Topics
4. Fractions
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AustraliaNSW
Stage 3

4.01 Fractions on a number line

Lesson
Practice
Lesson

Are you ready

Let's try this problem to help us remember how to locate a  fraction on a number line  .

Examples

Example 1

Plot \dfrac{1}{10} on the number line.

01
Worked Solution
Create a strategy

Start at zero and jump to the right 1 space.

Apply the idea

The number line is already divided into 10 spaces, so each space represents \dfrac{1}{10}. We just need to move right 1 space.

01
Idea summary

When plotting a fraction on a number line:

  • the denominator (bottom number) shows how many parts there should be between each whole number.

  • the numerator (top number) shows the number of parts to move to the right from the previous whole number.

Fractions on a number line

Let's look at how to plot fractions on a number line.

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Examples

Example 2

Plot \dfrac{4}{3} on the number line.

012
Worked Solution
Create a strategy

The space between 0 and 1 on the number line has been divided into 3 equal spaces. Use the fraction bar model to help you count up to \dfrac{4}{3}.

A number line from 0 to 2 divided into 3 equal spaces. Above each spaces is the fraction one-third.
Apply the idea

To plot \dfrac{4}{3}, we can start at zero and jump right 4 spaces, since each space represents \dfrac{1}{3}.

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Idea summary

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.

Compare unit fractions on a number line

This video shows how to compare unit fractions on a number line.

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Examples

Example 3

Think about the fractions \dfrac{1}{8} and \dfrac{1}{10}.

a

Plot the number \dfrac{1}{8} on the number line.

01
Worked Solution
Create a strategy

Start at zero and jump to the right 1 space.

Apply the idea

The number line is already divided into 8 spaces, so we just need to move right 1 space.

01
b

Plot \dfrac{1}{10} on the number line.

01
Worked Solution
Create a strategy

Start at zero and jump to the right 1 space.

Apply the idea

The number line is already divided into 10 spaces, so we just need to move right 1 space.

01
c

The two numbers can be shown on the same number line like this:

A number line starting at 0 and ending at 1. 1 eighths and 1 tenths are plotted. 1 eighths is to the right of 1 tenths.

Which number is smaller?

A
\dfrac{1}{8}
B
\dfrac{1}{10}
Worked Solution
Create a strategy

Compare the plotted points. The smaller number is further to the left on the number line.

Apply the idea

We can see that \dfrac{1}{10} is further to the left, so it is the smaller number.

The answer is Option B.

Idea summary

To plot a proper fraction on a number line:

  • Start the number line at 0 and end it at 1.

  • Divide the number line into the number of parts equal to the denominator.

  • From 0, count to the right the number of parts equal to the numerator.

  • Plot the point.

To compare fractions on a number line, the fraction furthest to the right is the largest.

Outcomes

MA3-7NA

compares, orders and calculates with fractions, decimals and percentages

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