Solve Fraction Division: 5/2 ÷ 1/4 Step-by-Step

Dividing by a fraction means "how many groups of that size fit into the first number?" When you flip and multiply, you're finding how many $\frac{1}{4}$'s fit into $\frac{5}{2}$.

The reciprocal means flipping the fraction upside down. The reciprocal of $\frac{1}{4}$ is $\frac{4}{1} = 4$. For any fraction $\frac{a}{b}$, the reciprocal is $\frac{b}{a}$.

You could, but it's often messier! $\frac{5}{2} = 2.5$ and $\frac{1}{4} = 0.25$, so $2.5 ÷ 0.25 = 10$. However, the flip and multiply method works for all fractions.

Multiply the numerator by the whole number: $\frac{5}{2} \times 4 = \frac{5 \times 4}{2} = \frac{20}{2} = 10$. The denominator stays the same!

That's fine! You can leave it as an improper fraction or convert to a mixed number. For example, $\frac{20}{2} = 10$ is already a whole number here.