Lesson 5: Solving Rational Equations

Property

A proportion is a statement that two ratios are equal. For example, $\frac{a}{b} = \frac{c}{d}$.

If $\frac{a}{b} = \frac{c}{d}$, then $ad = bc$, as long as $b, d \neq 0$. This shortcut is known as cross-multiplying.

Examples

• To solve the proportion $\frac{8}{3} = \frac{x}{9}$, we can cross-multiply. This gives $8 \cdot 9 = 3 \cdot x$, so $72 = 3x$. Dividing by 3, we find $x=24$.