## What are equivalent fractions?

Equivalent fractions are fractions that are **equal in size**, even though they have **different numerators and denominators**.

Equivalent fractions are fractions that are **equal in size**, even though they have **different numerators and denominators**.

If the denominator is **exactly double** the numerator, then the fraction is **equivalent to one half**.

If the denominator is **exactly three times** the numerator, then the fraction is **equivalent to one third**.

If the denominator is **exactly four times** the numerator, then the fraction is **equivalent to one quarter**.

To find an equivalent fraction of a given fraction, you need to **multiply or divide the numerator and denominator** by the same number.

1. In this missing number question, we have a missing **numerator**.

2. Look at the **denominators**. What would you multiply the first denominator by to make it equal the second denominator?

In this case, 8 **x 2** = 16.

3. To find the missing number, we now need to multiply the numerator of the first number by **2**.

In this case, 2 **x **2 = 4.

The missing numerator is **4**.

1. In this missing number question, we have a missing **denominator**.

2. Look at the **numerators**. What would you divide the first numerator by to make it equal the second numerator?

In this case, 12 **÷ 4** = 3.

3. To find the missing number, we now need to divide the denominator of the first number by **4**.

In this case, 20 **÷ **4 = 5.

The missing denominator is **5**.

In the National Curriculum, equivalent fractions are first introduced in Year 3. Here are the objectives for KS2, taken from the *Number - Fractions* strand:

- recognise and show, using diagrams, equivalent fractions with small denominators

*If you are looking for ready-to-teach lessons that cover this objective, you might be interested in our Finding Fractions scheme, or our Fractions in Action scheme for Year 3.*

- recognise and show, using diagrams, families of common equivalent fractions

*If you are looking for ready-to-teach lessons that cover this objective, you might be interested in our Fractions and Time scheme, or our Proportion Problems scheme for Year 4.*

- identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths

*If you are looking for ready-to-teach lessons that cover this objective, you might be interested in our Fractions and Proportion scheme, or our Decimals and Fractions scheme for Year 5.*

- add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions

*If you are looking for ready-to-teach lessons that cover this objective, you might be interested in our Calculating Fractions and Decimals scheme for Year 6.*