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

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, $\displaystyle \frac{a\cdot c}{b\cdot c}=\frac{a}{c}.$ Examples of using the Principle: reducing fractions: $\displaystyle \quad\frac{10}{15}=\frac{2\times 5}{3\times 5}=\frac{2}{5}$ expanding to a higher denominator:$\displaystyle \quad\frac{3}{7}==\frac{3\times 5}{7\times 5}=\frac{15}{35}$