Solve Fraction Division: 1/2 ÷ 2/3 Step-by-Step

Division by a fraction is the same as multiplication by its reciprocal. Think of it this way: dividing by $\frac{2}{3}$ asks "how many $\frac{2}{3}$'s fit into $\frac{1}{2}$?" Flipping and multiplying gives us this answer directly!

Simply flip the numerator and denominator! The reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$. For whole numbers like 5, write it as $\frac{5}{1}$ first, then flip to get $\frac{1}{5}$.

That's completely normal! When you divide by a fraction smaller than 1, your answer will be larger than the original number. For example, $\frac{1}{2} ÷ \frac{1}{4} = 2$ because four quarters fit into a half twice.

Always simplify to lowest terms! In this problem, $\frac{3}{4}$ is already simplified since 3 and 4 share no common factors. Check if your numerator and denominator have any common factors to divide out.

Multiply your answer by the original divisor (second fraction). If you get the dividend (first fraction) back, you're right! Here: $\frac{3}{4} × \frac{2}{3} = \frac{6}{12} = \frac{1}{2}$ ✓