PROBLEM VIII. To multiply fractional quantities together. RULE.* Multiply the numerators together for a new numerator, and the denominators for a new denominator; and it will give the product required. * 1. When the numerator of one fraction, and the denominat or of the other, can be divided by some quantity, which is common to both, the quotients may be used instead of them. 2. When a fraction is to be multiplied by an integer, the prod tict is found by multiplying the numerator by it; and if the integer be the same with the denominator, the numerator may be taken for the product. 3. When a fraction is to be multiplied by any quantity, it is the same thing, whether the numerator be multiplied by it, or the denominator divided by it, PP Multiply the denominator of the divisor by the numer ator of the dividend for a new numerator, and the nu merator * 1. If the fractions to be divided have a common denomi nator, take the numerator of the dividend for a new numerator, and the numerator of the divisor for the denominator. 2. When a fraction is to be divided by any quantity, it is the same thing, whether the numerator be divided by it, or the denominator multiplied by it. 3. When the two numerators, or the two denominators, can be divided by some common quantity, that quantity may be thrown out of each, and the quotients used instead of the fractions first proposed. merator of the divisor by the denominator of the dividend for a new denominator. Or, invert the terms of the divisor, and then multiply by it, exactly as in multiplication. Here X ===1 1 is the quotient required. 3 2.x 6x Here 2x-2=ad is the quotient required. X 46 4bc 2bc 5x+a_5x2+6ax+a the quotient required. 3. Divide x + a 2x by Fa INVOLUTION is the continual multiplication of a quantity into itself, and the products thence arising are called the powers of that quantity, and the quantity itself is called the root. Or it is the method of finding the square, cube, biquadrate, &c. of any given quantity. RULE Multiply the quantity into itself, till the quantity be taken for a factor as many times as there are units in the index, and the last product will be the power required. -Or, Multiply the index of the quantity by the index of the power, and the result will be the power required. * Any power of the product of two or more quantities is equal to the same powers of the factors, multiplied together. And any power of a fraction is equal to the same power of the numerator, divided by the same power of the denominator, |