6. What is the cost of 254 bbls. of apples at $4.95 a barrel? 7. Multiply each of the following numbers by 10. .62 15.8 1.86 .2 215.06 2.5 State a rule for moving the decimal point when multiplying by 10. 8. Multiply each of the following numbers by 100. What is the rule for multiplying by 100? 14.8 9. Multiply each of the following numbers by 1000. 24.045 .0564 4.34 5.136 What is the rule for multiplying by 1000? 15.68 10. Multiply 4.5 by 20; by 30; by 50; by 60; by 70; by 80. Can you state an easy way to multiply by 20? by 30? by 60? 11. Multiply forty-two and fifty-four thousandths by eight and five hundredths. 12. If a farmer sold 156.5 bushels of wheat at $1.05 a bushel, how much should he receive? 13. 20.5 yards of cloth at $1.55 a yard = ? 14. Multiply each of the following and then add the products. 15. In former days a man bought 15 sheep at $.61 apiece. What did they cost him? 16. In 1 rod there are 16.5 feet. How many feet in 35.75 rods? 17. An automobile made a uniform speed of 45.56 miles an hour for 6.5 hours. How far did it go? 18. Lieut. Commander Richard E. Byrd flew to the North Pole and back in an airplane at an average speed of 85.75 miles an hour for 15.50 hours. How far did he go? LIEUT. COMMANDER BYRD ON HIS WAY TO THE POLE 19. A speedboat made an average speed of 48.25 miles an hour for 3 hours. How far did it go? 20. My automobile tire has a diameter of 34.5 inches. If the distance around it is 3.14 times the diameter, what is the circumference? 21. The Twentieth Century Limited traveled 67.25 miles an hour for 2.16 hours. How far did it go in that time? 22. A cow was tied to a stake by a rope 20.5 feet long. What was the circumference of the circle of grass she could eat in the pasture where she was grazing? See pages 147 and 148. Division of Decimals. — Decimals may be divided (I) by a whole number, or (II) by another decimal. (I) When the divisor is an integer the division is performed as shown below. Illustrative Examples. State the quotient in each of the following: The above examples illustrate the following rule. If a decimal number is divided by an integer, the quotient has the same number of decimal places as the number of places in the dividend. Dividing Decimals I. R. B. Test [4]. Enter First Trial scores. amples 1-12 for this test. Work ex 9. 18.92 100. 10. .6 30. 11. .006 ÷ 600. 12. .0084 ÷ 40. 13. Can you state an easy way of dividing by 10? By 100? By 1000? By 20? State your easy way. (II) When the divisor is a decimal we divide as follows: = 60 ÷ 30. You will observe that 6 ÷ 3 Also 4 ÷ 2 = 4020 or 400 200 or 4000 ÷ 2000. From a study of the above examples you will note that the quotient is the same if we multiply both the dividend and the divisor by 10, 100, or 1000. Now let us work the following Illustrative Example 1. .024.6. Solution: If we can get rid of the decimal in the divisor, we shall have a simple example like those under (I) on the preceding page. So we multiply both the dividend and the divisor by 10. We now have .24 6. This gives us an example like those in (I) above and our result is .04. Illustrative Example 2. Divide 4.864 by .16. Explanation. To get rid of the decimal in the divisor the divisor and dividend are each multiplied by 100, thus moving the decimal point to the right of the 6 in the divisor and making it an integer. The point is moved two places to the right in the dividend. The old decimal points are crossed out. The division is then performed as in the division by an integer. The quotient has as many decimal places as the number of places that remain in the new dividend. The above examples lead us to the following rule: To divide by a decimal 1. Move the decimal point of the divisor to the right end of the divisor. 2. Make a new dividend by moving the decimal point to the right as many places as the decimal point of the divisor has been moved. 3. Divide as in whole numbers. 4. Point off as many places in the quotient as remain in the new dividend. Dividing Decimals by Decimals Find the quotient in each of the following: 1. .456.03. 4. 456.03. 2. 45.6.03. 5. 456.003. 3. 4.56.03. 6. .875 2.5. 7. 6.25 2.5. 8. 16.9 1.3. 10. A tank contains 1860 cubic inches. A gallon of water contains 231 cubic inches. How many gallons will the tank hold? 11. A bushel contains 2150.42 cu. in. How many cubic inches in a peck? in a quart? 12. A farm containing 234.85 acres was divided into lots of .35 of an acre each. If 3.5 acres were used up for streets, how many lots were there? 13. Sheets of paper .02 of an inch thick were piled up into a pile which was 3.8 inches thick. How many sheets in the pile? 14. A railroad company laid 3745 miles of track at a cost of $17,827,885.25. What was the average cost a mile? 15. The product is .002814, the multiplier is .067. Find the multiplicand. Changing Decimals to Common Fractions. Illustrative Example 1. Change .25 to a common frac What do you do to 25% to obtain ? Example 2. Reduce .12 to a common fraction. Example 3. Change the mixed decimal 4.75 to a mixed number. To change decimal fractions to common fractions, write the numerator over the denominator and reduce the result to the lowest terms. |