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Year 6 Maths Adding & Subtracting Fractions

Subtract fractions - From a whole

20 practice questions 0 video lessons Theory + worked examples
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Theory

To take a fraction away from a whole number, rename one whole as a fraction with the same denominator: \(1 = \dfrac{5}{5}\), so \(1 - \dfrac{3}{5} = \dfrac{2}{5}\). With more wholes, keep the rest: \(2 - \dfrac{3}{5} = 1\dfrac{2}{5}\). This Year 6 maths page shows how, including taking a fraction from a mixed numeral.

One whole can be written as any fraction with the same numerator and denominator: \(1 = \dfrac{5}{5} = \dfrac{8}{8} = \dfrac{12}{12}\).

From 1: rename \(1\) with the fraction’s denominator, then subtract. \(1 - \dfrac{5}{8} = \dfrac{8}{8} - \dfrac{5}{8} = \dfrac{3}{8}\).

From a whole number: trade one whole. \(5 - \dfrac{1}{6} = 4\dfrac{6}{6} - \dfrac{1}{6} = 4\dfrac{5}{6}\).

From a mixed numeral: if the fraction part is too small, trade a whole into it. \(3\dfrac{1}{6} = 2\dfrac{7}{6}\).

One whole and what is left after taking three fifths Two bars the same length, each split into 5 equal parts. The top bar is fully shaded: 5 fifths make one whole. The bottom bar has 2 parts shaded: what is left after 3 fifths are taken away. 55 25
\(1 = \dfrac{5}{5}\), and \(\dfrac{5}{5} - \dfrac{3}{5} = \dfrac{2}{5}\).
Two wholes take away three fifths Two bars each split into 5 equal parts. The first bar is fully shaded and the second has 2 parts shaded: 7 fifths, or 1 and 2 fifths, left after taking 3 fifths from 2 wholes. 1 whole 25
\(2 - \dfrac{3}{5} = 1\dfrac{5}{5} - \dfrac{3}{5} = 1\dfrac{2}{5}\).
Counting back three fifths from 2 A number line from 0 to 2 marked in fifths. A red arrow points to 1 and 2 fifths, three fifths back from 2. 0152535451657585952
Count back \(3\) fifths from \(2\) to land on \(1\dfrac{2}{5}\).

Taking a fraction from wholes:

\[ 1 = \dfrac{n}{n} \]
1= n / n
\[ 1 - \dfrac{a}{n} = \dfrac{n - a}{n} \]
1− a / n =( n − a )/ n
\[ 5 - \dfrac{1}{6} = 4\dfrac{6}{6} - \dfrac{1}{6} = 4\dfrac{5}{6} \]
5−1/6=46/6−1/6=45/6
Only one whole is renamed. In \(5 - \dfrac{1}{6}\), four wholes stay as they are; only one becomes \(\dfrac{6}{6}\).
Fractional parts in wholes. Each whole has \(n\) parts of size \(\dfrac{1}{n}\): there are \(15\) fifths in \(3\).

How to subtract a fraction from a whole number

  1. Take one whole and rename it with the fraction’s denominator (\(1 = \dfrac{n}{n}\)).
  2. Subtract the numerators.
  3. Write the wholes that are left in front.

How to subtract from a mixed numeral

  1. Check the fraction part is big enough to subtract from.
  2. If not, trade one whole into the fraction part.
  3. Subtract the fractions and simplify.
Example 1 — From 1
Work out \(1 - \dfrac{3}{5}\).
Solution
\(\dfrac{5}{5} - \dfrac{3}{5}\)\(=\)\(\dfrac{2}{5}\)
5/5−3/5=2/5

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

Example 2 — Eighths and twelfths
Work out:
(i) \(1 - \dfrac{5}{8}\)
(ii) \(1 - \dfrac{7}{12}\)
Solution
\(\dfrac{8}{8} - \dfrac{5}{8}\)\(=\)\(\dfrac{3}{8}\)
\(\dfrac{12}{12} - \dfrac{7}{12}\)\(=\)\(\dfrac{5}{12}\)
3/85/12

(i) \(\dfrac{3}{8}\)
(ii) \(\dfrac{5}{12}\)

Example 3 — From 2
Work out \(2 - \dfrac{3}{5}\).
Solution
\(1\dfrac{5}{5} - \dfrac{3}{5}\)\(=\)\(1\dfrac{2}{5}\)
15/5−3/5=12/5

\(1\dfrac{2}{5}\) (second and third diagrams).

Example 4 — Bigger wholes
Work out:
(i) \(5 - \dfrac{1}{6}\)
(ii) \(3 - \dfrac{5}{8}\)
Solution
\(4\dfrac{6}{6} - \dfrac{1}{6}\)\(=\)\(4\dfrac{5}{6}\)
\(2\dfrac{8}{8} - \dfrac{5}{8}\)\(=\)\(2\dfrac{3}{8}\)
45/623/8

(i) \(4\dfrac{5}{6}\)
(ii) \(2\dfrac{3}{8}\)

Example 5 — From a mixed numeral
Work out \(3\dfrac{1}{6} - \dfrac{5}{6}\) in simplest form.
Solution
\(2\dfrac{7}{6} - \dfrac{5}{6}\)\(=\)\(2\dfrac{2}{6}\)
\(2\dfrac{2}{6}\)\(=\)\(2\dfrac{1}{3}\)
27/6−5/6=22/6=21/3

\(\dfrac{1}{6}\) is too small to take \(\dfrac{5}{6}\) from, so trade a whole: \(2\dfrac{1}{3}\).

Example 6 — Parts in wholes
How many fifths are in \(3\) wholes?
Solution
\(3 \times 5\)\(=\)\(15\)
3×5=15

\(15\) fifths: \(3 = \dfrac{15}{5}\).

Example 7 — Juice
There are \(4\) L of juice in a jug. Mia pours out \(\dfrac{3}{10}\) L. How much is left?
Solution
\(3\dfrac{10}{10} - \dfrac{3}{10}\)\(=\)\(3\dfrac{7}{10}\)
310/10−3/10=37/10

\(3\dfrac{7}{10}\) L.

Example 8 — Fraction of a whole left
A cake is cut into twelfths and \(\dfrac{7}{12}\) is eaten at a party. What fraction of the cake is left?
Solution
\(\dfrac{12}{12} - \dfrac{7}{12}\)\(=\)\(\dfrac{5}{12}\)
12/12−7/12=5/12

\(\dfrac{5}{12}\) of the cake.

Example 9 — Find the mistake
Leo wrote \(3 - \dfrac{2}{5} = \dfrac{1}{5}\). What is right?
Solution
\(2\dfrac{5}{5} - \dfrac{2}{5}\)\(=\)\(2\dfrac{3}{5}\)
25/5−2/5=23/5

Leo subtracted the numerator from the whole number. Taking less than one whole from \(3\) must leave more than \(2\): the answer is \(2\dfrac{3}{5}\).

Common pitfalls

Renaming every whole. \(5 - \dfrac{1}{6}\) is \(4\dfrac{5}{6}\), not \(\dfrac{5}{6}\): keep the other wholes.
Writing 1 as 1/1. Use the same denominator as the fraction: for eighths, \(1 = \dfrac{8}{8}\), not \(\dfrac{1}{1}\).
Subtracting the numerator from the whole number. \(3 - \dfrac{2}{5}\) is not \(\dfrac{1}{5}\).
Not trading when needed. In \(3\dfrac{1}{6} - \dfrac{5}{6}\), trade a whole: \(2\dfrac{7}{6}\).

Frequently asked questions

How do I take a fraction away from 1?

Rename \(1\) with the same denominator: \(1 - \dfrac{3}{5} = \dfrac{5}{5} - \dfrac{3}{5} = \dfrac{2}{5}\).

How do I take a fraction away from 4?

Rename one whole: \(4 = 3\dfrac{n}{n}\), then subtract the fraction.

How many eighths are in one whole?

\(8\).

What if the fraction part of a mixed numeral is too small?

Trade one whole into the fraction part, then subtract.

How can I check my answer?

Add it back: \(1\dfrac{2}{5} + \dfrac{3}{5} = 2\).

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