The difference between $\frac{1}{3}$ and $\frac{1}{5}$ is $\frac{1}{3}-\frac{1}{5}= \frac{2}{15}$.

This section of the number line is divided into $16$ intervals, each of length $\frac{2}{15}\div 16 = \frac{1}{120}$.

The difference between $\frac{1}{4}$ and $\frac{1}{5}$ is $\frac{1}{4}-\frac{1}{5}= \frac{1}{20}= \frac{6}{120}$, and hence $\frac{1}{4}$is six smaller intervals from $\frac{1}{5}$.

*This problem is taken from the UKMT Mathematical Challenges.*

View the current weekly problem