Topics
5. Fractions
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AustraliaNSW
Stage 2

5.06 Compare fractions

Lesson
Practice
Lesson

Are you ready

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.

01
Worked Solution
Create a strategy

Start at zero and jump to the right 1 space.

Apply the idea

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

Compare fractions using area models

This video looks at comparing fractions using area models.

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Examples

Example 2

Which fraction is smaller?

A
An area model with 6 equal parts with 2 shaded. The fraction underneath is 2 over 6.
B
An area model with 6 equal parts with 3 shaded. The fraction underneath is 3 over 6.
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.

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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:

01

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}.

01
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:

01

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}.

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. 3 quarters and 4 fifths are plotted. 4 fifths is to the right of 3 quarters.

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.

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.

Compare fractions greater than one

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

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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:

11\frac{1}{9}1\frac{2}{9}1\frac{1}{3}1\frac{4}{9}1\frac{5}{9}1\frac{2}{3}1\frac{7}{9}1\frac{8}{9}2

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

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

11\frac{1}{9}1\frac{2}{9}1\frac{1}{3}1\frac{4}{9}1\frac{5}{9}1\frac{2}{3}1\frac{7}{9}1\frac{8}{9}2

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

11\frac{1}{9}1\frac{2}{9}1\frac{1}{3}1\frac{4}{9}1\frac{5}{9}1\frac{2}{3}1\frac{7}{9}1\frac{8}{9}2

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

MA2-7NA

represents, models and compares commonly used fractions and decimals

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