# 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

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