EXAMPLES WITH RADICAL SIGNS. 1.-Divide a3 + a√d + Nab + √63 by Na + vb. index of a = = a3, we find the index of the first term for the quotient, that is, from 3, 1 remains for the index of a in the quotient; the rest is evident from what has been before explained relative to indices. Ans...x+x3y + x2y2 + xy3 + y*. (ap)x2 + (ap + q)x aq by тъ 5 5.-Divide (a2 - 4) (a2 — 4a) by a2 + 2a. 6+2a 8 + a 10 by a 3+ a 5 Ans...a ·3+ a-5 It is evident that these negative powers, as well as positive, are divided by subtracting the indices; the Answers can be also written as follow: ALGEBRAIC FRACTIONS. The operations in Arithmetic and Algebraic Fractions being nearly similar, it is judged unnecessary to say much on the subject. To reduce a mixed quantity to an improper fraction. A mixed number is that which contains a whole number and a fraction, viz., 4 + is a mixed number, and, in reducing it to an improper fraction, we must find how many 8ths are in the whole number, thus, 32 + 5 4 x 8 + 5 = the improper fraction required. 8 RULE. Multiply the whole number by the denominator of the fraction, and connect the numerator by the proper sign, placing the denominator under all. It will be here required to remember, that when a minus sign stands before a fraction with a compound numerator, each sign in that fraction must be changed. To reduce an improper fraction to a whole or mixed number. RULE. Divide the numerator by the denominator, as in Arithmetic. Multiply each numerator into all the denominators except its own, for a new numerator of each fraction; and all the denominators into each other, for a new denominator, which will be common to each fraction. nator. 4x X b x 3 = 3 X b x 5 156 for a common denomiTherefore the new fractions will be, To find the greatest common measure of two RULE. Divide the greater by the less, and divide the preceding divisor by the remainder, repeating the operation until nothing remains; the last divisor will be the common measure required. 1. Find the greatest common measure of a2 + a and a2 + 2a a2 + a - 3. - 2 a 3(1 - 1)a2 + a − 2(a + 2 a |