 # 4.01 Fractions on a number line

Lesson

## Ideas

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.

Worked Solution
Create a strategy

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.

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.

### Examples

#### Example 2

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

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}.

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}.

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.

### 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.

Worked Solution
Create a strategy

Apply the idea

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

b

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

Worked Solution
Create a strategy

Apply the idea

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

c

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

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.

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