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Year 6 Maths Adding & Subtracting Fractions

Subtract fractions - Related denominators

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Theory

To subtract fractions with related denominators, rename one fraction so both have the same denominator, then subtract the numerators and keep the denominator. This Year 6 maths page shows the steps, how to simplify the answer, and how to use subtraction to find what is left or how much more is needed.

Subtracting fractions works like adding: the parts must be the same size, so the denominators must match.

For \(\dfrac{3}{5} - \dfrac{1}{10}\), the common denominator is \(10\): \(\dfrac{3}{5} = \dfrac{6}{10}\).

Then subtract the numerators: \(\dfrac{6}{10} - \dfrac{1}{10} = \dfrac{5}{10}\), and simplify to \(\dfrac{1}{2}\).

Subtraction answers questions like "how much is left?" and "how much more is needed?".

Three fifths take away one tenth Three bars the same length: 3 of 5 parts shaded; 6 of 10 parts shaded (the same length); and 5 of 10 parts shaded, which is what is left after taking away 1 tenth. 35 610 510
\(\dfrac{3}{5} = \dfrac{6}{10}\); take away \(\dfrac{1}{10}\) to leave \(\dfrac{5}{10} = \dfrac{1}{2}\).
Seven twelfths take away one quarter Four bars the same length: 7 of 12 parts shaded; 1 of 4 parts shaded; 3 of 12 parts shaded (the same as one quarter); and 4 of 12 parts shaded for the answer. 712 14 312 412
\(\dfrac{7}{12} - \dfrac{3}{12} = \dfrac{4}{12} = \dfrac{1}{3}\).

Subtracting with related denominators:

\[ \dfrac{a}{n} - \dfrac{b}{n} = \dfrac{a - b}{n} \]
( a / n )−( b / n )=( a − b )/ n
\[ \dfrac{3}{5} - \dfrac{1}{10} = \dfrac{6}{10} - \dfrac{1}{10} = \dfrac{5}{10} = \dfrac{1}{2} \]
3/5−1/10=6/10−1/10=5/10=1/2
Keep the denominator. \(\dfrac{6}{10} - \dfrac{1}{10} = \dfrac{5}{10}\), never \(\dfrac{5}{0}\).
Check by adding. Answer \(+\) the part taken away should give the first fraction: \(\dfrac{5}{10} + \dfrac{1}{10} = \dfrac{6}{10}\).

How to subtract fractions with related denominators

  1. Choose the larger denominator as the common denominator.
  2. Rename the other fraction.
  3. Subtract the numerators; keep the denominator.
  4. Simplify the answer.
Example 1 — Fifths and tenths
Work out \(\dfrac{3}{5} - \dfrac{1}{10}\).
Solution
\(\dfrac{6}{10} - \dfrac{1}{10}\)\(=\)\(\dfrac{5}{10}\)
\(\dfrac{5}{10}\)\(=\)\(\dfrac{1}{2}\)
6/10−1/10=5/10,5/10=1/2

\(\dfrac{1}{2}\).

Example 2 — Twelfths and quarters
Work out \(\dfrac{7}{12} - \dfrac{1}{4}\).
Solution
\(\dfrac{7}{12} - \dfrac{3}{12}\)\(=\)\(\dfrac{4}{12}\)
\(\dfrac{4}{12}\)\(=\)\(\dfrac{1}{3}\)
7/12−3/12=4/12=1/3

\(\dfrac{1}{3}\).

Example 3 — Sixths and twelfths
Work out \(\dfrac{5}{6} - \dfrac{1}{12}\) in simplest form.
Solution
\(\dfrac{10}{12} - \dfrac{1}{12}\)\(=\)\(\dfrac{9}{12}\)
\(\dfrac{9}{12}\)\(=\)\(\dfrac{3}{4}\)
10/12−1/12=9/12=3/4

\(\dfrac{3}{4}\).

Example 4 — Half minus tenths
Work out \(\dfrac{1}{2} - \dfrac{3}{10}\).
Solution
\(\dfrac{5}{10} - \dfrac{3}{10}\)\(=\)\(\dfrac{2}{10}\)
\(\dfrac{2}{10}\)\(=\)\(\dfrac{1}{5}\)
5/10−3/10=2/10=1/5

\(\dfrac{1}{5}\).

Example 5 — Ninths and thirds
Work out \(\dfrac{8}{9} - \dfrac{2}{3}\).
Solution
\(\dfrac{8}{9} - \dfrac{6}{9}\)\(=\)\(\dfrac{2}{9}\)
8/9−6/9=2/9

\(\dfrac{2}{9}\).

Example 6 — Sixteenths
Work out \(\dfrac{15}{16} - \dfrac{5}{8}\).
Solution
\(\dfrac{15}{16} - \dfrac{10}{16}\)\(=\)\(\dfrac{5}{16}\)
15/16−10/16=5/16

\(\dfrac{5}{16}\).

Example 7 — How much is left?
A water tank is \(\dfrac{9}{10}\) full. Half of the tank is used for the garden. What fraction of the tank is still full?
Solution
\(\dfrac{9}{10} - \dfrac{5}{10}\)\(=\)\(\dfrac{4}{10}\)
\(\dfrac{4}{10}\)\(=\)\(\dfrac{2}{5}\)
9/10−5/10=4/10=2/5

\(\dfrac{2}{5}\) of the tank.

Example 8 — How much more?
A recipe needs \(\dfrac{3}{4}\) cup of sugar. Eli has \(\dfrac{7}{12}\) cup. How much more does he need?
Solution
\(\dfrac{9}{12} - \dfrac{7}{12}\)\(=\)\(\dfrac{2}{12}\)
\(\dfrac{2}{12}\)\(=\)\(\dfrac{1}{6}\)
9/12−7/12=2/12=1/6

\(\dfrac{1}{6}\) cup.

Example 9 — Find the mistake
Zac wrote \(\dfrac{7}{10} - \dfrac{2}{5} = \dfrac{5}{5} = 1\). What is right?
Solution
\(\dfrac{7}{10} - \dfrac{4}{10}\)\(=\)\(\dfrac{3}{10}\)
7/10−4/10=3/10

Zac subtracted the denominators too. Rename \(\dfrac{2}{5} = \dfrac{4}{10}\): the answer is \(\dfrac{3}{10}\).

Common pitfalls

Subtracting the denominators. The denominator stays the same; only the numerators are subtracted.
Renaming the wrong fraction. Rename the one with the smaller denominator: \(\dfrac{2}{5}\) becomes \(\dfrac{4}{10}\).
Forgetting to simplify. \(\dfrac{4}{12}\) is \(\dfrac{1}{3}\) in simplest form.
Taking the smaller from the larger by habit. Check which fraction is first: \(\dfrac{7}{12} - \dfrac{1}{4}\), not \(\dfrac{1}{4} - \dfrac{7}{12}\).

Frequently asked questions

How do I subtract fractions with different denominators?

Rename them with a common denominator, then subtract the numerators.

Do I subtract the denominators?

No. Keep the denominator.

How do I check my answer?

Add the answer to the fraction you took away; you should get the first fraction.

What is 3/5 − 1/10?

\(\dfrac{1}{2}\).

When do I use subtraction in a word problem?

For "how much is left", "how much more" and "what is the difference".

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