Add and subtract non-related fractions with different denominators | Maths

Starter quiz

Related fractions are fractions where:
- 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.
What is the value of the numerator in the diagram?
- '6' ✓
Tick the pairs of related fractions.
- ${1} \over {4}$ ${2} \over {16}$ ✓
- ${1} \over {4}$ ${5} \over {12}$ ✓
- ${3} \over {4}$ ${4} \over {14}$
- ${1} \over {4}$ ${1} \over {10}$
$What operation has taken place to scale the original fraction?$

What operation has taken place to scale the original fraction?
- × 3
- ÷ 3
- ÷ 5 ✓
- × 5
${1} \over {3}$ + ${3} \over {18}$ = ___
- ${3} \over {18}$
- ${6} \over {18}$
- ${4} \over {18}$
- ${4} \over {3}$
- ${9} \over {18}$ ✓
${4} \over {5}$ + ${6} \over {20}$ = ___
- ${22} \over {5}$
- ${22} \over {20}$ ✓
- ${22} \over {25}$
- ${10} \over {20}$
- ${10} \over {25}$

Exit quiz

Non-related fractions are fractions in which:
- 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.
Tick the correct symbol to compare these expressions.
- <
- > ✓
- =
Tick the correct symbol to compare these expressions.
- < ✓
- >
- =
Tick the multiple that could be used as a common denominator for ${1} \over {5}$ and ${1} \over {6}$
- 10
- 12
- 20
- 30 ✓
Tick the correct solution for ${3} \over {4}$ + ${2} \over {7}$ =
- ${21} \over {28}$
- ${29} \over {28}$ ✓
- ${29} \over {7}$
- ${5} \over {11}$
What number is missing from the equation?
- '4' ✓

Worksheet

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Lesson Details

Key learning points

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

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.

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.