How to find equivalent fractions

Key points

Fractions are equivalent if they are of equal value. can have different and .

Equivalent fractions can be found by:

using a or a
multiplying both the numerator and denominator of a fraction by the same number
dividing both the numerator and denominator of a fraction by a

Learning about common factors may be useful when finding equivalent fractions.

How to find equivalent fractions

A is made up of several bars, all of equal length. Each complete bar represents one whole. It can have several bars so more fractions can be compared.

To find equivalent fractions on a fraction wall:

Locate the fraction on the fraction wall.
Draw a vertical line to the right of the fraction.
Any will be aligned to this line.

Example: using a fraction wall

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$A fraction wall with six rows going from one whole down to one sixth.$
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A fraction wall can be used to compare fractions and find equivalent fractions.
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One whole is the same as two halves. It is also the same as three thirds.
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1⁄2 is equivalent to 2⁄4. Both fractions have the same value.
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2⁄3 is equivalent to 8⁄12. Both fractions have the same value.
$A fraction wall with six rows going from one whole down to one sixth.$
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Create a fraction wall by starting with one whole. Then create several bars split into 2, 3, 4, 5 and 6 equal parts. This can be extended to include more rows when necessary.
$The same fraction wall. A divider line is placed down the middle - to the right of one half.$
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What fractions are equivalent to 1⁄2?
$The same fraction wall. It is faded out to show that one half has the same value as two quarters and three sixths. These fractions are written out, too.$
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Draw a line to the right of 1⁄2 on the fraction wall. 1⁄2 is equivalent to 2⁄4 and 3⁄6

How to create equivalent fractions

To create equivalent fractions using multiplication and division:

Multiply both the numerator and the denominator by the same number. An infinite number of can be created this way.
Divide both the numerator and denominator by a . There may be more than one possible common factor.

To decide if two fractions are equivalent:

each fraction by dividing the numerator and denominator by their .
Compare the simplified fractions.
If they are the same, the original fractions are equivalent.

Example: using multiplication and division

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Image caption,
1⁄2 is equivalent to 12⁄24
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1⁄2 is equivalent to 12⁄24. The numerator and the denominator have both been multiplied by 12
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3 is a common factor of 6 and 9. Divide both the numerator and denominator by 3. This gives 2⁄3. 6⁄9 is equivalent to 2⁄3
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12⁄18 is equivalent to 24⁄36. It is also equivalent to 36⁄54. An infinite number of equivalent fractions can be created this way.
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12⁄18 is equivalent to 4⁄6. It is also equivalent to 6⁄9. Equivalent fractions can only be created this way by dividing by a common factor.
$The two fractions fourteen twentieths and thirty five fiftieths.$
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Are 14⁄20 and 35⁄50 equivalent fractions?
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The highest common factor of 14 and 20 is 2. 14⁄20 simplifies to 7⁄10. The highest common factor of 35 and 50 is 5. 35⁄50 simplifies to 7⁄10
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Both 14⁄20 and 35⁄50 simplify to 7⁄10. The fractions have the same value - they are equivalent.

Game - Equivalent fractions

Put your equivalent fractions skills into practice with these puzzles from our Divided Islands maths game.

Play the full Divided Islands game.

How to work out a missing value in an equivalent fraction

To work out the value of a missing numerator:

Find the or by dividing the larger denominator by the smaller denominator.
To find the numerator for the larger denominator, multiply by the number you found.
To find the numerator for the smaller denominator, divide by the number you found.

To work out the value of a missing denominator:

Find the multiplier or divisor by dividing the larger numerator by the smaller numerator.
To find the denominator for the larger numerator, multiply by the number you found.
To find the denominator for the smaller numerator, divide by the number you found.

Examples: missing values

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$Two diagrams laid out like fractions. The first diagram has the fractions consist of the word numerator over the word denominator. The second fractions have the word 'missing value' where the numerator in one fraction and then the denominator in the other fractionshould be.$
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These are equivalent fractions with one value missing.
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The two fractions are equivalent. Find the missing numerator.
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Divide the larger denominator by the smaller denominator. 45 divided by 9 is 5. 5 is the multiplier. The numerator and denominator should both be multiplied by 5
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9 multiplied by 5 is 45. 4 multiplied by 5 is 20. The missing numerator is 20. 4⁄9 and 20⁄45 are equivalent.
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The two fractions are equivalent. Find the missing denominator.
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Divide the larger numerator by the smaller numerator. 27 divided by 9 is 3. 3 is the divisor. The numerator and denominator should both be divided by 3
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27 divided by 3 is 9. 36 divided by 3 is 12. The missing denominator is 12. 27⁄36 and 9⁄12 are equivalent.
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The two fractions are equivalent. Find the value of the missing denominator.
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90 divided by 9 is 10 and 10 multiplied by 2 is 20. The numerator and denominator both need to be divided by 9 and then multiplied by 2
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90 divided by 9 is 10, and 99 divided by 9 is 11. 10 multiplied by 2 is 20, and 11 multiplied by 2 is 22. The missing denominator is 22. 90⁄99 and 20⁄22 are equivalent.

Game - Equivalent fractions

Try out these extra equivalent fractions puzzles from our Divided Islands game.

Play the full Divided Islands game.

Practise equivalent fractions

Try this quiz to practise finding and creating equivalent fractions by simplifying them.

Quiz

Real-world maths

Close up shot of scale model house on table. A black architect is leaning over, looking at the model. A white architect with glasses is pointing at it with a pen. — Image caption,
Architects may use equivalent fractions when preparing models.

Equivalent fractions are used in industries like architecture. Architects prepare scale models and drawings of their designs. They use equivalent fractions in a practical setting.

Equivalent fractions can also be used in cooking or baking to adjust a recipe. For example, a cupcake recipe may make enough for [24] cupcakes. A home baker may want to change that number of cupcakes to [12]. They would need to work out the fraction of each ingredient to make sure it is equivalent to the original recipe.