CHAP. VI. To change an Integral Quantity into a Fraction 72 To change an Integral Quantity into a Fraction, To multiply a Fraction by an Integral Quantity 85 To multiply one Fraction by another II. Involution of Compound Quantities.. To involve a Fraction ..... III. The Binomial Theorem.. Application of the Binomial Theorem to Polyno- 19. To divide a given Quantity into unequal Parts.... Common Method of Completing the Square.... 226 Rule for solving Affected Equations.... Another Way to Complete the Square..... CHAP. XII. FIRST LESSONS IN ALGEBRA CHAPTER I. INTRODUCTION. SECTION I. Letters and Coefficients. 1. A BOY bought a peach and a melon for 12 cents, and the melon cost three times as much as the peach. What was the price of each? Let the letter a represent the number of cents the boy gave for the peach; then, as he gave one x for the peach, whatever the value of x may be, and as the melon cost three times as much, he must have given three x's for that; and, of course, he gave one x and three x's, that is, four x's for both. But, by the question, he gave 12 cents for both; therefore, the four a's must be equal in value to the 12 cents. But, if four x's are equal to 12 cents, one x must be equal to one fourth part of 12 cents, or 3 cents, which was the price of the peach; and if one r be |