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Year 6

Use knowledge of adding and subtracting related unit fractions to solve problems

I can use knowledge of adding and subtracting related unit fractions to solve problems.

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Share activities with pupils
New
New
Year 6

Use knowledge of adding and subtracting related unit fractions to solve problems

I can use knowledge of adding and subtracting related unit fractions to solve problems.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. When adding and subtracting fractions with the same denominators you just add or subtract the numerators.
  2. Common multiples help you to convert a fraction to a common denominator.
  3. The language of unitising helps you to add and subtract fractions with the same denominators.
  4. When adding and subtracting fractions with the same denominators you just add the numerators.

Common misconception

Pupils compare expressions by only ever calculating the value of each expression before comparing.

Encourage pupils to consider the magnitude of the fractions they are adding or subtracting. Comparing fractions to one-half is an effective way to help identify their magnitude and whether then expression would be larger or smaller.

Keywords

  • Related fractions - When the denominator of one fraction is a multiple of the denominator of another fraction, we can say these fractions are related fractions.

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

When looking to convert to a common denominator to help add or subtract fractions, regularly encourage pupils to ask whether each fraction is a large part of a whole or a smaller part of a whole. This can help pupils to reason about the size of the product each time.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.
Fractions have a common denominator when:
one has a denominator that is a multiple of the other fraction’s denominator.
they have the same number for the numerator.
Correct answer: they have the same number for the denominator.
they have the same numerator and denominator.
Q2.
Type in the number to show how the numerator and denominator has been multiplied to create a related fraction.
An image in a quiz
Correct Answer: 4
Q3.
This image shows $$ {1} \over {5}$$ − $$ {1} \over {10}$$ = ____ Tick the equation which shows the appropriate related fraction.
An image in a quiz
Correct answer: $$ {2} \over {10}$$ − $$ {1} \over {10}$$ = ____
$$ {3} \over {15}$$ − $$ {1} \over {10}$$= ____
$$ {4} \over {20}$$ − $$ {1} \over {10}$$ = ____
$$ {5} \over {25}$$ − $$ {1} \over {10}$$ = ____
Q4.
Tick the correct equation once it has been adjusted to include a the most appropriate related fraction. $$ {1} \over {3}$$ − $$ {1} \over {15}$$ = ___
$$ {1} \over {15}$$ − $$ {1} \over {15}$$ = ___
$$ {2} \over {15}$$ − $$ {1} \over {15}$$ = ___
$$ {3} \over {15}$$ − $$ {1} \over {15}$$ = ___
Correct answer: $$ {5} \over {15}$$ − $$ {1} \over {15}$$ = ___
Q5.
Tick the correct solution: $$ {1} \over {9}$$ − $$ {1} \over {18}$$ = ___
$$ {1} \over {9}$$
$$ {1} \over {2}$$
Correct answer: $$ {1} \over {18}$$
$$ {2} \over {18}$$
Q6.
Tick the correct solution: $$ {2} \over {3}$$ − $$ {2} \over {15}$$= ___
Correct answer: $$ {8} \over {15}$$
$$ {8} \over {3}$$
$$2 {1} \over {3}$$
$$ {10} \over {3}$$

Exit quiz

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6 Questions

Q1.
Match the fractions with common denominators.
Correct Answer:$$ {1} \over {4}$$,$$ {9} \over {4}$$

$$ {9} \over {4}$$

Correct Answer:$$ {1} \over {12}$$ ,$$ {4} \over {12}$$

$$ {4} \over {12}$$

Correct Answer:$$ {1} \over {9}$$,$$ {5} \over {9}$$

$$ {5} \over {9}$$

Correct Answer:$$ {5} \over {3}$$,$$ {12} \over {3}$$

$$ {12} \over {3}$$

Q2.
Tick the equations where all three fractions are related fractions.
Correct answer: $$ {1} \over {3}$$ + $$ {1} \over {6}$$+ $$ {1} \over {2}$$
$$ {1} \over {8}$$ + $$ {1} \over {6}$$+ $$ {1} \over {12}$$
Correct answer: $$ {1} \over {2}$$ + $$ {1} \over {8}$$ + $$ {1} \over {24}$$
Correct answer: $$ {2} \over {3}$$ + $$ {1} \over {9}$$ + $$ {1} \over {18}$$
Q3.
Tick the equations where all three fractions are related fractions.
$$ {1} \over {4}$$ + $$ {1} \over {6}$$ + $$ {1} \over {2}$$
$$ {1} \over {5}$$ + $$ {1} \over {6}$$ + $$ {1} \over {35}$$
$$ {1} \over {2}$$ + $$ {3} \over {5}$$ + $$ {1} \over {24}$$
Correct answer: $$ {2} \over {3}$$ + $$ {1} \over {9}$$ + $$ {1} \over {18}$$
Q4.
Tick the sum for the following equation: $$ {1} \over {2}$$ + $$ {1} \over {8}$$ + $$ {1} \over {16}$$ =
$$ {3} \over {16}$$
$$ {2} \over {8}$$
1
Correct answer: $$ {11} \over {16}$$
$$ {16} \over {2}$$
Q5.
Tick the sum for the following equation: $$ {1} \over {2}$$ − $$ {1} \over {8}$$ − $$ {1} \over {16}$$ =
Correct answer: $$ {9} \over {16}$$
$$ {3} \over {2}$$
$$ {3} \over {16}$$
$$ {1} \over {4}$$
Q6.
Compare the expressions using < > or = $$ {1} \over {5}$$ − $$ {1} \over {10}$$ − $$ {2} \over {20}$$ $$ {2} \over {5}$$ − $$ {2} \over {10}$$ − $$ {4} \over {20}$$
Correct Answer: <