It was shown in Arithmetic, Art. XXII, that a common denominator may frequently be found much smaller than that produced by the above rule. This is much more easily done in algebra than in arithmetic. Here the denominators will be alike, if each be multiplied by all the factors in the others not common to itself. If the first be multiplied by e g, the second by c2g, and the third by bce, each becomes b c eg. Then each numerator must be multiplied by the same quantity by which its denominator was multiplied, that the value of the fractions may not be altered. ebcf The fractions then become aeg The answer is c2 dg and beeg beeg a e g + c d g + b c e f 10. Add together 11. Add together 12. Add together 13. Add together beeg and 13 c d. and 2 a c-5 b. cbeg sign was changed to +. See Art. VI, example 6th XIX. Division of whole numbers by Fractions, and Fractions by 1. How many times is Fractions. contained in 7? Ans. is contained in 7, 35 times, and is contained as many times; that is, 35 or 11 times. 2. How many times is contained in a ? Ans. is contained in a, 8 a times, and is contained as many times; that is, a. contained in c? is contained b c times in c, and is contained α b α Hence, to divide a whole number by a fraction, multiply it by the denominator of the fraction, and divide the product by the numera tor. How many times 35 Solution. Reducing them to a common denominator, is , and is 3.4 is contained in as many times as 24 is contained in 35; that is, or 1. Ans. 1. 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. |