Rational numbers — representation on number line

To place a fraction on a number line, we divide each unit interval into a number of equal parts equal to the denominator of the fraction.

The fraction is $\frac{3}{8}$. The denominator is 8, so each unit must be divided into 8 equal parts.

Count 3 parts to the right of zero. Each part represents $\frac{1}{8}$, so 3 parts land at $\frac{3}{8}$.

Each unit must be divided into 8 equal parts.

The number of equal parts per unit interval equals the denominator of the fraction being placed.

Using 3 parts per unit would place fractions with denominator 3 (like $\frac{1}{3}$). The fraction $\frac{3}{8}$ has denominator 8, not 3. Eliminate.

4 parts would suit fractions like $\frac{3}{4}$, not $\frac{3}{8}$. 16 parts would work but is unnecessarily fine — $\frac{3}{8}=\frac{6}{16}$, which is not the simplest approach. Eliminate both.

The denominator of $\frac{3}{8}$ is 8, so we divide each unit into 8 equal parts and count 3 from zero. The answer is 8.