## How to find an equivalent fraction

This page will show you how to find an equivalent fraction. First, we will give a brief description of an equivalent fraction.

Then we will give some examples and as per usual we will finnish with questions and answers.

This topic is really, really important in the understanding of adding and subtracting fractions. This needs to be cracked before moving onto harder fraction topics.

**What is an equivalent fraction?**

If we look up the word equivalent in the dictionary, we would find something along the lines of, 'equal in value, force or measure'.

So, as this word suggests, an equivalent fraction is a fraction that has the same value as another fraction, **only the numbers are different.**

This means we can have millions and trillions of equivalent fractions, but still they would have the same weight or value as each other. How is this possible? Does this even make sense?

**Lets look at finding equivalent fractions.**

Example 1 : Find 5 equivalent fractions for ^{1}⁄_{2}

To start, lets to this diagrammatically, look at the blocks below. The first block is a whole block. The next block is chopped in half.

Everything that is the same size as one of those half's is considered an equivalent fraction to it.

If we chop those half blocks again, we get quarters. Please note the shading on one side of the bars. This is what we are looking at. A half is equal to a ^{1}⁄_{4} and a ^{1}⁄_{4}.

A quarter plus a quarter is 2/4 (more of this in adding and subtracting fractions).

Maths for this: ^{1}⁄_{4}+^{1}⁄_{4}=^{2}⁄_{4}

So, ^{1}⁄_{2} is equal to ^{2}⁄_{4}. They are both equal to each other even though the numbers are different. Also the picture above shows it, so there is no denying it.

Can you work out another equivalent fraction from the diagram above? There are 3 more examples from the diagram.

If we chop that whole bar into six pieces, we get sixths.

Half of this bar would be 3 of those sixths added together.

^{1}⁄_{6}+^{1}⁄_{6}+^{1}⁄_{6}=^{3}⁄_{6}

So, ^{3}⁄_{6} is equal to ^{1}⁄_{2} which is also equal to ^{2}⁄_{4}.

The other 2 equivalent fractions from the diagram are : ^{4}⁄_{8} and ^{5}⁄_{10}.

All of these fractions are equal to each other, they are equivalent fractions : ^{1}⁄_{2}, ^{2}⁄_{4}, ^{3}⁄_{6}, ^{4}⁄_{8}, ^{5}⁄_{10}, ^{6}⁄_{12}, ^{7}⁄_{14}

**Spot the Pattern**

Can you spot the pattern? Can you see that at each stage the top and bottom number is being multiplied by the same number.

So, to get from ^{1}⁄_{2} to ^{2}⁄_{4}, we have multiplied the top and bottom part of ^{1}⁄_{2} by 2.

And to get from ^{1}⁄_{2} to ^{3}⁄_{6}, we have multiplied the top and bottom part of ^{1}⁄_{2} by 3.

And to get from ^{1}⁄_{2} to ^{4}⁄_{8}, we have multiplied the top and bottom part of ^{1}⁄_{2} by 4.

And so on. Remember, the list of equivalent fractions is endless.

Example 2 : Find 5 equivalent fractions for ^{2}⁄_{3}

We will try and work this out from the diagram and then work it out mathematically. The first block is a whole one. The second block is chopped into thirds. Since we are looking for ^{2}⁄_{3}, we have colored in 2 parts.

If we chop the ^{2}⁄_{3} parts again we get sixths. From the diagram we can see that 4 parts are shaded. The 4 parts shaded is exactly equal to the 2 parts as shown from the thirds grid. So, ^{4}⁄_{6} is an equivalent fraction to ^{2}⁄_{3}.

**How do we do this mathematically? **

By multiplying the top and bottom part of the fractions by 2.

From the diagram another equivalent fraction would be ^{8}⁄_{12}, just by counting the twelfths shaded blocks.

Mathematically, we would do this by multiplying the top and bottom of ^{2}⁄_{3} by 4

Now we will try finding equivalent fractions with out the diagram.

Let us multiply the top and bottom of ^{2}⁄_{3} by 3

Multiply top and bottom of ^{2}⁄_{3} by 5, we get ^{10}⁄_{15}

Multiply top and bottom of ^{2}⁄_{3} by 10, we get ^{20}⁄_{20}

and so on...

So 5 equivalent fractions of ^{2}⁄_{3} would be ^{4}⁄_{6}, ^{6}⁄_{9}, ^{8}⁄_{12}, ^{10}⁄_{15} and one for good luck ^{20}⁄_{30}

...**but remember** there are millions and trillions of equivalent fractions for ^{2}⁄_{3}, we have only given 5.

Try these questions (answers will be at the bottom of the page)

1. Find 5 equivalent fractions for:

a. ^{4}⁄_{5}

b. ^{2}⁄_{7}

c. ^{1}⁄_{3}

d. ^{7}⁄_{8}

e. ^{6}⁄_{7}

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Answers will follow shortly, so come back here to find them!

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