You may have already looked at representing fractions as 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 five tenths 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.

Worked examples

To plot $\frac{3}{10}$310 on a number line:

Divide a number line between $0$0 and $1$1 into ten equal parts to make tenths.

Count along to the third tenth to indicate $\frac{3}{10}$310.

Try this question for yourself:

Question 1:

Plot $\frac{1}{10}$110 on the number line.

Example 2:

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

The number line is divided into sixths (six equal parts between each whole number). The first red rectangle is indicating the point $\frac{3}{6}$36 on the number line. The second red rectangle is $1\frac{2}{6}$126.

Try this question for yourself:

Question 2:

What value is missing from each number line below?

Example 3:

When a fraction has a whole number before it we call it a mixed number. For example, we could have $3\frac{2}{3}$323, this fraction is between $3$3 and $4$4 on the number line.

Try this question for yourself:

Question 3:

Consider the number lines below.

Plot the mixed number $1\frac{1}{4}$114 on the number line below.

Now plot the mixed number $3\frac{4}{8}$348 on the number line below.

Remember!

The denominator shows how many parts make the whole

The numerator is the number of parts within this fraction

A mixed fraction includes a whole number and a fraction