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      Explain with and without images how to add and subtract related non-unit fractions bridging a whole

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      Lesson details

      Learning outcome

      I can explain with and without an image how to add and subtract related non-unit fractions that bridge a whole.

      Key learning points

      1. Fractions need to have the same denominator if you are to add and subtract them.
      2. When adding or subtracting fractions with the same denominators you just add or subtract the numerators.
      3. When the sum of the numerators is greater than the denominator you can convert the improper fraction to a mixed number.

      Keywords

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

      Common misconception

      Pupils think that the largest denominator of the related fraction should only be used as the common denominator.

      Provide examples where fractions can be scaled up or scaled down to find an appropriate common denominator and encourage pupils to discuss which strategy they prefer and why.

      Teacher tip

      Encourage pupils to reason about what the best common denominator is in each case. Is it better to scale each fraction up or down? Encourage pupils to be wary when choosing a common denominator that results in the numerator being scaled so it is no longer a whole number.

      Licence

      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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      Prior knowledge starter quiz

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      6 Questions

      Q1.
      Tick the non-unit fractions.

      Correct answer: $$ {3} \over {6}$$
      Correct answer: $$ {9} \over {4}$$
      $$ {1} \over {7}$$
      Correct answer: $$ {2} \over {1}$$

      Q2.
      12 inches is equivalent to one __________.

      metre
      yard
      Correct answer: foot
      kilogram

      Q3.
      Tick the pairs of related fractions.

      $$ {1} \over {5}$$ $$ {2} \over {9}$$
      Correct answer: $$ {1} \over {4}$$ $$ {7} \over {12}$$
      Correct answer: $$ {3} \over {6}$$ $$ {4} \over {24}$$
      Correct answer: $$ {1} \over {5}$$ $$ {1} \over {25}$$

      Q4.
      Select the fraction which is $$ {6} \over {9}$$ in its simplest form.

      $$ {1} \over {6}$$
      $$ {1} \over {3}$$
      Correct answer: $$ {2} \over {3}$$
      $$ {1} \over {9}$$

      Q5.
      $$ {1} \over {5}$$ + $$ {3} \over {15}$$ = ___

      $$ {3} \over {20}$$
      $$ {1} \over {20}$$
      $$ {3} \over {15}$$
      Correct answer: $$ {6} \over {15}$$
      Correct answer: $$ {2} \over {5}$$

      Q6.
      Match each fraction to a related fraction.

      Correct Answer:$$ {1} \over {4}$$,$$ {5} \over {16}$$

      $$ {5} \over {16}$$

      Correct Answer:$$ {1} \over {9}$$,$$ {8} \over {36}$$

      $$ {8} \over {36}$$

      Correct Answer:$$ {1} \over {5}$$,$$ {6} \over {35}$$

      $$ {6} \over {35}$$

      Correct Answer:$$ {1} \over {6}$$,$$ {32} \over {66}$$

      $$ {32} \over {66}$$

      Assessment exit quiz

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      6 Questions

      Q1.
      One foot is equivalent to inches.

      Correct Answer: 12

      Q2.
      What is the value of the numerator in this diagram?

      An image in a quiz
      Correct Answer: 9

      Q3.
      What is the value of the missing numerator?

      An image in a quiz
      Correct Answer: 2

      Q4.
      Tick the expressions that represent the shaded parts of these bars being added together.

      An image in a quiz
      $$ {3} \over {4}$$ + $$ {3} \over {12}$$
      $$ {3} \over {12}$$ + $$ {4} \over {3}$$
      Correct answer: $$ {3} \over {4}$$ + $$ {4} \over {12}$$
      Correct answer: $$ {9} \over {12}$$ + $$ {4} \over {12}$$

      Q5.
      $$ 1{{4} \over {12}}$$ − $$ {10} \over {24}$$ =

      $$ {20} \over {22}$$
      Correct answer: $$ {22} \over {24}$$
      $$ {2} \over {12}$$
      Correct answer: $$ {11} \over {12}$$
      $$ {12} \over {24}$$

      Q6.
      $$ 1 {{3} \over {6}}$$ − $$ {8} \over {12}$$ + $$ {4} \over {24}$$ =

      $$ {1} \over {24}$$
      Correct answer: $$ {12} \over {12}$$
      $$ {24} \over {12}$$
      Correct answer: $$ {24} \over {24}$$
      Correct answer: $$ {6} \over {6}$$

      To help you plan your 6 maths lesson on: Explain with and without images how to add and subtract related non-unit fractions bridging a whole, download all teaching resources for free and adapt to suit your pupils' needs...