Topics
5. Fractions
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AustraliaNSW
Stage 3

5.08 Add and subtract like fractions

Lesson
Practice
Lesson

Are you ready?

We can use  models to write fractions  . Let's try this problem to practice.

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 find a fraction from an area model:

  • To find the numerator, count the number of parts shaded.

  • To find the denominator, count the total number of parts.

Add and subtract fractions

This video introduces the idea of adding and subtracting fractions.

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Examples

Example 2

What is \dfrac{1}{12} + \dfrac{1}{12}.

Worked Solution
Create a strategy

Use area models.

Apply the idea
Two circles with plus sign in between. Each circle is divided into 12 equal parts with 1 shaded part.

\dfrac{1}{12} means means one twelfth or 1 part out of 12 parts should be shaded in an area model.

Here is the area model of \dfrac{1}{12} + \dfrac{1}{12}.

A circle divided into 12 equal parts with 2 shaded parts.

We can see that adding the two shaded parts means we get 2 shaded parts out of 12 parts.

This can be written as the fraction \dfrac{2}{12}.

\dfrac{1}{12}+\dfrac{1}{12}= \dfrac{2}{12}

Idea summary

We can add or subtract fractions by using area models.

Add and subtract larger fractions

What if the fractions have a value greater than 1? Yes, we can still add or subtract them.

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Examples

Example 3

Find the value of \dfrac{4}{7} - \dfrac{3}{7}.

Worked Solution
Create a strategy

Subtract the numerators since both of these fractions have the same denominator.

Apply the idea
\displaystyle \dfrac{4}{7} - \dfrac{3}{7}\displaystyle =\displaystyle \dfrac{4-3}{7}Subtract the numerators
\displaystyle =\displaystyle \dfrac{1}{7}
Idea summary

Adding or subtracting fractions with the same denominator is very similar to adding or subtracting with whole numbers. The difference is we are counting fraction parts instead.

Outcomes

MA3-7NA

compares, orders and calculates with fractions, decimals and percentages

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