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Year 6

Add and subtract non-related fractions with different denominators

I can add and subtract non-related fractions with different denominators.

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Year 6

Add and subtract non-related fractions with different denominators

I can add and subtract non-related fractions with different denominators.

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Lesson details

Key learning points

  1. Common denominators for non-related fractions can be found using common multiples of the denominators.
  2. Fractions need to have the same denominator if we are to add and subtract them.
  3. In equivalent fractions, the numerators and denominators have been scaled up or down by the same factor.

Keywords

  • Common denominator - When two or more fractions share the same denominator, you can say they have a common denominator.

  • Related fractions - Related fractions are when the denominator of one fraction is a multiple of the denominator of the other fraction.

  • Non-related fractions - Non-related fractions are when the denominator of one fraction is not a multiple of the denominator of the other fraction.

  • Common multiple - A multiple that is common between two or more numbers is known as a common multiple.

Common misconception

When adding or subtracting fractions with different denominators, you just add or subtract the denominators from each other.

Encourage the children to use prior generalisations such as when the numerators are the same, the fraction with the largest denominator is the smallest, to help them reason about the above misconception.


To help you plan your year 6 maths lesson on: Add and subtract non-related fractions with different denominators, download all teaching resources for free and adapt to suit your pupils' needs...

Avoid rushing into calculating. Allow pupils to continue to visualise the equations presented and use their sense of magnitude for each fraction to help them estimate the answer to the equation. Ensure pupils are aware there are multiple alternatives to the common denominators they could apply.
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This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
Related fractions are fractions where:
Correct answer: one denominator is a multiple of the other denominator.
one numerator is a multiple of the other denominator.
the denominators are the same.
the numerators are the same.
Q2.
What is the value of the numerator in the diagram?
An image in a quiz
Correct Answer: 6
Q3.
Tick the pairs of related fractions.
Correct answer: $$ {1} \over {4}$$ $$ {2} \over {16}$$
Correct answer: $$ {1} \over {4}$$ $$ {5} \over {12}$$
$$ {3} \over {4}$$ $$ {4} \over {14}$$
$$ {1} \over {4}$$ $$ {1} \over {10}$$
Q4.
What operation has taken place to scale the original fraction?
An image in a quiz
× 3
÷ 3
Correct answer: ÷ 5
× 5
Q5.
$$ {1} \over {3}$$ + $$ {3} \over {18}$$ = ___
$$ {3} \over {18}$$
$$ {6} \over {18}$$
$$ {4} \over {18}$$
$$ {4} \over {3}$$
Correct answer: $$ {9} \over {18}$$
Q6.
$$ {4} \over {5}$$ + $$ {6} \over {20}$$ = ___
$$ {22} \over {5}$$
Correct answer: $$ {22} \over {20}$$
$$ {22} \over {25}$$
$$ {10} \over {20}$$
$$ {10} \over {25}$$

Exit quiz

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6 Questions

Q1.
Non-related fractions are fractions in which:
Correct answer: neither denominator is a multiple of each other.
neither numerator is a multiple of each other.
the denominators are not the same.
the numerators are not the same.
Q2.
Tick the correct symbol to compare these expressions.
An image in a quiz
<
Correct answer: >
=
Q3.
Tick the correct symbol to compare these expressions.
An image in a quiz
Correct answer: <
>
=
Q4.
Tick the multiple that could be used as a common denominator for $$ {1} \over {5}$$ and $$ {1} \over {6}$$
10
12
20
Correct answer: 30
Q5.
Tick the correct solution for $$ {3} \over {4}$$ + $$ {2} \over {7}$$ =
$$ {21} \over {28}$$
Correct answer: $$ {29} \over {28}$$
$$ {29} \over {7}$$
$$ {5} \over {11}$$
Q6.
What number is missing from the equation?
An image in a quiz
Correct Answer: 4