Represent fractions on a number line

A number line models the whole interval from 0 to 1 partitioned into $b$ equal lengths, so each mark represents the unit fraction $1/b$ and the point $a/b$ is the $a$ th equal step from 0. This connects the denominator to the size of each part and the numerator to the number of parts, supporting fraction magnitude and order; the scope is fractions from 0 through 1, not improper fractions, mixed numbers, or fractions beyond one.

Detailed Explanation: 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.

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

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

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 $1$ .

Learn by doing: Represent fractions on a number line

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Number Line - Simple Fractions (Not Simplified), Read Number - Labelled

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