Topics
4. Fractions
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AustraliaNSW
Stage 3

4.04 Order fractions

Lesson
Practice
Lesson

Are you ready?

Being able to identify a  fraction using a model  will help us in this lesson. Let's try a practice problem now.

Examples

Example 1

Below is a fraction bar.

A fraction bar divided into 3 equal parts with 1 shaded part.

What is the fraction of the coloured piece?

A
\dfrac{2}{3}
B
\dfrac{3}{4}
C
\dfrac{1}{4}
D
\dfrac{1}{3}
Worked Solution
Create a strategy

Write the fraction as: \,\, \dfrac{\text{Number of shaded parts}}{\text{Total number of parts}}.

Apply the idea

There is 1 shaded part and 3 total parts in the fraction bar. So the fraction is \dfrac{1}{3}.

The correct option is D.

Idea summary

To represent a fraction with a fraction model:

The numerator tells us how many parts should be shaded in. The denominator tells us how many parts to divide the shape into.

Order unit fractions

This video looks at how to compare unit fractions.

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Examples

Example 2

Using the fraction wall, which of the following fractions is smaller?

This image shows 5 rows divided into different parts with a written unit fraction. Ask your teacher for more information.
A
\dfrac{1}{6}
B
\dfrac{1}{7}
Worked Solution
Create a strategy

Compare the size of the bricks for the given fractions.

Apply the idea
This image shows a fraction wall for quarters, fifths, sixths, sevenths and eighths. Ask your teacher for more information.

Here are the bricks for each fraction.

The denominator of the fraction tells us how many parts the whole is divided into. The smaller brick will represent the smaller fraction.

Looking from the top to the bottom of the fraction wall, the fraction become smaller and smaller.

We can see that the brick for \dfrac{1}{7} is smaller than the brick for \dfrac{1}{6}.

So \dfrac{1}{7} is the smaller fraction. The answer is option B.

Idea summary

The bigger the denominator the smaller the fraction.

Order and count fractions

This video looks at how to compare fractions with the same denominators.

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Examples

Example 3

Order these fractions from smallest to largest.

Three fractions represented in symbols, words and pictures. Ask your teacher for more information.
Worked Solution
Create a strategy

Write each fraction with the same denominator.

Apply the idea

The shape has 3 parts and 2 are shaded. So it represents the fraction \dfrac{2}{3}.

3 thirds is equal to \dfrac{3}{3}.

So we have to order the fractions: \dfrac{2}{3}, \, \dfrac{3}{3}, \, \dfrac{1}{3}.

1 is the smallest numerator, then 2 and then 3. So the fractions in order are: \dfrac{1}{3}, \, \dfrac{2}{3}, \, \dfrac{3}{3}.

The order of the original fractions is:

Three fractions represented in symbols, words and pictures. Ask your teacher for more information.
Idea summary

In comparing fractions with the same bottom numbers (denominator), the higher the top number (numerator) is, the larger the value.

Remember to count up all the pieces to find the denominator, not just the unshaded ones. Count the shaded pieces to find the numerator.

Order and count mixed and improper fractions

What about if we have mixed numbers or improper fractions. How do we order fractions then?

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Examples

Example 4

Choose the largest number from the options below.

A
1
B
\dfrac{1}{2}
C
\dfrac{3}{2}
Worked Solution
Create a strategy

Plot the numbers on a number line.

Apply the idea

Here is the number line from 0 to 2 with 2 parts between each whole number. Each of the 2 spaces represents \dfrac{1}{2}.

The 3 numbers are plotted on the number line.

0\frac{1}{2}1\frac{3}{2}2

We can see that \dfrac{3}{2} is furthest to the right, so \dfrac{3}{2} is the largest number.

The answer is option C.

Idea summary

A mixed fraction is another way to express an improper fraction, and vice-versa, so you can rename them if you need to.

To compare fractions, we can plot them on the 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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