100 8. James bought 2.5 cwt, of sugar, 23.265 cwt. of hay and 4.2657 of rice. How much did he buy in all? Ans, 30.0307cwt. 9. James is 14 years old, John 15,25 and Thomas 16,75 What is the sum of all their ages? Ans. 46.5 years. 10. What is the sum of one and five tenths; forty-five and three hundred and forty nine thousandths; and sixteen hundredths? Ans. 47.009. SUBTRACTION OF DECIMALS. RULE. Write the larger number first, and the smaller one under it; then subtract as in Simple Subtraction; observing, that the dividing point in the answer, or remainder, must be placed under those in the sum. 4. Bought a hogshead of molasses, containing 60.72 gallons and sold 40.721 gallons. in the hogshead? 5. A merchant, owing $270.42, much did he then owe? How much was left Ans. 19.999 galls. paid $191.626; how Ans. 78.794. 6. I bought 20,25 yards of cloth and sold 5.75 yards. How much had I left? Ans. 14.50 yds. 7. From .650 of a barrel take .6 of a barrel. Ans. .050 barrel. 8. From 22 of a bushel take of a bushel. 1000 Ans. .126 bushel. 9. A farmer was 42.075 years old when he came to the Western country, and is now 64.67 years of age. How long since he emigrated? Ans. 22.595 years. 10. Take one hundredth from on tenth. Ans. .09. 100 MULTIPLICATION AND DIVISION OF DECIMALS. MULTIPLICATION OF DECIMALS. RULE. Place the multiplier under the multiplicand, and multiply as in Simple Multiplication; then point off as many places for decimals as there are decimals in the multiplicand and multiplier. If there be not so many figures in the product as there are decimals in both factors, the deficiency must be supplied by prefixing cyphers. 4. Multiply .63478 by 8204. Ans. 520772512. 5. Multiply 385746 by .00464. Ans, 00178986144. 6. What will 5.66 bushels of wheat cost at $1.08 a bushel? Ans. $6.1128, or $6.11c. 2m. 7. What will 8.6 pounds of flour come to at $.04 a pound? Ans. $34cts, 4m. 8. At $25c. a bushel, what will 12.67 bushels of apples cost? Ans. 3.1675. 9. If I travel 30.75 miles a day, how far shall I travel in 8.325 days? Ans, 255,99375 miles. DIVISION OF DECIMALS. RULE. Divide as in Simple Division, and point off as many figures from the right hand of the quotient, for decimals, as the decimal figures in the dividend exceed in number those in the divisor. When there are not so many figures in the quotient as this rule requires, the deficiency must be supplied by prefixing cyphers to the left of the quotient. When there are more decimal figures in the divisor than in the dividend, place as many cyphers to the right of the dividend as will make them equal.-When the number of decimals in the divisor, and the number in the dividend are equal, the quotient will always be in whole numbers, unless there should be a remainder after the dividend is all brought down. When there is a remainder, cyphers must be annexed to it and the division continued and the quotient thence arising will be decimals. Ans. 3,653. Ans. 17.825. Ans. 21.7568. 5. Divide 234.70525 by 64.25. 6. Divide 14 by .7854. 7. Divide 2175.68 by 100. 8. If you divide 116.5 barrels of flour equally among 5 men, how many barrels will each have? Ans. 23.3 barrels. 9. At $25 a bushel, how many bushels of corn may be bought for $300.50: * Ans. 1202 bushels. 10. At $124 or $125 a yard, how many yards of cloth may be bought for $16?? Ans. 128 yds. 11. Bought 128 yards of tape, for $64; how much was that a vard? Ans. $.005, or 5 mills. REDUCTION OF DECIMALS. CASE I. To reduce a vulgar fraction to a decimal. RULE. Place cyphers to the right of the numerator until you can divide it by the denominator; and divide till nothing remains; or, if it be a number that will not divide without a remainder, then divide until you get three or more figures for the quotient. The quotient will be the vulgar fraction expressed in decimals, Ans. .375. 3. Reduce 2 to a decimal. 4. Change,,, and to decimals. Ans. .125, .5, .75, 04. 5. What decimal is equal to? Ans. .05. What is equal to ? Ans. 2. What is equal to ? Ans. .3333+. 6. Change 64 bushels to its equivalent value. Ans. 64.25 bushels. CASE II. To reduce any sum, or quantity, to the decimal of any given denomination. RULE. Reduce the quantity to the lowest denomination, and reduce the proposed integer to the same denomination; then divide the quantity by the amount of the integer, and the quotient will be the answer. EXAMPLES. 1. Reduce 3s. 9d. to the fraction of a pound. One pound reduced to pence makes 240; and 3s. 9d reduced to pence makes 45. Then, 240)45.0000(.1875 Answer. 240 2100 1920 1800 1680 1200 1200 The same sum may be done by writing the given numbers from the least to the greatest in a perpendicular column, and dividing each of them by such number as will reduce it to the next denomination, annexing the quotient to the succeeding number. Thus, 12/9.00 20 3.7500 .1875 Answer. Ans. .02734375. 2. Reduce 7 drams to the decimal of a pound, Avoirdupois Weight. 3. Reduce 14 minutes to the decimal of a day. Ans. .009722. 4. Reduce 21 pints to the decimal of a peck. Ans. 1,3125. 5. Reduce 15s. 6d. to the decimal of a pound. Ans. .775. 6. Reduce 56 gallons 3 quarts 1 pint to the decimal of a hogshead, Ans. .9027. 7. Reduce 12 dwts. 16grs, to the decimal of a pound Troy Weight. Ans. .0527. 8. Reduce 4 mills to the decimal of a dollar. Ans. .004. Note-In doing sums in this rule, it will be necessary to keep in mind the tables of the different weights, measures, money, &c. |