You may have already looked at representing fractions with fraction bars. Now watch this video to learn about fractions as a point on the number line.

Representing fractions

We can represent fractions using:

area

segments of lines

collections; and

as points on the number line.

The number line

Fractions are used to describe points between whole numbers. For example, one and a half is halfway between one and two.

To represent fractions as a point on the number line we:

divide the number line into the number of equal parts indicated by the denominator.

count along the number of parts using the numerator.

Being able to plot fractions on the number line is important for understanding the value of different fractions.

Example 1

To plot $\frac{3}{5}$35 on a number line:

Divide a number line between $0$0 and $1$1 into five equal parts to make fifths

Count along to the third fifth to indicate $\frac{3}{5}$35

Try this question for yourself:

Question 1:

Plot $\frac{1}{2}$12 on the number line.

Example 2

Can you work out what fraction the diagram below is indicating on the number line?

The number line is divided into thirds (three equal parts between each whole number). The red rectangle is indicating the second point along the line, so it is $\frac{2}{3}$23.

Try this question for yourself:

question 2

Look at the fraction bar and the number line below.

What fraction does each piece of the bar represent?

What fraction of the bar is shaded below?

What fraction is marked by the empty box below?

Question 3

Plot $\frac{4}{5}$45 on the number line.

This applet will help you to practice more fractions on a number line.