In such cases the remainder is usually expressed by a 25 17 5 39. = .413 12 40. 1.061 1 18 3 1. Change to decimals: 2, 5, 14, 32, 48, 16, 175. .44, .96, .096, .816, .486, .375. 49 6 806 364 3. Change to decimal form: 100, 1000, 1000, 10000. 4. Express in decimal form: 78%, 29180, 46180, 281006. 5. Express as common fractions in lowest terms: .6, .8, .2121, .0871, .4331. 6. Change to mixed numbers in simplest form: 8.51, 9.051, 6.3, 16.181, 7.001, 5.163. 7. Name the numerators of the following decimals: .5, .06, .54, .004, .406, .362, .0006, .0042. 8. Name the denominators of the following decimals: .8, .05, .63, .007, .309, .532, .0009, .0076, .1, .061, .663, .501, .64301. 9. Read: .50106, 9.20, .020, 90.0057, 500.005 .00600, 2.0002, .2222, .02002. 10. of 4 equals how many tenths? 11. .71 dredths? = how many hundredths? = how many hun 3 12. State the value of each in hundredths: 1, 2, 1, 4, 1, §,.3, §, 12, 12, 12, 16, 8%, 31%, .31, 371%, 621%, 6.21. ADDITION LESSON 72 1. Find the sum of 18.3, .04, 2.106, and .0051. Since only similar units can be added, we write tenths in one column, hundredths in another, and thousandths in another, etc., and add and carry as in whole numbers. Find the sum of: 2. 3.42, .006, .41, 46.81, and 281.004. OPERATION 18.3 .04 2.106 .0051 20.4511 Ans. 3. .08, 1.641, 1.71, 72.301, 463.1, and .0004. 4. 1.665, .3842, 78.005, .5101, 84.3, and 91.91. 5. .006, 4.001, 3.8406, .004, 9.2, and .31365. 6. Find the sum of 8 tenths, twenty-one hundredths, 16 thousandths, 31 ten-thousandths, 62 millionths. 7. Find the sum of 9, and 3 tenths; 42, and 16 hundredths; 33 thousandths; 18, and 5 thousandths; 21, and 21 ten-thousandths; 160, and 316 ten-thousandths. 8. Write and add: six thousand, and six thousandths; seven hundred five, and seventeen hundredths; ninety, and nine millionths; eight hundred forty hundredthousandths. GRAD. ARITH. V. — -6 1. From 92.61 take 84.006. The minuend and subtrahend are written so that units of the same order stand in the same column. When the number of decimal places in the subtrahend exceeds the number in the minuend, ciphers are generally annexed to the minuend to make them equal. Subtract: 2. 18.03 from 32.06 8. 3.8749 from 16.001 9. 4.9999 from 5.0014 OPERATION 92.610 84.006 8.604 Ans. 10. .99999 from 1.1 18. From 4 hundred and 4 hundredths take 399 and 99 hundredths. 19. From 6060 and 606 millionths take 24 and 79 tenthousandths. 20. From 6.05 take 4.0075. From 1.1 take .9099. 21. Mr. Bright who owned 160.8 acres of land, sold 13} acres at one time and 16.004 at another time. acres had he left? How many 22. From the sum of 13.5 and 8.7 take their difference. 23. How many tons are there in 183 tons +16.8 tons +663 tons +93 tons? MULTIPLICATION LESSON 74 1. 16×10=180.01; or, .1 x .1 = .01. 2. 10 × 10=106.21; or, .7 x .3 .21. 3 = 3. 10 X 180 1876.027; or, .3 x .09 .027. = 56 = 4. 180 x 100 = 10000 = .0056; or, .08 x .07 .0056. 5 5. 1% x7 = 35 = 3.5; or, .5 x 7 = 3.5. 10 6. Multiply 3.2 by 2.4. = It will be seen from the preceding exercises that we multiply decimals like whole numbers, and point off from the right of the product as many decimal places as there are in the multiplicand and multiplier together, prefixing ciphers when the number of figures in the product does not equal the number of decimal places in both factors. 17. What must be paid for 33.6 tons of coal at $3.75 a ton? 18. Find the cost of 8.384 thousand feet of boards at $13.35 per thousand. DIVISION LESSON 75 1. Divide 1282.56 by 76.8. OPERATION As the dividend is the product of the divisor 76.8)1282.56(16.7 and quotient, the number of decimal places in the dividend should equal the number in the divisor and quotient taken together. Since there are two decimal places in the divi dend and one in the divisor, there must be the 768 5145 4608 5376 5376 difference between two and one, or one decimal place in the quotient. 2. Divide 136.318 by 3.185. When there is a remainder, ciphers may be annexed to the dividend and the division continued as shown in the operation. When the division will not terminate, and an exact quotient cannot be expressed decimally, the remainder may be expressed by a common fraction; or, when OPERATION 3.185)136.3180(42.8 Ans. 12740 8918 6370 25480 25480 a number of decimal places sufficient for practical purposes has been obtained, the sign "+" may be annexed to indicate that the division is not complete. (See operations following.) |
