75. If I give $141 for a piece of cloth containing 48 yards, how much must I sell it for to gain $1 a yard? Ans. $189. 76. A man who owned the following quantities of land, 500 acres, 17 acres, 121 acres, and 98 acres, sold 325 acres; how much did he have left? Ans. 411 acres. 77. What number subtracted from 2,521 leaves 178? Ans. 2,343. 78. How long will it take a steamboat to go 345 miles, if she moves 15 miles an hour? Ans. 23 hours. 79. A man sold a cargo of salt for $2,300, and made on it $625; what did it cost him? Ans. $1,675. 80. How many 4 gallon kegs, 5 gallon kegs, 7 gallon kegs, and 8 gallon kegs, and of each an equal number, can be filled from 8 casks of wine, each containing 36 gallons? Ans. 12 of each. DECIMAL FRACTIONS. 17 A decimal fraction is a fraction whose denominator is 10, 100, 1000, or some other power of 10. A decimal fraction is usually expressed by writing the numerator only, with a point prefixed to it; thus, 100, 100, &c., are decimal fractions, and are expressed thus, .3, .17, .436, &c.; when a whole number and decimal are written together, the deci mal point is placed between them thus, 37.4, is 37, 6.37, is 6,37%. Whole numbers increase in value, in a tenfold proportion, from right to left, and decimals decrease in the same proportion, from left to right. Ciphers annexed to decimals, neither increase nor decrease their value; thus, .7, .70, .700, are of the same value, being 70, 700, 7000, but ciphers prefixed to decimals, decrease their value in a tenfold proportion; thus, .7, .07, .007, are of different values. Hence it will be perceived that decimals may be operated upon in precisely the same manner as whole numbers are, only observing to write the decimal point in its proper place. ADDITION OF DECIMALS. RULE. Place the numbers so that the decimal points may stand directly under each other, then add as in whole numbers, and write the point in the sum immediately below the other points. 3. Add 6.43, .0075, 19.6,4.76, and 34.5. Ans. 65.2975. 4. Add 72.4, 36.147, 8.6245, 79.482, 96.37. 5. Add 364., 74.3, .047, 87.63478, 47.39. SUBTRACTION OF DECIMALS. RULE. Place the less number under the greater, and subtract as in whole numbers, and point off as many figures for decimals as there are in that number, which contains the greatest number of decimals. Ans. 2118.6376. 4. From 2167. take 48.3624. 5. From 3704.3678 take 21.96843. 6. From 6749.358702 take 4.70069. 7. From 24.0603 take 7.90485. 8. From seven hundred and thirty-eight, and seventeenhundredths, take eighty-three, and twenty-nine thousanths. Ans. 655.141. 9. A man owning a farm containing 325.13 acres, sold off 59.325 acres, how many acres had he left? 10. From 37640. take .0462. Ans. 265.805 acres. MULTIPLICATION OF DECIMALS. RULE. Multiply as in whole numbers, and point off as many figures for decimals, in the product, as there are decimals in the multiplicand and multiplier, but if there be not so many figures in the product as there are decimal figures in both factors, prefix ciphers to supply the deficiency. 14. What will 37.48 bushels of wheat cost at $1.175 per bushel? Ans. $44.039. NOTE. The learner will observe that the answer contains but three decimals, whereas there should be five, according to the rule, but the two figures to the right of the 39 being ciphers are of no account, and are therefore omitted. DIVISION OF DECIMALS., Divide as in whole numbers, and point off as many deci mals in the quotient, as the number of decimals in the dividend exceeds those of the divisor. If there be not so many figures in the quotient as the rule directs to be pointed off, prefix ciphers to supply the defect. If the number of decimal figures in the divisor be greater than that of the dividend, annex ciphers to the dividend. |