ADDITION OF DECIMALS. 207. Addition of Decimals is the process of finding the sum of two or more decimals. 1. What is the sum of 11.96, 25.075, 84.306, 90.728? OPERATION. 11.96 25.075 84.306 90.728 SOLUTION. We write the numbers so that terms of the same order shall stand in the same column, and begin at the right to add. 8 thousandths, plus 6 thousandths, plus 5 thousandths, are 19 thousandths, which equals 1 hundredth and 9 thousandths; we write the 9 thousandths, and add the 1 hundredth to the next column: 2 hundredths, plus 7 hundredths, plus 6 hundredths, equal 15 hundredths, and the 1 hundredth added is 16 hundredths, which equals 1 tenth and 6 hundredths; we write the 6 hundredths, etc. 212.069 Rule.-I. Write the numbers so that terms of the same order stand in the same column. II. Add as in whole numbers, and place the decimal point between the units and tenths of the sum. 2. Find the sum of 79.76, 85.08, 36.125, 140.309. Ans. 341.274. 3. Find the sum of 87.09, 58.37, 95.42, 237.675. Ans. 478.555. 4. Add 18.79, 147.072, 856.709, 185.8761, 397.05784. Ans. 1605.50494. 5. Add 59.874, 435.095, 672.328, 976.309, 8467.500843. Ans. 10611.106843. 6. What is the sum of $25, $371, $28.37, $50.06. $15.371, $573, $157, and $23.871? Ans. $253.883. 7. Add 9 and 7 tenths, 41 and 8 hundredths, 75 and 54 hundredths, 128 and 187 thousandths. Ans. 254.507. 18. Add 187 and 5 thousandths, 49 and 9 hundred-thousandths, 1876 and 245 millionths, 187 ten-thousandths, and 999 ten-millionths. Ans. 2112.0241349. 9. Add 798 and 9 ten-thousandths, 17 millionths, 18 thousandths and 98 ten-millionthis, 67 hundred-thousandths, and 95 ten-milliouths. Ans. 798.0196063. 10. Find the sum of 3 decimal units of the 1st order, 61 decima! units of the 2d order, 44 of the 3d order, 31 of the 4th order, and 64 of the 5th order. Ans. .3696245. SUBTRACTION OF DECIMALS. 208. Subtraction of Decimals is the process of finding the difference between two decimals. 1. From 972.163 take 856.235. OPERATION. 972.163 856.235 115.928 SOLUTION. We write the numbers so that terms of the same order stand in the same column, and begin at the right to subtract. We cannot subtract 5 thousandths from 3 thousandths, hence we add ten thousandths to 3 thousandths, which equals 13 thousandths; 5 thousandths from 13 thousandths leaves 8 thousandths, which we write in the order of thousandths: since we have added 10 thousandths or 1 hundredth to the minuend, we must add 1 hundredth to the subtrahend; 1 hundredth and 3 hundredths are 4 hundredths; 4 hundredths from 6 hundredths leaves 2 hundredths, etc. Rule.-I. Write the subtrahend under the minuend, so that terms of the same order stand in the same column. II. Subtract as in whole numbers, and place the decimal point between the units and tenths of the remainder. 2. From 707.325 take 623.452. 4. From 78.3057 take 29.084. Ans. 83.873. Ans. 91.502. Ans. 49.2217. Ans. 846.0839. Ans. .637235. 7. From .3 take 3 hundred-millionths. Ans. .29999997. MULTIPLICATION OF DECIMALS. 209. Multiplication of Decimals is the process of finding the product when one or both factors are decimals. 1. Multiply 7.23 by .46. SOLUTION.-7.23 multiplied by 46 equals 332.58, and multiplied by 46 hundredths the product is 1 hundredth as great, which, by removing the decimal point two places to the left, becomes 3.3258. Hence, 7.23 multiplied by 46 equals 3.3258. OPERATION. 7.23 .46 4338 2892 3.3258 SOLUTION 2D.-7.23.46-728x+6=33258=1000033258=3.3258. From either of these solutions we derive the following Rule.- Multiply as in whole numbers, and from the righɩ of the product point off as many decimal places as there are in both factors, prefixing ciphers when necessary. 2. Multiply 27.13 by .67. 3. Multiply 43.08 by 2.36. 4. Multiply 79.52 by .019. 5. Multiply 8.534 by 20.074. 6. Multiply 123.107 by 1.52. 7. Multiply 512.073 by 35.08. 8. Multiply 54.0079 by 7.072. 9. Multiply 1.08096 by 3.5702. 10. Multiply .03507 by .005873. 11. Multiply 2.0709 by .000246. 12. Value of 91 ×.083×10? 13. Value of .5 of 7×.051? 14. Value of .07 of 300.09% ? Ans. 18.1771. Ans. 101.6688. Ans. 1.51088. Ans. 171.311516. Ans. 187.12264. Ans. 17963.52084. Ans. 381.9438688. Ans. 3.859243392. Ans. .00020596611. Ans. .0005094414. Ans. 8.3125. Ans. .0175. Ans. 1.65. Ans. $91.8575. × of 7)? Ans. 164.7432. 17. Multiply 1 hundredth by 1 thousandth, and add 1 tenth to the product. Ans. .10001. 18. What is the product of one-tenth by one-tenth? one hundred by one-hundredth? one million by one millionth? DIVISION OF DECIMALS. 210. Division of Decimals is the process of finding the quotient when one or both terms are decimals. divisor; hence there should be four minus two, or two decimal places in the quotient, therefore the quotient is 5.26. 123084 1 2 3 0 8 4 ÷ 2 3 4 = 1230084 X 181=100X234 10000 SOLUTION 28.-12.3084-2.34=128 = 100x1230841 of 526=5.26. From either of these solutions we derive the following Rule.-I. Annex ciphers to the dividend, if necessary to make the number of decimals equal to the number of decimal places in the divisor. II. Divide as in whole numbers, annexing ciphers to the dividend when needed to continue the division. III. Point off as many decimals in the quotient as the number of decimal places in the dividend exceeds the number in the divisor. NOTES.-1. When there are ciphers at the right of the divisor, cut them off, divide by the significant part, and then point off as many decimal places as before, plus the number of ciphers cut off. 2. Make complex decimals pure or divide them like common mixed numbers, or multiply both by the L. C. M. of the denominators, and then divide. Ans. 2.5. 17. 1÷.125. Ans. 8. Ans. 34 Ans. 2480 Ans. .00025 15. .012.06? 16. .001 2.5? Ans. .0016. 21. 25÷.00625. Ans. 4000 22. (2.04÷17+47-200 x 5000)-7? Ans. 1174.245. 23. (789-789) (.75-.075x75 of 8)? Ans. 194.62. 24. 45×.181+3.6×.31÷(3.5—3-43)? Ans. 8.5436314. 25. ($347.84 $10.87) x .0025+.013× 50? Ans. 32. 26. ($1080 × 3.27) ÷$10.90—($790÷$3.95)? Ans. 124 MISCELLANEOUS EXAMPLES. 1. What common fraction equals .00096? Ans. 125. Ans. 131. Ans. 21. Ans. .03006 cwt. 10 Ans. 5 tons. .7 6. Multiply 1.25 of .83 of 9 by .8 of 1 of 8.75. .2 Ans. 3075 27 7. Divide 1181 by .04; also 2.4001 by 1.56 Ans. 26273; 1.53919. 8. Divide 14- square yards by 11 24/ 28 13 4 9. Divide £2403 by of of of 1. 10. What number multiplied by 73 will give 63 for a product? Ans. 11. Divide seven millionths by twelve and a half ten-millionths. 1.25 781 131 Ans. £2851. Ans. 5.6. 12. Add 1, 8/1/2 .375, and .5, and multiply the sum by 6.24 14. Multiply the sum of.5 and by the difference be 81 tween and 10 17 262 621 1000 Ans. 3 15. Multiply by 25 millionths, and divide the pro duct by 125 hundred-thousandths. Ans. .00125. 16. The product of two numbers is, and one of them is of of 2; what is the other ? Ans. 1 |