7. Add together 124, 33, and 44. 8. Add 6 of roof, and 7 together. Ans. 1 68 Ans. 592 Ans. 18. Ans. 2012. Ans. 14. NOTE. In the following questions the given fractions must be reduced to their proper quantities by Case XI. in Reduction of Vulgar Fractions, and then added as in Compound Addition. 9. Add of a pound to of a shilling. 14. Add a yard to of a foot. Ans. 6 fu. 28 po. Ans. 2ft. 2in. 15. Add of a chaldron of coals to of a bushel. Ans. 16 bush. 3 pecks. SUBTRACTION OF VULGAR FRACTIONS. When a vulgar fraction is given to be subtracted from another given one. 1. If they are of different denominations, "or in high terms, reduce them as directed in Addition of Vulgar Fractions. 2. Subtract the lesser numerator from the greater, and under the remainder place the common denominator. NOTE 1. When whole numbers are given with fractions, the lower numerator will sometimes be the greatest, in which case subtract it from the denominator, and to the remainder add the upper numerator, and carry one to the unit's place of the lower whole number. Nare 2. This rule is proved by addition. NOTE. In the following examples the given fraction* must be reduced to their proper quantities, and then su tracted as in Compound Subtraction. 9. From of a pound (money) take of a shilling, 10. From a shilling take 4 of a penny. 7 Ans. 51d of an ounce Troy take of a penny 12. From cwt. take of a pound. Ans. I qr 13. From of a league take 14. From 1 Ell English, take 15. From of a hogshead of Ans. 11dwt. 3gr. 8 27 lb. 6oz. 10 dr. TT. of a mile. Ans. 1m. 2fu. 16po. of a yard. Ans. 2 qr. O na. T beer take 1 gallon. Ans. 12 gallons. 16. From of a chaldron of coals take of a bushel. Ans. 17 bu. 1 peck. MULTIPLICATION AND DIVISION OF VULGAR FRACTIONS. 1. Prepare the given fraction by reduction (if necessary) by reducing them to their lowest terms, if mixed fractions, reduce to single ones. 2. Multiply the numerators together for a new nu merator. 3. Multiply the denominators together for a new deminator.. NOTE. When any number, either whole, fractional, or mixed, is multiplied by a fraction, the product will be less than the multiplicand, in the same proportion as the multiplying fraction is less than 1, or an unit. In Division of Vulgar Fractions prepare the given fractions (if necessary) as for multiplication; then invert the divisor, i. e. place its denominator for its numerator, or uppermost, and its numerator lowermost, and then proceed as in multiplication, by multiplying the two uppermost, or those now in the place of numerators together, for a new numerator, then multiply the two lowermost together for a new denominator. NOTE. When mixed numbers are given to be divided, as pounds, shillings, and pence, hundreds, and quarters, &c. Reduce the dividend and divisor to the lowest denomination mentioned, and to a common denominator, then divide this reduced numerator of the dividend by the reduced numerator of the divisor, and under the quotient place the common denominator, or invert the reduced divisor, and then multiply as above directed, the result will be the quotient in a fraction of the highest denomination mentioned. NOTE. Multiplication and Division of Vulgar Fractions, prove each other.* * When fractions only are divided by fractions only, then if the dividend is greater than the divisor, the quotient will be greater than the dividend, but if the dividend is less than the divisor, the quotient will be less than the dividend, and in the same proportion as an unit or 1, is greater or less than the divisor. |