# 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.