Solve Fraction Division: 1/2 ÷ 5/3 Step-by-Step

Dividing by a fraction is the same as multiplying by its reciprocal. Think of it as: "How many $\frac{5}{3}$'s fit into $\frac{1}{2}$?" This is easier to calculate by multiplying $\frac{1}{2} \times \frac{3}{5}$.

A reciprocal is when you flip a fraction upside down. The reciprocal of $\frac{5}{3}$ is $\frac{3}{5}$. For whole numbers like 4, the reciprocal is $\frac{1}{4}$.

Multiply straight across: numerator × numerator and denominator × denominator. So $\frac{1}{2} \times \frac{3}{5} = \frac{1×3}{2×5} = \frac{3}{10}$.

Yes! Look for common factors to cancel first. In this problem, 1 and 3 have no common factors with 2 and 5, so we multiply first then check if the result can be simplified.

Multiply your answer by the divisor (the second fraction). If you get the first fraction back, you're correct! $\frac{3}{10} \times \frac{5}{3} = \frac{1}{2}$ ✓