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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.

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:

\(5 \frac{2}{3} - 2\frac{2}{9} = 3 \frac{4}{9}\)

Change the mixed numbers into improper fractions.

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

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:

\( 2 \frac{1}{5} - 1 \frac{5}{25} = 1\)

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.

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