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Year 5 Maths Adding & Subtracting Fractions

Subtract fractions - Same denominator

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Theory

Subtracting fractions with the same denominator works like adding: the parts are the same size, so subtract the numerators and keep the denominator. \(\dfrac{6}{7} - \dfrac{3}{7} = \dfrac{3}{7}\). This Year 5 maths page shows how to simplify the answer, find a difference in a word problem, and subtract from one whole.

\(\dfrac{6}{7}\) is \(6\) sevenths. Taking away \(3\) sevenths leaves \(3\) sevenths: \(\dfrac{6}{7} - \dfrac{3}{7} = \dfrac{3}{7}\).

The denominator stays the same. Subtracting the denominators would give \(0\), which makes no sense as a part size.

The difference between two fractions is how much more one is than the other. Subtract the smaller from the larger.

To subtract from \(1\), write \(1\) as a fraction with the same denominator: \(1 - \dfrac{3}{8} = \dfrac{8}{8} - \dfrac{3}{8} = \dfrac{5}{8}\).

Six sevenths take away three sevenths Two bars, each split into 7 equal parts. The top bar has 6 parts shaded. The bottom bar shows the 3 sevenths that are left after 3 sevenths are taken away. 67 37
\(\dfrac{6}{7} - \dfrac{3}{7} = \dfrac{3}{7}\).
One whole take away three eighths Two bars, each split into 8 equal parts. The top bar is fully shaded, showing one whole as 8 eighths. The bottom bar shows the 5 eighths left after taking away 3 eighths. 88 58
\(1 - \dfrac{3}{8} = \dfrac{8}{8} - \dfrac{3}{8} = \dfrac{5}{8}\).

Subtract the numerators; keep the denominator:

\[ \dfrac{6}{7} - \dfrac{3}{7} = \dfrac{6 - 3}{7} = \dfrac{3}{7} \]
6/7−3/7=3/7
\[ \dfrac{9}{10} - \dfrac{1}{10} = \dfrac{8}{10} = \dfrac{4}{5} \]
9/10−1/10=4/5
\[ 1 - \dfrac{3}{8} = \dfrac{5}{8} \]
1−3/8=5/8
Keep the denominator. Only the number of parts changes. The size of the parts stays the same.
Check by adding. \(\dfrac{3}{7} + \dfrac{3}{7} = \dfrac{6}{7}\), so \(\dfrac{6}{7} - \dfrac{3}{7} = \dfrac{3}{7}\) is right.

How to subtract fractions with the same denominator

  1. Check the denominators are the same.
  2. Subtract the numerators.
  3. Keep the denominator.
  4. Simplify if you can.

Subtracting from one

  1. Write \(1\) as a fraction with the same denominator, such as \(\dfrac{8}{8}\).
  2. Subtract the numerators.
Example 1 — Subtract the parts
Work out \(\dfrac{4}{5} - \dfrac{2}{5}\).
Solution
\(\dfrac{4}{5} - \dfrac{2}{5}\)\(=\)\(\dfrac{2}{5}\)
4/5−2/5=2/5

\(\dfrac{2}{5}\).

Example 2 — Simplify
Work out \(\dfrac{7}{9} - \dfrac{1}{9}\) in simplest form.
Solution
\(\dfrac{7}{9} - \dfrac{1}{9}\)\(=\)\(\dfrac{6}{9}\)
\(\dfrac{6}{9}\)\(=\)\(\dfrac{2}{3}\)
7/9−1/9=2/3

\(\dfrac{2}{3}\).

Example 3 — Numerator and denominator
Consider \(\dfrac{5}{8} - \dfrac{1}{8}\).
(i) What is the numerator of the difference?
(ii) What is the denominator?
(iii) Write the answer in simplest form.
Solution
\(5 - 1\)\(=\)\(4\)
\(\dfrac{4}{8}\)\(=\)\(\dfrac{1}{2}\)
5/8−1/8=1/2

(i) \(4\)
(ii) \(8\)
(iii) \(\dfrac{1}{2}\)

Example 4 — How much more?
A green ribbon is \(\dfrac{9}{12}\) m long and a yellow ribbon is \(\dfrac{5}{12}\) m long. How much longer is the green ribbon, in simplest form?
Solution
\(\dfrac{9}{12} - \dfrac{5}{12}\)\(=\)\(\dfrac{4}{12}\)
\(\dfrac{4}{12}\)\(=\)\(\dfrac{1}{3}\)
9/12−5/12=1/3

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

Example 5 — Tenths
By how many tenths is \(\dfrac{9}{10}\) greater than \(\dfrac{1}{10}\)? Write the difference in simplest form.
Solution
\(9 - 1\)\(=\)\(8\)
\(\dfrac{8}{10}\)\(=\)\(\dfrac{4}{5}\)
9/10−1/10=4/5

By \(8\) tenths, which is \(\dfrac{4}{5}\).

Example 6 — From one whole
A pizza is cut into eighths and \(\dfrac{3}{8}\) is eaten. What fraction is left?
Solution
\(\dfrac{8}{8} - \dfrac{3}{8}\)\(=\)\(\dfrac{5}{8}\)
1−3/8=5/8

\(\dfrac{5}{8}\) of the pizza is left.

Example 7 — Find the mistake
Zoe wrote \(\dfrac{6}{7} - \dfrac{3}{7} = \dfrac{3}{0}\). Explain the mistake.
Solution
\(\dfrac{6}{7} - \dfrac{3}{7}\)\(=\)\(\dfrac{3}{7}\)
6/7−3/7=3/7

She subtracted the denominators as well. The parts are still sevenths, so the answer is \(\dfrac{3}{7}\).

Common pitfalls

Subtracting the denominators. \(\dfrac{6}{7} - \dfrac{3}{7}\) is \(\dfrac{3}{7}\), not \(\dfrac{3}{0}\).
Subtracting the wrong way round. For a difference, take the smaller fraction from the larger one.
Not simplifying. \(\dfrac{4}{12}\) should be written as \(\dfrac{1}{3}\) when simplest form is asked for.
Treating 1 as 1/1 when subtracting. Write \(1\) with the same denominator: \(\dfrac{8}{8}\), not \(\dfrac{1}{1}\).

Frequently asked questions

How do you subtract fractions with the same denominator?

Subtract the numerators and keep the denominator: \(\dfrac{4}{5} - \dfrac{2}{5} = \dfrac{2}{5}\).

Why does the denominator stay the same?

The parts are all the same size. Taking some away does not change their size.

How do you find how much more one fraction is?

Subtract the smaller from the larger: \(\dfrac{9}{12} - \dfrac{5}{12} = \dfrac{4}{12} = \dfrac{1}{3}\).

How do you subtract a fraction from 1?

Write \(1\) as a fraction with the same denominator, then subtract: \(1 - \dfrac{3}{8} = \dfrac{5}{8}\).

How can you check a subtraction?

Add the answer to the number you took away. You should get back the first fraction.

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