Page:Elementary algebra (1896).djvu/125

107 Rh CHAPTER XIII.

Fractions.

133. Definition. If a quantity x be divided into b equal parts, and of these parts be taken, the result is called the fraction {a}{b} of x.

If a be the unit, the fraction {a}{b} of x is called simply "the fraction {a}{b}" ; so that the fraction {a}{b} represents a equal parts, b of which make up the unit.

The quantity above the horizontal line is spoken of as the numerator, and that below the line as the denominator of the fraction.

134. A Simple Fraction is one of which the numerator and denominator are whole numbers.

REDUCTION OF FRACTIONS.

135. To reduce a fraction is to change its form without changing its value.

136. To prove that {a}{b} = {ma}{mb} where a, b, m are positive integers.

By {a}{b} we mean a equal parts, b of which make up the unit, (1);

by {ma}{mb} we mean ma equal parts, mb of which make up the unit, (2).