Solve the Fraction Division: 1/4 ÷ □ = 1/2

Division by a number is the same as multiplying by its reciprocal. So $\frac{1}{4} \div x$ becomes $\frac{1}{4} \times \frac{1}{x} = \frac{1}{4x}$, which is easier to solve!

The answer depends on the numbers in the problem. Since we're dividing $\frac{1}{4}$ by something to get $\frac{1}{2}$ (which is larger), the divisor must be a fraction less than 1.

Yes! You can think: "What times $\frac{1}{2}$ equals $\frac{1}{4}$?" This gives $x \times \frac{1}{2} = \frac{1}{4}$, so $x = \frac{1}{4} \times 2 = \frac{1}{2}$.

When you divide by a fraction less than 1, the result gets larger! Since $\frac{1}{2} > \frac{1}{4}$, we needed to divide by $\frac{1}{2}$ (which is less than 1) to make the result bigger.

Substitute back: $\frac{1}{4} \div \frac{1}{2} = \frac{1}{4} \times \frac{2}{1} = \frac{2}{4} = \frac{1}{2}$ ✓ The result matches what we wanted!