# 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
- 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 \(\frac{9}{5}\).

## 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.**

# Play

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