.875 yards cost? 11. Change 1, 4, 3, 1% 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. |