# Subtract two mixed numbers

## Home learning focus

Learn all about subtracting two mixed numbers.

This includes:

- one video
- learning summary
- two activities

# Learn

### Subtracting mixed numbers

This video from White Rose Maths demonstrates different methods for subtracting mixed numbers.

When subtracting mixed numbers, you can use a similar method to subtracting two fractions, but you have an added step of subtracting integers.

Here are **two** main methods that you can use.

**Method 1**

This method allows you to break down (partition) the mixed numbers into fractions and whole numbers so that you can subtract them separately.

5 ²/₃ - 2 ²/₉

**Step 1:** Partition the mixed numbers so you are left with the whole numbers together and the fractions together.

²/₃ - ²/₉ =

5 - 2 = 3

You can quickly subtract the whole numbers to make 3.

**Step 2:** Focus on the fractions now. They have different denominators so you need to change one into its equivalent fraction, so they have the same denominator.

You can’t simplify ²/₉any further so you have to change ²/₃

Multiply the numerator and denominator by 3.

**Step 3:** Subtract the numerators now.

⁶/₉ - ²/₉ = ⁴/₉

**Step 4:** Now you have to add the two answers from the whole numbers and fractions together so that they become a mixed number again.

3 + ⁴/₉ = 3 ⁴/₉

Here’s a checklist to remind you of the steps for this method:

- Partition and subtract whole numbers
- Check and change denominators
- Subtract the numerators
- Whole numbers answer + fractions answer = final answer!

**Method 2**

This method requires you to change the mixed numbers into **improper fractions**.

Remember, an **improper fraction** is a fraction where the numerator is greater than the denominator like ⁹/₅

2 ¹⁄₅ - 1 ⁵/₂₅

**Step 1**: Change the fractions so that they have the same denominator.

Divide the numerator and denominator by 5.

**Step 2:** Convert the mixed numbers into **improper fractions**.

2 ¹⁄₅ - 1 ¹⁄₅ =

¹¹⁄₅ - ⁶/₅ =

Reminder:

- Multiply the integer (whole number) by the denominator.
- Add that to the numerator.
- Write the answer on top of the original denominator.

**Step 3:** Subtract the numerators.

⁵/₅ is one whole so can be written as 1.

Another example of when **Method 2** might prove useful is this sum:

3 ¹⁄₉ – 1 ⁴⁄₉

⁴⁄₉ is larger than ¹⁄₉ therefore we can’t partition in the same way as **Method 1** and it is harder to solve mentally as involves exchange.

As the denominators are the same we can move straight to **Step 2** and convert the mixed numbers into improper fractions.

3 ¹⁄₉ = ²⁸/₉

1 ⁴⁄₉ = ¹³/₉

**Step 3:** Subtract the numerators.

²⁸/₉ – ¹³/₉ = ¹⁵/₉ = 1 ⁶/₉

Here’s a checklist to remind you of the steps for this method while you work:

- Check and change denominators
- Convert to improper fractions.
- Subtract the numerators.
- If needed, convert answer back to a mixed number.

# Practise

## Activity 1

**Subtracting mixed numbers worksheet**

Have a go at completing this subtracting mixed numbers worksheet from Pearson

Click here for the answers.

## Activity 2

**A4 fraction subtraction activity**

Try this activity from NRICH Maths using A4 paper to subtract fractions.

# There's more to learn

Have a look at these other resources around the BBC and the web.