1st division. 2b5ab3+5a2b2 5a3b+3a2b3-11ab2+8a2b+6a3 -- 2b-11ab3+8a2b2 + 6a3b 6ab3-3a2b2 — 11a3b+3a1 30a2b235a3b-15a4, or 5a2(662-7ab3a2). 2d division. 1b+3a 3 x 2b3-11ab2+8a2b + 6a3) 6b27ab-3a2 4. Find the greatest common divisor of a3 ab2 and Ans. a+b.. Ans. 5a1+5a3x To reduce a mixed quantity to an improper fraction. RULE. (22.) Multiply the quantity to which the fraction is annexed by the denominator of the fraction, and connect the product, by its proper sign, with the numerator. The sign before the fractional part, shows that the whole fraction is to be subtracted from 52; and hence, the signs of the numerator are to be changed, when we connect it with the product of 5 by the denominator. (23.) Divide the numerator by the denominator, and if there be a remainder, write the divisor beneath it, and connect the fraction so formed, by its proper signs, with the quotient. (24.) Multiply the numerators together for a new numerator, and the denominators for a new denominator, and reduce the resulting fraction to its lowest terms. NOTE. When a fraction is to be multiplied by an entire quantity, the numerator may be multiplied, or the denominator divided by this quantity (Arith. 20); and hence, if the multiplier be the same as the denominator, the denominator becomes unity, and therefore, to multiply a fraction by a quantity equal to its denominator, it is only necessary to expunge the denominator. |