OPERATION. 378.6 35 195.275 183.3 6 0 remainder. 2. From 462.3 take 218.15. 3. From 16.705 take 7.6845. 4. From 132.4 take 36.36. 5. From 127.05 take 66.006. Rem. 244.15. Rem. 9.0205. Rem. 61.044. 6. From 100.001 take 77.77. Rem. 22.231. 7. From five hundred and thirty-six, and fifteen hundredths, take two hundred and thirty-six, and eighteen hundredths. Rem. 299.97. 8. From six dollars take fifty-five cents. Rem. $5.45. 9. From one dollar take one mill. Rem. .999 mills. 10. From 16 dollars take nineteen cents and one mill. Rem. $15.809. MULTIPLICATION OF DECIMALS. RULE.-Multiply as in whole numbers, and point off as many decimals in the product as there are decimals in both factors. Whenever the decimals in the product are not as many as those of the factors, the deficiency must be supplied by placing cyphers on the left of them. Ex. 1. Multiply 25.16 by 3.45. 25.16 3.45 12580 10064 7548 8 6.8 0 2 0 Four figures are cut off in the product as decimals, in ac cordance with the rule, there being four decimals in the two factors. Ans. 8010.144. 2. Multiply 175.2 by 45.72. 3. Multiply 15.75 by 1.05. 4. Multiply 37.99 by 25.77. 5. Multiply 100.00 by 0.01. 6. Multiply 3.45 by .16. 7. Multiply 25.238 by 12.17. 8. Multiply 27.56 by 12.22. 9. Multiply .01 by .01. 10. Multiply 7.02 by 5.27. 11. Multiply .001 by .001. 12. Multiply.25 cents by .25 cents. Ans. 307.14646. Ans. 36.9954. Ans. .000001. Ans. .0625, or 64 cts. Note. To multiply a decimal by 10, 100, 1000, &c., it is necessary only to remove the decimal point as many places to the right as there are cyphers in the multiplier. 13. Multiply 1.56 by 10. Ans. 15.6. 14. Multiply 36.541 by 100. Ans. 3654.1. Ans. 46378.9. DIVISION OF DECIMALS. We are now to reverse the preceding operation. In multiplying decimals, we were directed to point off as many decimal figures in the product as there were in both factors. In Division, the dividend corresponds to the product in Multiplication, and the divisor to one of the factors which produced that dividend, and we are required to obtain the other factor. Therefore the decimals of the quotient and divisor united must equal those of the dividend. RULE.-Divide as in Simple Numbers, and point off from the right of the quotient as many decimals as are equal to the excess of decimals in the dividend, over those in the di visor. Note 1st.-If the decimal places in the divisor be more than those in the dividend, annex cyphers to make them equal. 2d. If, after dividing, there be a remainder, cyphers may be annexed to the remainder and the division continued. The cyphers thus added are decimals. 3d. If the decimals in the divisor and dividend are equal, and there is no remainder after dividing, the quotient will be a whole number. 4th. If the figures in the quotient do not equal the excess of decimal places in the dividend over those of the divisor, supply the defect by prefixing cyphers. 5th. To divide the decimal number by 10, 100, 1000, &c., it is necessary only to remove the point as many figures to the left, as there are cyphers in the divisor. Ex. 1. Divide 34.317 by 21.75. PERFORMED. 21.75) 34.3 17 (1.577+ 12 567 10 875 16920 15225 16950 15225 17 2 5 remainder. In the solution of this example, two cyphers have been added to the remainders of the dividend. By Note 2d, the whole number of decimals in the dividend is therefore five, and there are two in the divisor; three should, therefore, be " cut off from the quotient. The plus sign in the quotient always implies a remainder. 2. Divide 30515.50 by 100. Ans. 305.1550. For the solution of the preceding sum, see Note 5th. 3. Divide 483.125 by 386.5. Ans. 1.25. 6. Divide 99.99 by 33.3. Ans. 3.0027.+ 7. Divide 1.00 by .12. 8. Divide 14325.16 by 1.33. 9. Divide 36.5 by 10. 10. Divide 36.5 by 100. 11. Divide 981 by 1000. Ans. 10770.721.+ Ans. 3.65. 12. Divide 543.67 by 3.46. Ans. .981. Ans. 157.13.+ APPLICATION. 1. If 36.34 bushels of corn grow on an acre, how many acres will produce 674 bushels ? Ans. 17.804 acres. 2. If 6 yards of cloth cost $24.48, what was the price per yard? Ans. $4.08. 3. Bought 56.87 yards of cloth at $2.31 per yard; what was the whole cost? Ans. $131.3697. 4. The first of three men possessed $685.423; the second, $746.03; and the third, $10864.273. How much had they all? Ans. 12295.726. 5. What cost 9.6 yards of cloth at $6.42 per yard? Ans. $61.632. 6. If a man earn 2 dollars 2 mills per day, how much would he earn in 93.5 days? Ans. $187.1870. 7. What cost .675 of a cord of wood at $3 a cord? Ans. 2.025. 8. If a yard of cloth cost $5.5625, how much will .25 of a yard cost? Ans. 1.3906. REDUCTION OF VULGAR AND DECIMAL FRACTIONS. The value of a vulgar fraction is the quotient arising from dividing the numerator by the denominator. Therefore, CASE 1st.-TO REDUCE A VULGAR FRACTION TO A DECIMAL. RULE.-Annex cyphers to the numerator, and divide it by the denominator. Note.-If the given fraction be proper, the quotient will always be a decimal, and will consist of figures equal in number to the cyphers annexed; or, if the number of figures be less, cyphers must be prefixed to complete the number. 'CASE 2d.-TO REDUCE A DECIMAL TO A VULGAR FRACTION. RULE.-Write down the given decimal as a numerator, and for a denominator, write 1 with as many cyphers annexed as there are figures in the numerator, and then reduce the fraction to its lowest terms. (See remarks introductory to Decimals.) |