Cross-Multiplying

Sometimes an equation is one fraction equal to another, like $\frac{x}{4} = \frac{3}{8}$. You can multiply both sides by both denominators to clear everything at once. The shortcut is called cross-multiplying: the top of the left fraction times the bottom of the right equals the top of the right fraction times the bottom of the left.

$$8x = 12$$

$$x = \frac{3}{2}$$

Check the answer: $\frac{\frac{3}{2}}{4} = \frac{3}{8}$. The answer is a fraction. A solution does not have to be a whole number.

Cross-multiplying is the same as multiplying both sides by both denominators, as long as neither denominator is zero. Use it only when each side is a single fraction. In $\frac{x}{4}+1 = \frac{3}{8}$ the left side has two terms, so first add them into one fraction, or multiply every term by the common denominator 8.