The numerator (top number) is the number of parts shaded to represent the fraction.
The denominator (bottom number) is the number of equal parts the shape is divided into.

Equivalent fractions

How can we identify equivalent fractions? This video will show us.

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Examples

Example 2

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

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

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

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:

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

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}

Compare fractions with different denominators

Here we look at comparing using equivalent fractions.

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Exploration

Using the geogebra applet, slide the slider to see what some fractions out of 8 look like.

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The number of shaded parts equals the top number (numerator).

Examples

Example 3

We are going to compare the two fractions \dfrac{1}{8} and \dfrac{1}{4}.

Turn \dfrac{1}{4} into a fraction in eighths.

Worked Solution

Create a strategy

Multiply the numerator and denominator by 2.

Apply the idea

Since 4 \times 2 =8, we should multiply the numerator and denominator by 2 to change the fraction into eighths.

\displaystyle \dfrac{1}{4}	\displaystyle =	\displaystyle \dfrac{1}{4} \times \dfrac{2}{2}	Multiply the top and bottom by 2
	\displaystyle =	\displaystyle \dfrac{2}{8}	Perform the multiplications

Which fraction is larger?

The fractions are the same size.

\dfrac{1}{8}

\dfrac{1}{4}

Worked Solution

Create a strategy

Remember that \dfrac{1}{4} = \dfrac{2}{8} as found in part (a).

Apply the idea

\dfrac{1}{4}=\dfrac{2}{8} which is shown in the model below:

\dfrac{1}{8} is shown in the model below:

The model for \dfrac{1}{4} has more shaded parts than the model for \dfrac{1}{8}.

So \dfrac{1}{4} is the larger fraction, the answer is option C.

Idea summary

To compare fractions, model both fractions using area models with the same number of parts. Then count the number of shaded parts in each model.

Whole numbers as fractions

This next video shows us that whole numbers can also be written as fractions.

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Examples

Example 4

Fill in the blank to find an equivalent fraction to 5:

5= \dfrac{⬚}{2}

Worked Solution

Create a strategy

Write 5 as a fraction and then multiply the numerator and denominator to find the equivalent fraction.

Apply the idea

5 as a fraction is \dfrac{5}{1}.

But we want a denominator of 2. So we need to multiply the denominator and the numerator by 2.

\displaystyle \dfrac{5}{1}	\displaystyle =	\displaystyle \dfrac{5 \times 2}{1 \times 2}	Multiply by 2
	\displaystyle =	\displaystyle \dfrac{10}{2}

5=\dfrac{10}{2}

Idea summary

Equivalent fractions represent the same size, but have different numerators and denominators.

To find an equivalent fraction we can multiply the numerator and denominator by the same number.

5.07 Equivalent fractions

Ideas

Are you ready?

Examples

Example 1

Equivalent fractions

Examples

Example 2

Compare fractions with different denominators

Exploration

Examples

Example 3

Whole numbers as fractions

Examples

Example 4

Outcomes

ACMNA077

What is Mathspace

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