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      Checking understanding of multiplication with fractions

      I can use the mathematical structures that underpin the multiplication of fractions.

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      Lesson 3 of 10
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      • Year 7

      Checking understanding of multiplication with fractions

      I can use the mathematical structures that underpin the multiplication of fractions.

      Lesson details

      Key learning points

      1. An array can help expose the structure behind multiplying fractions.
      2. The denominators give us the number of rows and columns.
      3. By shading one fraction of the whole, you can then shade a fraction of the fraction shown.
      4. When multiplying you multiply the numerators together and the denominators together.
      5. You can use equivalent fractions to be more efficient.

      Keywords

      • Numerator - The expression in a fraction that is written above the fraction line. It is the dividend.

      • Denominator - The expression in a fraction that is written below the fraction line. It is the divisor.

      Common misconception

      Use of inefficient methods to multiply fractions, i.e. not considering common factors.

      The use of fractions with large numerators and denominators can be used to highlight when this is a useful method.

      Many pupils will be able to multiply fractions but have no understanding. The area model is invaluable here. To deepen understanding give pupils a fraction and ask them to draw a diagram that would give that product.
      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.
      What is the name of a fraction where the numerator is greater than or equal to the denominator?

      Correct Answer: improper fraction, improper

      Q2.
      Which of the following is $$2 {{3} \over {5}}$$ as an improper fraction?

      $${{10} \over {5}}$$
      Correct answer: $${{13} \over {5}}$$
      $${{23} \over {5}}$$
      $${{30} \over {5}}$$

      Q3.
      Which of the following shows a correct first step to calculate $$3 {{2} \over {5}}$$ - $$1 {{5} \over {8}}$$?

      Correct answer: $${17}\over{5}$$ - $${13}\over{8}$$
      $${10}\over{5}$$ - $${11}\over{6}$$
      Correct answer: (3 - 1) + $$\left(\frac25-\frac58\right)$$
      (3 - 1) - $$\left(\frac25-\frac58\right)$$

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

      Correct answer: $${5}\over{8}$$ - $${6}\over{24}$$
      $${1}\over{7}$$ + $${3}\over{8}$$
      $${2}\over{5}$$ - $${5}\over{12}$$
      Correct answer: $${5}\over{10}$$ + $${7}\over{12}$$

      Q5.
      What is the missing digit in this calculation $$2 {{\square} \over {8}}$$ - $$1 {{3} \over {4}}$$ = $${{3} \over {8}}$$?

      Correct answer: 1
      2
      3
      4
      5

      Q6.
      Calculate $$3 {{2} \over {5}}$$ - $$1 {{2} \over {3}}$$, give your answer in its simplest form.

      $${12}\over{2}$$
      $${26}\over{15}$$
      Correct answer: $$1 {{11} \over {15}}$$
      $$2 {{11} \over {15}}$$

      Assessment exit quiz

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      6 Questions

      Q1.
      What is the product of 8 and 4?

      2
      4
      12
      Correct answer: 32

      Q2.
      What fraction of the rectangle is shaded?

      An image in a quiz
      $${6}\over{9}$$
      $${6}\over{12}$$
      Correct answer: $${6}\over{15}$$
      $${6}\over{18}$$

      Q3.
      What calculation is represented by the area of the rectangle shaded?

      An image in a quiz
      2 × 3
      $${1}\over{3}$$ × $${3}\over{5}$$
      Correct answer: $${2}\over{3}$$ × $${3}\over{5}$$
      $${2}\over{3}$$ × $${4}\over{5}$$

      Q4.
      Calculate $${2}\over{3}$$ × $${3}\over{5}$$.

      $${5}\over{15}$$
      $${6}\over{3}$$
      $${6}\over{8}$$
      Correct answer: $${6}\over{15}$$

      Q5.
      Calculate $${2}\over{3}$$ × $${3}\over{4}$$ × $${2}\over{5}$$.

      $${7}\over{20}$$
      $${7}\over{60}$$
      Correct answer: $${12}\over{60}$$
      $${15}\over{60}$$

      Q6.
      Calculate $${8}\over{12}$$ × $${3}\over{4}$$ × $${2}\over{3}$$, give your answer in its simplest form. Try to simplify before calculating.

      $${48}\over{144}$$
      $${4}\over{12}$$
      Correct answer: $${1}\over{3}$$
      $${1}\over{4}$$

      Lesson appears in

      UnitMaths / Arithmetic procedures with fractions

      Maths

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