Skill: Represent fractions on a number line

A fraction $\frac{a}{b}$ tells you how far to move from $0$ to $1$:

• The denominator $b$ tells you to divide the space from $0$ to $1$ into $b$ equal parts.
• The numerator $a$ tells you how many parts to count from $0$.

Example: Place $\frac{3}{5}$ on a number line.

1. The denominator is $5$, so divide the interval from $0$ to $1$ into 5 equal parts.
2. Each part is $\frac{1}{5}$.
3. Start at $0$ and count 3 steps:

$$0 \rightarrow \frac{1}{5} \rightarrow \frac{2}{5} \rightarrow \frac{3}{5}$$

4. The third mark is $\frac{3}{5}$.

$$0\quad \frac{1}{5}\quad \frac{2}{5}\quad \frac{3}{5}\quad \frac{4}{5}\quad 1 \qquad\qquad\quad \star$$

The star belongs above the $\frac{3}{5}$ mark. So, $\frac{3}{5}$ is 3 equal parts out of 5 parts from $0$ to $1$.