tracted, the sign -was changed to +. See Art. VI. example 6th. XIX. Division of whole numbers by Fractions, and Fractions by Fractions. 1. How many times is contained in 7 ? Ans. is contained in 7, 35 times, and is contained 186 3. How many times is contained in c? α is contained b c times in c, and is contain a b Arith. Art. XXIII. α 4. Of what number is c the & part? a Ans. If c is the part of some number, will be b part Arith. Art. XXIV. Hence to divide a whole number by a fraction, multiply it by the denominator of the fraction, and divide the product by the numerator. How many times is contained in 7. Solution. Reducing them to a common denominator, 24 is 24, and is 35. 2 is contained in times as 24 is contained in 35; that is, 25 as many 3 4 or 111. Ans. 111. α 6. How many times is contained in? Solution. Reducing them to a common denominator, b c many times as a d is contained in bc; that is, ad Hence, to divide a fraction by a fraction, multiply the numerator of the dividend by the denominator of the divisor, and the denominator of the dividend by the numerator of the divisor. Or more generally, when the divisor is a fraction, multiply the dividend (whether whole number or fraction) by the divisor inverted. Arith. Arts. XXIII. and XXIV. |