DRILL IN DIVISION Divide. Check by casting out 9's or 11's. See §§ 82, 83. Find the results in the following as suggested in §§ 84, 85: 31. 32. 33. 3940 100 36. 760000 1000 41. 27450 1000 37. 875000 4000 39840 ÷ 200 34. 17854300 ÷ 1000 5937000 800 42. 92750000 ÷ 5000 38. 1952000 ÷ 300 43. 75280000 ÷ 200 39. 2460000 ÷ 5000 44. 8624400 200 35. 825750 500 40. 3780000 ÷ 600 45. 751945600 ÷ 2000 Find the results in the following by the method of § 86: Find the results in the following by the method of § 87: DRILL ON FRACTIONS Give orally as many as possible of the following : 43. 16 X 37 44. 27 X2 14 - 63 Before solving the following, study again the examples solved on page 103. MISCELLANEOUS WORK 1. A picture 12 inches long and 8 inches wide is put in a frame 2 inches wide outside the picture. What are the dimensions of the frame? 2. is what part of? 3. is of what number? 4. If a wheel goes 92 feet at each revolution, how many times will it turn around in going 150 miles? 5. A farm containing 74 acres was sold for $10,000. What was the price per acre? 6. An aëroplane went 342 miles in 21 minutes. What was its speed in miles per hour? 7. A field containing 481 acres yields 924 bushels of wheat. At this rate what would be the yield of a field containing 267 acres? 8. In one department of a store the sales of eight clerks for one week were: $347.20, $412.60, $298.40, $481.25, $397.50, $407.65, $424.85, $445.65. What is the average of these sales? 9. July 1st, 1917, W. K. Warren had a balance in his bank of $4795.80. During the next week he made deposits of $465.40, $276.80, $194.70, $562.67, $845.92, $374.50 and withdrew by checks $100.00, $87.20, $25.00, $2850.00, $32.50, $35.00, $65.80, $294.65,, $1720.35. What was his balance at the end of the week? Arrange the work as in § 45. 10. One day the collection department of a certain bank showed the following: A. Face of paper, $2160; discount, $12.80; commission and exchange, $5.60; B. Face of paper, $3500; discount, $41.60; commission and exchange, $12.50; C. Face of paper, $340; discount, none; Commission and exchange, $2.50; D. Face of paper, $950; discount, none; commission and exchange, none; E. Face of paper, $5265.50; discount, $94.75; commission and exchange, $25.00; F. Face of paper, $720, discount, none; commission and exchange, $7.20. Arrange the work and show totals as on page 39. CHAPTER XII DECIMALS 143. Decimals in Business. A very large part of the fractions encountered in business are in the form of decimals. In fact, decimals occur nearly as frequently as ordinary integers. Hence, the prospective business man should not only understand the theory of decimals, but he should acquire effectiveness in handling them. 144. Decimal Fractions. Fractions whose denominators are 10, 100, 1000, etc., are called decimal fractions and are written in a special way. Thus is written .1, roo is written .01, is written .17, and 88 is written .038. 38 The most common use of decimal fractions in the United States is in representing amounts of money. Thus, 10 cents, or of a dollar, is written $.10 and 15 cents, or of a dollar, is written $.15. 145. The Principle of Place Value in Decimals. — A period, called the decimal point, is used to separate the integers from the decimal fractions. The first place to the left of the decimal point is one's place; the second place to the left, ten's place; and so on, as in the case of purely integral numbers. A digit in the first place to the right of the decimal point represents tenths; a digit in the second place to the right of the decimal point represents hundredths; and so on. Thus, in the number 1234.5678, the 1 represents one thousand; the 2 represents hundreds; the 3, tens, and the 4, ones. The 5 represents tenths; the 6, hundredths; the 7, thousandths, and the 8, ten-thousandths. Thus, we see that in a decimal number representing an integer or a fraction, or both, any digit represents ten times as much as the same digit in the next place to the right of it. This enables us to add, subtract, multiply, and divide decimal fractions, or mixed integers and decimal fractions, exactly as we do integral numbers. The only difficulty is in placing the decimal point in the result. Hence, placing the decimal point is the only new element of arithmetic in performing the fundamental operations on decimals. 146. Reading Decimals. In the number .178, there are 1 tenth, 7 hundredths, 8 thousandths. This makes 178 thousandths and is read 178 thousandths. The number 14.78 is read 14 and 78 hundredths. ORAL EXERCISES Read each of the following numbers: 1. 8.94, 2.748, 1.904, .37, .07, .004, .0008, .042, .0741, .1901. Write the following numbers, using figures: 2. One hundred forty-six and thirteen hundredths. 3. Four-hundred ninety-six thousandths. 4. Three million forty thousand ten-millionths. 5. Ninety-nine thousand and nineteen-billionths. 6. One trillionth. 7. Ten thousand one hundred and three hundred sixty-one hundred-thousandths. 147. Addition of Decimals. To add decimals they should be so placed that the decimal points stand in a column. Thus, to add 12., 1.49, .078, 640.2, 4.904, .007, write the numbers as follows: 12. 640.2 The first column to the right represents thousandths. Adding, we get 19 thousandths. Write 9 in thousandths' place in the sum, and carry 10 thousandths, or 1 hundredth. The next column represents hundredths, and its sum including the 1 carried is 17 hundredths. Write 7 in hundredths' place in the sum, and carry 1. Proceed in this manner until all the columns have been added. The decimal point in the sum is placed directly under the decimal points in the addends. Thus we see that the process of addition is exactly the same when decimal fractions are involved as it is in the case of ordinary integers. Care must be taken, as in the addition of integers, that digits of the same order are added. That is, we must add thousandths to thousandths, hundredths to hundredths, and tenths to tenths. For this reason the decimal points are placed in a straight column. Sometimes zeros are annexed to the right to make the number of decimal places the same in all the numbers. Thus, the numbers added above on this page may be written as at the right. 12.000 1.490 .078 640.200 4.904 .007 |