RULE. If the quantities to be multiplied are mixed, reduce them to a fractional form ; then multiply the numerators together for a numerator and the denominators together for a denominator. ExAMPLES. 1. Multiply of by s. 7 - Operation. We first reduce the com- 1 of 3. _3 pound fraction to the sim- 6 7–15, ple one #3, and then the 1_25 mixed number to the equiva- s}=#. lent fraction *; after which, we multiply the Hence, $2.É.-33–3. numerators and denomina- 42 3, 126 42. tors together. - Ans. 25 42' 3. Required the product of ; and ; Ans. 9ax Hence, . . Ans. Quest.—58. How do you multiply fractions together CASE VIII. 59. To divide one fractional quantity by another. RULE. Reduce the mixed quantities, if there are any, to a fractional form; then invert the terms of the divisor, and multiply the fractions together as in the last case. EXAMPLES. - - 10 5 1. Divide . . . . 24 by TS If the divisor were 5, the Operation. quotient would be Toj. But, *— 5 × 1 since the divisor is # of 5, 8 T 8 the true quotient must be 8 10 10 times too, for the eighth of 31-2-TET a number will be contained 10 80 2 in the dividend 8 times more T20 ×8=T30-3. than the number itself. In this operation we have actually multiplied the numerator of the dividend by 8 and the denominator by 5; that is, we have inverted the terms of the divisor and multiplied the fractions CHAPTER III. Of Equations of the First Degree. 60. An Equation is the expression of two equal quantities with the sign of equality placed between them. Thus, rea--b is an equation, in which a is equal to the sum of a and b. 61. By the definition, every equation is composed of two parts, separated from each other by the sign = . The part on the left of the sign, is called the first member; and the part on the right, is called the second member. Each member may be composed of one or more terms. Thus, in the equation wi-a+b, r is the first member, and a-i-b the Second. ...-a 62. Every equation may be regarded as the enunciation, in algebraic language, of a particular question. Thus, the equation a + æ-30, is the algebraic enunciation of the following question: Quest.—60. What is an equation! 61. Of how many parts is every equation composed? How are the parts separated from each other? What is the part on the left called! What is the part on the right called! May each member be composed of one or more terms! In the equation r=a+b, which is the first member ? Which the second How many terms in the first member 7 How many in the second? - ..." |