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5.08 Add and subtract like fractions


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


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?

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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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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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.

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