# Subtract mixed numbers

## Learning focus

Learn all about subtracting two mixed numbers.

This lesson includes:

- a learning summary
- a quiz

# Quiz

See how well you know this topic by taking this quiz.

# Learn

When subtracting mixed numbers, you can use a similar method to subtracting two fractions, but this time you have to subtract whole numbers as well.

Remember, a mixed number is a combination of an integer (a whole number) and a fraction, like \( 3 \frac{1}{2} \).

Let's have a look at **two** methods for subtracting mixed numbers.

## Method 1

Partition the mixed numbers into fractions and whole numbers, and then subtract them separately.

**Step 3:** Subtract the numerator.

\(\frac{6}{9} - \frac{2}{9} = \frac{4}{9}\)

### Method 1 checklist

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

## Method 2

Change the mixed numbers into **improper fractions**.

Remember, an improper fraction is a fraction where the numerator is greater than the denominator, like \(\frac{9}{5}\).

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

To do this, multiply the integer (whole number) by the denominator, and then add that to the numerator.

\(2 \frac{1}{5} - 1 \frac{1}{5}\)

becomes

\( \frac{11}{6} - \frac{6}{5}\)

## Example 3

**Solve**

\(3 \frac{1}{9} - 1 \frac{4}{9}\)

Which method would be best?

**Method 1** would need you to subtract \(\frac{4}{9}\) from \(\frac{1}{9}\). This is difficult to solve as it involves exchange.

As the denominators are the same, it is easier to use **Method 2**. Convert the mixed numbers into improper fractions.

\(3 \frac{1}{9} = \frac{28}{9}\)

and

\(1 \frac{4}{9} = \frac{13}{9}\)

Subtract the numerators.

\(\frac{28}{9} - \frac{13}{9} = \frac{15}{9} = 1 \frac{6}{9}\)

### Method 2 checklist

- 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

Check here for the answer sheet

## Activity 2

**A4 fraction subtraction activity**

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

# Play

Play **Guardians: Defenders of Mathematica** to learn more and sharpen your skills on this topic.