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      Securing understanding of addition and subtraction with fractions

      I can generalise and fluently use addition and subtraction strategies to calculate with fractions and mixed numbers.

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      Lesson 2 of 10
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      • Year 7

      Securing understanding of addition and subtraction with fractions

      I can generalise and fluently use addition and subtraction strategies to calculate with fractions and mixed numbers.

      Lesson details

      Key learning points

      1. To make the denominators the same, you may need to scale up or down.
      2. It can be easier to add/subtract the wholes and then add/subtract the fractions.
      3. Improper fractions can help when exchanging/regrouping is required.

      Keywords

      • Improper fraction - An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

      • Mixed number - A mixed number is an improper fraction written as its integer part plus the fractional part where the fractional part is a proper fraction.

      • LCM - LCM is an abbreviation for lowest common multiple.

      Common misconception

      When partitioning mixed numbers and subtracting incorrectly subtracting the fractional part.

      Use an integer example to show the structure of partitioning. E.g. 28 - 15 = (20 + 8) - (10 + 5) = (20 - 10) + (8 - 5) not (20 - 10)-(8 - 5)

      In the second learning cycle get pupils to create their own questions to go into the 2 boxes, 'simplify first' and 'common denominator'.
      Teacher tip

      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.
      When subtracting fractions you must have .

      a common numerator
      Correct answer: a common denominator
      the largest fraction first

      Q2.
      Which of the following are not common denominators of $${1}\over{4}$$ and $${7}\over{20}$$?

      Correct answer: 4
      20
      Correct answer: 24
      40

      Q3.
      Which symbol is missing here? $$\frac{2}{9} + \frac{1}{8} \square \frac{2}{9} + \frac{1}{7}$$.

      Correct answer: <
      >
      =
      ?

      Q4.
      Calculate $${7}\over{12}$$ - $${1}\over{3}$$.

      $${4}\over{9}$$
      Correct answer: $${3}\over{12}$$
      $${4}\over{12}$$
      $${8}\over{15}$$

      Q5.
      Which of the following is not a correct alternative for $${3}\over{8}$$ - $${3}\over{4}$$ + $${7}\over{16}$$?

      $${3}\over{8}$$ + $${7}\over{16}$$ - $${3}\over{4}$$
      $${3}\over{8}$$ + $${7}\over{16}$$ + $$\left(-\frac34\right)$$
      Correct answer: $${3}\over{8}$$ - $$\left(\frac{3}{4} + \frac{7}{16}\right)$$

      Q6.
      Calculate $${3}\over{8}$$ - $${3}\over{4}$$ + $${7}\over{16}$$.

      $$\left(-\frac4{16}\right)$$
      $${7}\over{4}$$
      $${7}\over{12}$$
      Correct answer: $${1}\over{16}$$

      Assessment exit quiz

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      6 Questions

      Q1.
      What is the name of a number that has both an integer part and a fractional part?

      Correct Answer: mixed number, mixed

      Q2.
      Which of the following is $$3 {{2} \over {3}}$$ as an improper fraction?

      $${32}\over{3}$$
      $${18}\over{3}$$
      Correct answer: $${11}\over{3}$$
      $${8}\over{3}$$

      Q3.
      Which of the following show a correct first step to calculate $$3 {{1} \over {3}}$$ - $$1 {{5} \over {6}}$$?

      Correct answer: $${10}\over{3}$$ - $${11}\over{6}$$
      $${7}\over{3}$$ - $${11}\over{6}$$
      Correct answer: (3 - 1) + $$\left(\frac13-\frac56\right)$$
      (3 - 1) - $$\left(\frac13-\frac56\right)$$

      Q4.
      Which of the following can be simplified before calculating?

      $${5}\over{8}$$ + $${3}\over{7}$$
      Correct answer: $${4}\over{9}$$ - $${5}\over{15}$$
      Correct answer: $${2}\over{5}$$ + $${4}\over{16}$$
      $${2}\over{3}$$ - $${2}\over{7}$$

      Q5.
      What is the missing digit in this calculation $$1 {{1} \over {3}}$$ + $$2 {{\square} \over {6}}$$ = $$4 {{1} \over {6}}$$?

      1
      2
      3
      4
      Correct answer: 5

      Q6.
      Calculate $$3 {{1} \over {3}}$$ - $$1 {{5} \over {6}}$$, give your answer in its simplest form.

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

      Lesson appears in

      UnitMaths / Arithmetic procedures with fractions

      Maths

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