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

Subtract mixed numbers worksheet

Check here for the answer sheet

Activity 2

A4 fraction subtraction activity

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

A4 fraction subtraction activity

Play

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

Guardians: Defenders of Mathematica

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