10. What decimal is equivalent to 17? 11. What decimal is equivalent to ? 12. What decimal is equivalent to? ADDITION. Ans. .04. Ans. .3125. Ans. .85. Ans. .1875. Ans. .016. 114. Since the same law of local value extends both to the right and left of units' place; that is, since decimals and simple integers increase and decrease uniformly by the scale of ten,it is evident that decimals may be added, subtracted, multiplied and divided in the same manner as integers. 1. What is the sum of 4.314, 36.42, 120.0042, and .4276?" OPERATION. 4.314 36.42 120.0042 ANALYSIS. Write the numbers so that the figures of like orders of units shall stand in the same columns; that is, units under units, tenths under tenths, hundredths under hundredths, etc. This brings the decimal points directly under each other. Commencing at the right hand, add each column separately, and carry as in whole numbers, and in the result place a decimal point between units and tenths, or directly under the decimal point in the numbers added. .4276 161.1658 RULE. I. Write the numbers so that the decimal points shall stand directly under each other. II. Add as in whole numbers, and place the decimal point, in the result, directly under the points in the numbers added. EXAMPLES FOR PRACTICE. 2. What is the sum of 2.7, 30.84, 75.1, 126.414 and 3.06 ? Ans. 238.114. 3. What is the sum of 1.7, 4.45, 6.75, 1.705, .50 and .05? Ans. 15.155. 4. Add 105.7, 19.4, 1119.05, 648.006 and 19.041. 5. Add 48.1, .0481, 4.81, .00481, 481. Ans. 1911.197. Ans. 533.96291. 6. Add 1.151, 13.29, 116.283, 9.0275 and .61. Ans. 140.3615. 7. Add .8, .087, .626, .8885 and .49628. 8. What is the sum of 91.003, 16.4691, 160.00471, 700.05, 900.0006, .0315? Ans. 1867.55891. 9. What is the sum of fifty-four, and thirty-four hundredths; one, and nine ten-thousandths; three, and two hundred seven millionths; twenty-three thousandths; eight, and nine tenths; four, and one hundred thirty-five. thousandths? Ans. 71.399107.. 10. How many acres of land in four farms, containing respectively, 61.843 acres, 120.75 acres, 142.4056 acres, and 180.750 acres? Ans. 505.7486. 11. How many yards of cloth in 3 pieces, the first containing 21 yards, the second 36 yards, and the third 40.15 yards? Ans. 98.40. 12. A man owns 4 city lots, containing 324, 36, 40%, 42.73 rods of land respectively; how many rods in all? Ans. 152.205 rods. SUBTRACTION. 115. From 124.2750 take 47.3126. OPERATION. Ans. 76.9624 ANALYSIS. Write the subtrahend under the minuend, placing units under units, tenths under tenths, etc. Commencing at the right hand, subtract as in whole numbers, and in the remainder place the decimal point directly under those in the numbers above. If the number of decimal places in the minuend and subtrahend are not equal, they may be reduced to the same number of decimal places before subtracting, by annexing ciphers. RULE. I. Write the numbers so that the decimal points shall stand directly under each other. II. Subtract as in whole numbers, and place the decimal point in the result directly under the points in the given numbers. Ans. 46.625. Ans. 5.5761. Ans. 87.553. 15. Subtract 37 from 84.125. 16. Subtract 34 from 9.3261. 17. Subtract 25.072 from 112§. 18. A man owned fifty-four hundredths of a township of land, and sold fifty-four thousandths of the same; how much did he still own? Ans. .486. 19. From 10 take three millionths. Ans. 9.999997. 20. A man owning 475 acres of land, sold at different acres, and 125.625 acres; how Ans. 168.5 acres. times 80.75 acres, 100 much land had he left? MULTIPLICATION. 116. 1. What is the product of .25 multiplied by .5. OPERATION. .25 .5 ANALYSIS. First multiply as in whole numbers; then, since the multiplicand has 2 decimal places and the multiplier 1, point off 2+1=3 decimal places in the product. The reason for this will be evident, by considering both factors common fractions, and then multiplying as in (99), thus: .25=, and .5=; and 1×100%, which written decimally is .125. .125, Ans. 125 RULE. Multiply as in whole numbers, and from the right hand of the product point off as many figures for decimals as there are decimal places in both factors. 1. If there be not as many figures in the product as there are decimals in both factors, supply the deficiency by prefixing ciphers. 2. To multiply a decimal by 10, 100, 1000. remove the point as many places to the right as there are ciphers on the right of the multiplier. 25. If a man travel 3.75 miles an hour, how far will he travel in 9.5 hours? Ans. 35.625 miles. 26. If a sack of salt contain 94.16 pounds, how many pounds will 17 such sacks contain? Ans. 1600.72 pounds. 27. If a man spend .87 of a dollar in 1 day, what will Ans. 13.50675 dollars. he spend in 15.525 days? 28. One rod is equal to 16.5 feet; how many feet in 30.005 rods? Ans. 495.0825. 29. How many gallons of molasses in .54 of a barrel, there being 31.5 gallons in 1 barrel? Ans. 17.01 gallons. |