19. One man does s of a piece of work and another man does of it. What fraction of the work remains to be done? 20. The regular fare from Los Angeles to San Francisco is $ 15. A round-trip excursion rate is made of one single fare and a third; children at half rates. What will round-trip tickets cost for two adults and two children ? 21. In 1916 Resta.drove a Peugeot Special at Santa Monica, Calif., 294 miles in 3 hours, 22 minutes, 48 seconds. What was his average speed per hour? 22. A boy attends a school twelve miles from his home. He spends daily, five days in the week, one hour and a half on his way to school, and two hours on his way home from school. How much time does he spend going and coming, between September 1 and July 1 ? How many miles does he travel during a four-year high school course? 23. A 62-ride ticket between San Francisco and Thousand Oaks costs $ 4. If a passenger rides twelve miles each trip, what does his traveling cost him per mile ? 24. What will 44,000 cubic feet of gas cost at $.90 per M? 25. At $15 a dozen what is the cost of a single article ? 26. On October 1, a gas meter reading was 32,600 cubic feet; on September 1 the reading was 30,400 cubic feet. At $.90 per M what was the gas bill for September ? 27. A pedestrian averages three miles an hour for five hours each day. How many weeks will it take him to walk one thousand miles ? 28. What must be added to y of in order that the sum may be equal to 'o of 3 ? 29. When O'Donnell drove a Duesenberg Special April 8, 1916, at Corona, Calif., 301.815 miles in 3 hours, 29 minutes, 52 seconds, what was his average speed ? CHAPTER IV DECIMALS. BILLS AND ACCOUNTS . Decimal Fractions. — A fraction whose denominator is not written, but is some power of 10, is called a decimal fraction, or simply a decimal. Thus, a number whose value is can be written either B or .5. The expression .5 is read “five tenths” and is called a decimal. So, also, can be written to or .75. Similarly, any fraction can be expressed decimally, for, since a common fraction can be considered as an indicated division, it can be changed to the decimal form by actually dividing the numerator by the denominator. Hence we have the following rule. Rule. - To change a common fraction to a decimal, divide the numerator by the denominator. EXAMPLE. Express as a decimal. .375 1. Exercise 7. Ž 13. 16 2. ģ 5. 1 8. 18 11. 32 14. 31 3. 1 6. 9. 1o 15.63 12.32 Such fractions as ļ, 4, etc., cannot be expressed exactly as decimals but can be expressed only approximately. EXAMPLE 1. Express as a decimal. .3333, etc. 3)1.0000 The result, correct to three places of decimals, reads .333; correct to two decimal places, the result is .33; to one place, .3. EXAMPLE 2. Express as a decimal. .6666, etc. 3)2.0000 Expressed correct to three places, the answer reads .667; correct to two places, .67. Exercise Express as decimals correct to three places the following fractions : 4. 13. $ 2. 4 5. 8.13 11. 13 14. 3. 6. į 12. } 1 1. 7. 3 10. 1 9. 1 15. Changing Decimals to Common Fractions Rule. — - To change a decimal to a common fraction write the decimal in fractional form and reduce to lowest terms. EXAMPLE. Change .875 to a common fraction. .875 = 875 175 = 36 = 1 1000 Exercise Addition and Subtraction of Decimals Rule. To add or subtract decimals set down the numbers so that the decimal points shall be under one another. EXAMPLE 1. Add .578, 4.331, 14.256, .361. .578 4.331 14.256 .361 19.526 EXAMPLE 2. From 4.472 subtract 2.968. 4.472 Exercise Find the sums of the following numbers : 1. 4.372, 6.876, 9.472, 8.437, 7.437, 6.874, 4.548, 4.759 2. 5.876, 6.678, 7.436, 6.538, 5.886, 4.535, 3.488, 7.768 3. 78.89, 43.64, 79.56, 58.86, 55.64, 87.53, 34.64, 56.87 4. 567.5, 78.76, 6.876, 66.67, 555.6, 44.85, 3.675, 37.72 5. 10.86, 71.85, 6.077, 177.6, 50.08, .6558, 7.876, .8892 6. 5.608, 74.43, 7.345, 73.45, 734.5, .7345, 56.08, 560.8 From the first number in each of the following examples, subtract the second number : 7. 57.86, 43.67 8. 89.76, 36.69 9. 643.7, 438.5 10. 4.786, 3.462 11. 555.5, 66.6 12. 58.92, 8.98 13. 789.6, 465.8 19. 876.7, 456.8 20. 968.9, 678.8 21. 7.886, 3.532 22. 589.8, 357.9 23. 64.08, 45.09 24. 845.5, 64.8 Multiplication of Decimals Rule. — To multiply one decimal by another, point off in the product a number of decimal places equal to the sum of the number of decimal places in the multiplicand and multiplier. 1. 67.6 x 5 6. 5.78 x 7.1 11. 65.8 x 7.6 2. 83.5 x 8 7. 65.2 x 6.6 12. 688 x 6.5 3. 5.56 X 4.6 8. 776 x 56.1 13. 538 X.65 4. 79.4 x 6.6 9. 6.5 X 4.7 14. 307 x 3.07 5. 835 X 8.34 10. 774 x 7.74 15. 866 x 5.11 16. 75.3 x 6.7 17. 46.7 X.9 18. .87 x .87 19. .08 x 1.66 20. 4.45 x .06 |