SUBTRACTION. EXAMPLES. 153. 1. From 91.73 take 2.18. SOLUTION. In each of these three examples, we write the subtrahend under the minuend, placing units under units, tenths under tenths, etc. Commencing at the right hand, we subtract as in whole numbers, and in the remainders we place the decimal points directly under those in the numbers above. In the second example, the number of decimal places in the minuend is greater than the number in the subtrahend, and in the third example the number is less. In each case we reduce both minuend and subtrahend to the same number of decimal places, by supposing ciphers to be annexed, before performing the subtraction. OPERATION. 91.73 2.18 Ans. 89.55 2. From 2.9185 take 1.42. OPERATION. 2.9185 1.42 Ans. 1.4985 3. From 124.65 take 95.58746. OPERATION. 124.65 95.58746 Ans. 29.06254 RULE.-I. Write the numbers so that the decimal points stand directly under one another. II. Subtract as in whole numbers, and place the decimal point in the result directly under the points in the given numbers. 4. Find the difference between 714 and .916. 6. From 21.004 take 75 hundredths. 7. From 10.0302 take two ten-thousandths. 8. From 900 take .009. 9. From two thousand take two thousandths. 10. From one take one millionth. Ans. 1.702. Ans. 20.254. Ans. 899.991. Ans. .999999. .35 .5 MULTIPLICATION. EXAMPLES. 154.-1. What is the product of .35 multiplied by .5? OPERATION. SOLUTION. We perform the multiplication in the same manner as in whole numbers. To determine how many places to point off, we may reduce the decimals to common fractions; thus, .175, Ans. .35=13% and .5%. Performing the multiplication, we have 15% × 1 = 15%, and this product, expressed decimally, is .175. Here we see that the product contains as many decimal places as are contained in both multiplicand and multiplier. 10009 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 are 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, etc., remove the point as many places to the right as there are ciphers on the right of the multiplier. 2. Multiply 1.245 by .27. 3. Multiply 79.347 by 23.15. 4. Multiply 350 by .7853. 5. Multiply one tenth by one tenth. 6. Multiply 25 by twenty-five hundredths. 7. Multiply .132 by .241. 8. Multiply 24.35 by 10. 9. Multiply .006 by 1000. Ans. 6. 10. Multiply .23 by .009. Ans. .00207. 11. Multiply sixty-four thousandths by thirteen millionths. Ans. .000000832. Ans. .33615. Ans. 1836.88305. Ans. .01. Ans. 6.25. Ans. .031812. 12. Multiply eighty-seven ten-thousandths by three hundred fifty-two hundred-thousandths. 13. Multiply one million by one millionth. Ans. 1. 14. Multiply sixteen thousand by sixteen ten-thousandths. Ans. 25.6. DIVISION. EXAMPLES. 155. 1. What is the quotient of .175 divided by .5? SOLUTION. We perform the division in the same manner as in whole numbers. To determine how many places to point off, we may reduce the decimals to common fractions; thus, .175 = 1, and .55. Performing the division, we have OPERATION. .5).175 35 175 5 173 10 35 = X 1000 10 1000 5 100 and this quotient, expressed decimally, is .35. Here we see that the dividend contains as many decimal places as are contained in both divisor and quotient. = RULE. Divide as in whole numbers, and from the right hand of the quotient point off as many places for decimals as the decimal places in the dividend exceed those in the divisor. 1. If the number of figures in the quotient is less than the excess of the decimal places in the dividend over those in the divisor, the deficiency must be supplied by prefixing ciphers. 2. If there is a remainder after dividing the dividend, annex ciphers, and continue the division; the ciphers annexed are decimals of the dividend. 3. The dividend must always contain at least as many decimal places as the divisor, before commencing the division. 4. In most business transactions, the division is considered sufficiently exact when the quotient is carried to 4 decimal places, unless great accuracy is required. 5. To divide by 10, 100, 1000, etc., remove the decimal point as many places to the left as there are ciphers on the right hand of the divisor. Divide: 2. .675 by .15. 3. .288 by 3.6. 6. 2.3421 by .211. 7. 8.297496 by .153. 8. 12 by .7854. 9. 15.34 by 2.7. Ans. 4.5. 10. 785.4 by 1000. 12. 45.30 by .015. 13. .003753 by 625.5. 14. 9 by 450. 15. 2.39015 by .007. 16. 365 by 100. PROMISCUOUS EXAMPLES. 1. Add six hundred, and twenty-five thousandths; four tenths; seven, and sixty-two ten-thousandths; three, and fifty-eight millionths; ninety-two, and seven hundredths. Ans. 702.501258. 2. What is the sum of 81.003 + 5000.4 + 5.0008 + 73.87563 +1000 + 25+ 3.000548 + .0315? 3. From eighty-seven take eighty-seven thousandths. 4. What is the difference between nine million and nine millionths? Ans. 8999999.999991. Ans. .05475. 5. Multiply .365 by .15. 6. Multiply three thousandths by four hundredths. 7. If one acre produces 42.57 bushels of corn, how many bushels will 18.73 acres produce? Ans. 797.3361. Ans. .000015625. 8. Divide .125 by 8000. 9. Divide .7744 by .1936. 10. Divide 27.1 by 100000. Ans. .000271. 11. If 6.35 acres produce 70.6755 bushels of wheat, what does one acre produce? Ans. 11.13 bushels. 12. Reduce .625 to a common fraction. Ans. g. 13. Express 26.875 by an integer and a common fracAns. 267. Ans. .016. tion. 14. Reduce to a decimal fraction. 83 15. Reduce to a decimal fraction. Ans. .5. 171 16. How many times will .5 of 1.75 be contained in .25 of 17? Ans. 5. 17. What will be the cost of 35 bales of cloth, each bale containing 36.75 yards, at $.85 per yard? 18. Traveling at the rate of 43 miles an hour, how many hours will a man require to travel 56.925 miles ? 19. Change to a mixed circulating decimal. 20. Change to a pure circulating decimal. DECIMAL CURRENCY. 156. Coin is money stamped, and has a given value established by law. 157. Currency is coin, bank bills, treasury notes, etc., in circulation as a medium of trade. A Decimal Currency is a currency whose denominations increase and decrease in a tenfold ratio. The currency of the United States is decimal currency, and is sometimes called Federal Money; it was adopted by Congress in 1786. NOTATION AND NUMERATION. 158. The Coin of the United States consists of gold, silver, nickel, and bronze. The Gold Coins are the double-eagle, eagle, halfeagle, quarter-eagle. The Silver Coins are the dollar, half-dollar, quarterdollar, and the ten-cent pieces. The Nickel Coin is the five-cent piece. 1. The mill is a denomination used only in computations; it is not a coin. 2. The character is supposed to be a contraction of U. S. (United States), the S being placed upon the U. 3. All gold and silver coins must consist of 9 parts pure metal and 1 part alloy. |