 # 5.06 Compare fractions

Lesson

Being able to plot a  fraction on a number line  can help us compare fractions in this lesson. Let's try this problem as a review.

### Examples

#### Example 1

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

Worked Solution
Create a strategy

Apply the idea

Since the number line is already divided into 10 spaces, 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.

## Compare fractions using area models

This video looks at comparing fractions using area models.

### Examples

#### Example 2

Which fraction is smaller?

A
B
Worked Solution
Create a strategy

Compare the number of parts shaded.

Apply the idea

Both options have the same total number of parts. Option A has 2 shaded parts and option B has 3 shaded parts.

Since 2 \lt 3, \, \,\dfrac{2}{6} is smaller than \dfrac{3}{6}.

The correct option is A.

Idea summary
• When comparing fractions, if the denominators are the same, then we can compare the numerators.

• The denominator also tells us how many parts make up one whole.

## Compare fractions using number lines

This video shows how to use number lines to compare fractions.

### Examples

#### Example 3

Think about the fractions \dfrac{3}{4} and \dfrac{4}{5}.

a

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

Worked Solution
Create a strategy

Divide the number line from 0 to 1 into 4 parts.

Apply the idea

Here is the number line:

Each of the 4 spaces represents \dfrac{1}{4}.

Count 3 spaces to the right from 0 and plot the point for \dfrac{3}{4}.

b

Plot the number \dfrac{4}{5} on the number line.

Worked Solution
Create a strategy

Divide the number line from 0 to 1 into 5 parts.

Apply the idea

Here is the number line:

Each of the 5 spaces represents \dfrac{1}{5}.

Count 4 spaces to the right from 0 and plot the point for \dfrac{4}{5}.

c

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

Which number is bigger?

A
\dfrac{3}{4}
B
\dfrac{4}{5}
Worked Solution
Create a strategy

Compare the plotted points. The larger number is further to the right on the number line.

Apply the idea

We can see that \dfrac{4}{5} is further to the right, so it is the bigger 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.

## Compare fractions greater than one

What about mixed numbers or improper fractions? This video shows us how to compare using these.

### Examples

#### Example 4

Compare the two fractions by using the greater than (\gt) or less than (\lt) symbol. 1 \dfrac{8}{9} \, ⬚ \, 1 \dfrac{4}{9}

Worked Solution
Create a strategy

Plot the numbers on a number line.

Apply the idea

Both fractions have the same whole number 1. So both fractions we lie between 1 and 2. Here is the number line with 9 parts between 1 and 2:

Each of the 9 spaces represents \dfrac{1}{9}.

Count 8 spaces to the right from 1 to plot 1\dfrac{8}{9}.

Count 4 spaces to the right from 1 to plot 1\dfrac{4}{9}.

We can see that 1\dfrac{8}{9} is further to the right, so 1\dfrac{8}{9} is greater than 1\dfrac{4}{9}:1 \dfrac{8}{9} \, \gt \, 1 \dfrac{4}{9}

Idea summary

To plot a mixed number on a number line:

• Start the number line at the whole number and end it at the next whole number.

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

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

• Plot the point.

To plot an improper fraction on a number line, convert the improper fraction to a mixed number. Then follow the above steps.

### Outcomes

#### VCMNA158

Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line