The fractions $$\frac{1}{5}$$ and $$\frac{1}{3}$$ are shown on the number line. In which position should $$\frac{1}{4}$$ be shown?
Solution
The gap between the two marked fractions is $$\frac{1}{3} - \frac{1}{5} = \frac{2}{15}$$, and the number line cuts this gap into 16 equal parts, so each small part is $$\frac{2}{15} \div 16 = \frac{1}{120}$$. Since $$\frac{1}{4} - \frac{1}{5} = \frac{1}{20} = \frac{6}{120}$$, the fraction $$\frac{1}{4}$$ lies 6 small parts to the right of $$\frac{1}{5}$$, which is the mark $$q$$.
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