MULTIPLICATION OF FRACTIONS. To multiply a fraction by a quantity that is not a fractional one. 43. Rule.-Multiply the numerator of the fraction by the quantity, and under the product place the denominator of the fraction; or ex α pressed algebraically xc= b ac b. For if the quantity a which is divided by b, be taken c times as great as before, and the divisor remain the same, then the quotient must likewise be c 44. If a fraction be multiplied by its denominator, the product is the numerator of the fraction. Examples x3=1, 1×4=3, also 1 To multiply two fractions together. 45. Rule. Multiply the numerators together for a new numerator, and the denominators to gether for a new denominator. Thus α ах = y by m, then (Art. 44) x=my =n, then (Art. 44) a=nb DIVISION OF FRACTIONS. 46. Rule.-Invert the numerator and denominator of the divisor; and proceed as in multi 2. Divide by Ans. 47. Involution is the process of determining the powers of quantities. This is done by multiplying the quantities into themselves the number of times equal to their respective indices. Or the results may be expressed by attaching the indices or exponents to the quantities. (Art. 9.) The square of a+b is expressed by (a+b)2 which is by multiplication a2+2ab+b*. The cube of a+b is expressed by (a+b), which is by multiplication a3+3a2b+3ab2+b3. The 4th power of a+b is expressed by (a+b)*, which is by multiplication a*+4a3b+6a2b2+ 4ab3+b1. 48. A simple quantity may be raised to any |