# What Are Equivalent Fractions? Explained For Primary School Parents

Equivalent fractions come up a lot in KS2 maths and some primary school parents can be a little unsure as to what they are and how to find them. This blog post aims to make things a little clearer.

This blog is part of our series of blogs designed for parents supporting home learning and looking for home learning resources during the Covid-19 epidemic.

### What are equivalent fractions?

Equivalent fractions are two or more fractions that are all equal. A fraction is a part of a whole: the denominator (bottom number) represents how many equal parts the whole is split into; the numerator (top number) represents the amount of those parts.

### Confused about fractions? You’re not alone

If the concept of equivalent fractions already sounds a bit confusing and you’re not yet clear on what the difference is between whole numbers, denominators of a fraction and different numerators you may want to loop back to our fractions for kids article

This breaks down the first fraction steps that Key Stage 1 and Key Stage 2 children must take at school, together with clear examples of how to find the value of a fraction using concrete resources, pictorial representations and number lines; the difference between unit fractions and non unit fractions; all the way up to proper and improper fractions.

It’s been written as a guide for children and parents to work through together in clear digestible chunks.

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### Equivalent fraction examples

For example, 4/6 = four out of six parts, also shown as:

Although 8/12 may look like a different fraction, it is actually equivalent to 4/6 because eight out of 12 parts is the same as four out of six parts, as shown below:

2/3, or two out of three, is another fraction equivalent to both 4/6 and 8/12.

The three fractions 2/3, 4/6 and 8/12 are shown below respectively in a fraction wall to demonstrate their equivalence.

### How to work out equivalent fractions

To calculate equivalent fractions, both the numerator and denominator must be multiplied by the same number. For example, to find fractions equivalent to 3/5:

3/5 x 2/2 = **6/10** (x 2/2 means multiplying both the numerator and denominator by 2. Any fraction where the numerator and denominator are the same is equal to 1. Multiplying anything by 1 doesn’t change the original number, so we know the fraction will be equivalent)

3/5 x 3/3 = **9/15**

3/5 x 4/4 = **12/20**

So, 3/5 = 6/10 = 9/15 = 12/20.

Another way to find equivalent fractions is to divide both the numerator and the denominator of the fraction by the same number – this is called simplifying fractions, because both the numerator and denominator digits will get smaller.

For example, to simplify 9/12, find a number that both the numerator and denominator can be divided by (also known as a ‘common factor’), such as 3.

9/12 ÷ 3/3 = 3/4, so 9/12 and 3/4 are equivalent fractions, with 3/4 being the fraction in its simplest form.

### When will my child learn about equivalent fractions in primary school?

#### Equivalent fractions KS2

The concept of equivalent fractions isn’t introduced until Year 3, where children *recognise and show, using diagrams, equivalent fractions with small denominators.*

In Year 4, they will *recognise and show, using diagrams, families of common equivalent fractions*. The National Curriculum’s non-statutory guidance also advises that *pupils use factors and multiples to recognise equivalent fractions and simplify where appropriate (for example, 6/9 = 2/3 or ¼ = 2/8).*

In Year 5, pupils are taught to i*dentify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths*. In Year 6, they will *add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions.* Non-statutory guidance for Year 6 suggests that *common factors can be related to finding equivalent fractions and that children practise calculations with simple fractions… including listing equivalent fractions to identify fractions with common denominators.*

### How do equivalent fractions relate to other areas of maths?

Children will need to understand equivalent fractions to be able to convert between fractions, decimals and percentages. Knowledge of times tables, the lowest common multiple and highest common factor are also important for equivalent fractions

### Equivalent fractions worksheet questions

1. Write the missing values: 3/4 = 9/? = ?/24

*(Answer: 12, 18)*

2. Circle the two fractions that have the same value:

2/10

1/3

½

5/10

¼

*(Answer: ½ and 5/10)*

3. Tick two shapes that have ¾ shaded.

*(Answer: top left (6/8) and bottom right (12/16) as both = 3/4)*

4. Shade ¼ of this shape.

*(Answer: Any 9 triangles shaded)*

5. Ahmed says, ‘One-third of this shape is shaded.’ Is he correct? Explain how you know.

*(Answer: Yes – it would be 2/6 (imagine the middle square split into halves too) which = 1/3)*

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