to a common denominator; then subtracting 7 from 108, the remainder is 101. Lastly, I reduce 101 252 L. to its proper quantity, which is shill. 63 34. From of a hhd. of wine take 3 gallons. 3 11. 5 5 x 63 315 945Į new numerators. MULTIPLICATION OF VULGAR FRACTIONS. 198. To multiply fractions together. RULE I. Multiply the numerators together for a numerator, and the denominators together for a denominator. II. If the new fraction be a proper fraction, reduce it to its lowest terms; if an improper one, reduce it to its equivalent whole or mixed number". I first multiply the numerators 3, 2, and 7 together, and the product is 42. a To multiply a fraction by a whole number, we must evidently multiply the numerator by the whole number; but to divide it, we must multiply the denominator by the whole number: thus, if be multiplied by 2, the pro 1 4 for two fourths are double of one fourth, and one eighth is the half of one fourth this being premised, let it be required to multiply by 3 5 now 2 multiplied by 4 equals 8; but it is not 2, but a third part of 2, which to be 8 3 multiplied, and therefore the product will be the third part of 8 only, or but the multiplier is not 4, but the fifth part of 4 only, wherefore the product will be the fifth part only of that is, 15 ; wherefore X 3 4 8 ; or 3' the numerators multiplied together give the numerators of the product, and the denominators multiplied give the denominators; which is the rule. Then I multiply the denominators 4, 3, and 8 together, and the product is 96. 199. When mixed numbers or complex fractions are to be multiplied. RULE. Reduce the mixed numbers to improper fractions, and the complex fractions to simple ones, and proceed as before. The reason of this process evidently follows from the preceding note. together, and reduce the product to its equivalent mixed num 30 200. To multiply a whole number and fraction together. RULE. Multiply the numerator of the fraction by the whole number, and under the product set the denominator; then reduce this fraction to its lowest or proper terms, as the case requires, and it will be the answer°. < Whatever parts a fraction consists of, its product when multiplied by any whole number will consist of like parts; thus two sevenths multiplied by three 201. When the whole number will divide the denominator of the fraction without remainder, divide by it, and set the quotient under the given numerator; this fraction reduced as before will give the answer. To divide the denominator by any number is the same as to multiply the the same holds true in every other instance: wherefore the truth of the rule is manifest. 1 and the quotient will be 4÷2 the same as by the former method; and |