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5.07 Simplify fractions


Are you ready?

Do you know how to find an  equivalent fraction  ?


Example 1

Fill in the blank to find an equivalent fraction to \dfrac{1}{3}:

\dfrac{1}{3}= \dfrac{⬚}{6}

Worked Solution
Create a strategy

Use fraction area models.

Apply the idea
A rectangle divided into 3 equal parts with 1 shaded part.

On the left of the equals sign we have \dfrac{1}{3} which looks like this.

A rectangle divided into 6 equal parts with 2 parts shaded.

1 out of the 3 squares are shaded. We want to write this as a fraction of 6. Dividing the model into 6 parts would look like this.

We can see that 2 out of 6 parts are shaded to get the same area. So:

\displaystyle \frac{1}{3}\displaystyle =\displaystyle \frac{2}{6}
Reflect and check

We also could have multiplied the numerator and denominator by 2 since 3\times 2=6.

\displaystyle \dfrac{1}{3}\displaystyle =\displaystyle \dfrac{1 \times 2}{3 \times 2}Multiply the numerator and denominator by 2
\displaystyle =\displaystyle \dfrac{2}{6}
Idea summary

Equivalent fractions look different but have the same value.

You need to multiply or divide both the numerator and the denominator of a fraction by the same number to work out the equivalent fraction.

Simplify fractions

How can we simplify fractions? This video shows us how.

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Example 2

Simplify the fraction \dfrac{14}{21}.

Worked Solution
Create a strategy

To simplify fractions, we need to divide the numerator and denominator by the same number.

Apply the idea

14 and 21 have a common factor of 7. So we can divide both by 7.

\displaystyle \dfrac{14}{21}\displaystyle =\displaystyle \dfrac{14\div 7}{21 \div 7}Divide both parts by 7
\displaystyle =\displaystyle \dfrac{2}{3}

2 and 3 only have a common factor of 1. So the fraction is simplified.


Idea summary

To simplify a fraction, we want to make the numerator and denominator smaller. To do that, we need to divide them both by a common factor.



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