Solve the Fraction Equation: 1/4 × ? = 1/5

Dividing by $\frac{1}{4}$ is the same thing as multiplying by 4! When you divide by a fraction, you multiply by its reciprocal. The reciprocal of $\frac{1}{4}$ is $\frac{4}{1} = 4$.

You must multiply both sides of the equation by 4. This keeps the equation balanced: $\frac{1}{4} \times ? \times 4 = \frac{1}{5} \times 4$, which gives us $? = \frac{4}{5}$.

Always check your work by substituting back! If you got $\frac{3}{5}$, test it: $\frac{1}{4} \times \frac{3}{5} = \frac{3}{20}$, which does not equal $\frac{1}{5}$.

Not directly! Cross-multiplication works when you have $\frac{a}{b} = \frac{c}{d}$. Here you have $\frac{1}{4} \times ? = \frac{1}{5}$. You'd need to rewrite it as $\frac{?}{1} = \frac{1/5}{1/4}$ first.

When you divide a smaller number by an even smaller number, you get a larger result! Think of it as: "How many $\frac{1}{4}$'s fit into $\frac{1}{5}$?" The answer $\frac{4}{5}$ makes sense.