# Subtracting mixed numbers

## Learning focus

Learn all about subtracting two mixed numbers.

This lesson includes:

• a learning summary
• two quizzes

# 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.

## Example 1

Solve

$$5 \frac{2}{3} - 2\frac{2}{9}$$

Step 1: Partition the mixed numbers so you have whole numbers together and the fractions together.

$$\frac{2}{3} - \frac{2}{9}$$

and

$$5 - 2$$

Subtract the whole numbers.

$$5 - 2 = 3$$

Step 2: Change one of the fractions into an equivalent fraction so both fractions have the same denominator.

You can’t simplify $$\frac{2}{9}$$ any further so you have to change $$\frac{2}{3}$$. 3 is a factor of 9 so multiply the numerator and denominator by 3.

$$\frac{2}{3} = \frac{6}{9}$$

Step 3: Subtract the numerator.

$$\frac{6}{9} - \frac{2}{9} = \frac{4}{9}$$

Step 4: Put the two answers from the whole numbers and fractions back together:

$$3 + \frac{4}{9} = 3 \frac{4}{9}$$

Therefore:

$$5 \frac{2}{3} - 2\frac{2}{9} = 3 \frac{4}{9}$$

### Method 1 checklist

• Partition and subtract whole numbers
• Check and change denominators
• Subtract the numerators

## 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 $$\frac{9}{5}$$.

## Example 2

Solve

$$2 \frac{1}{5} - 1 \frac{5}{25}$$

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

The denominators are 5 and 25.

5 goes into 25, so $$\frac{5}{25}$$ is equivalent to $$\frac{1}{5}$$.

$$1 \frac{5}{25} = 1 \frac{1}{5}$$

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

$$\frac{11}{6} - \frac{6}{5}$$

Step 3: Subtract the numerators.

$$\frac{11}{5} - \frac{6}{5} = \frac{5}{5}$$

$$\frac{5}{5}$$ is one whole, so it can be written as 1. So:

$$2 \frac{1}{5} - 1 \frac{5}{25} = 1$$

### Method 2 checklist

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

## 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.

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

# Practise

## Activity 1

Apply what you have learnt from this guide to the quiz! Tap on the correct answers.

You may need a piece of paper and pen to write down your working out.