## Introductory Algebra for College Students (7th Edition)

We apply the Fundamental Principle of Fractions: The value of a fraction does not change if both the numerator and the denominator are divided (or multiplied) by the same nonzero number. So, $\displaystyle \frac{a\cdot c}{b\cdot c}=\frac{a}{c}.$ To reduce a fraction to lowest terms means writing it in a form that can not be further reduced. 1. We write the prime factorizations of both the numerator and denominator. 2. Find the greatest common factor (gcf) 3. Divide both the numerator and denominator with the gcf. Example: $\displaystyle \frac{30}{42}=...$ $30=2\times 15=(2\times 3)\times 5$ $42=2\times 21=(2\times 3)\times 7$ $gcf=2\times 3=6$ $\displaystyle \frac{30}{42}=\frac{30\div 6}{42\div 6}=\frac{5}{7}$