Topics
4. Fractions
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Australia
Year 5

4.01 Fractions on a number line

Lesson
Practice

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.

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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

AC9M5N03

compare and order fractions with the same and related denominators including mixed numerals, applying knowledge of factors and multiples; represent these fractions on a number line

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