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      Securing understanding of multiplication with fractions

      I can multiply unit, non-unit and improper fractions.

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      Lesson 4 of 10
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      • Year 7

      Securing understanding of multiplication with fractions

      I can multiply unit, non-unit and improper fractions.

      Lesson details

      Key learning points

      1. When multiplying you multiply the numerators together and the denominators together.
      2. Any value can be written as a fraction with one as the denominator.
      3. You can use equivalent fractions to be more efficient.

      Keywords

      • Product - A product is the result of two or more numbers multiplied together.

      • Commutative - An operation is commutative if the values it is operating on can be written in either order without changing the calculation.

      • Prime factors - Prime factors are the factors of a number that are, themselves, prime.

      Common misconception

      When multiplying a fraction by an integer multiplying the numerator and denominator by the integer.

      If they do this they will have effectively multiplied by 1. Use an example to show you end up with the same fraction that you started with.

      In the first learning cycle when looking at products that are greater and less than 10, use mini whiteboards and ask the class to write down their own examples for each group.
      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 product of 12 and 3?

      4
      9
      15
      Correct answer: 36

      Q2.
      What fraction of the rectangle is shaded?

      An image in a quiz
      $${8}\over{7}$$
      $${7}\over{8}$$
      $${8}\over{12}$$
      Correct answer: $${8}\over{15}$$

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

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

      Q4.
      Calculate $${2}\over{3}$$ × $${4}\over{5}$$.

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

      Q5.
      Calculate $${2}\over{3}$$ × $${3}\over{5}$$ × $${1}\over{4}$$.

      Correct answer: $${6}\over{60}$$
      $${18}\over{60}$$
      $${24}\over{60}$$
      $${32}\over{60}$$

      Q6.
      Calculate $${3}\over{5}$$ × $${5}\over{9}$$ × $${3}\over{4}$$, give your answer in its simplest form. Try to simplify before calculating.

      $${45}\over{180}$$
      $${3}\over{12}$$
      $${1}\over{3}$$
      Correct answer: $${1}\over{4}$$

      Assessment exit quiz

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      6 Questions

      Q1.
      A prime number has exactly factors.

      Correct Answer: 2, two

      Q2.
      Which of the following will be less than 8?

      $${7}\over{5}$$ $$\times 8$$
      $${8}\times1 {{1} \over {8}}$$
      Correct answer: $${8}\over{9}$$ $$\times 8$$
      Correct answer: $${8}\times{36\over38}$$

      Q3.
      $${1}\over{7}$$ × $${1}\over{8}$$is than $${1}\over{6}$$ × $${1}\over{8}$$.

      Correct Answer: less, smaller

      Q4.
      Using this fact, $${8}\over{76}$$ × $${36}\over{150}$$ = $${144}\over{5700}$$, which of the following are true?

      Correct answer: $${4}\over{76}$$ × $${36}\over{150}$$ = $${72}\over{5700}$$
      Correct answer: $${8}\over{76}$$ × $${18}\over{150}$$ = $${72}\over{5700}$$
      Correct answer: $${16}\over{76}$$ × $${36}\over{150}$$ = $${288}\over{5700}$$
      $${20}\over{76}$$ × $${36}\over{150}$$ = $${350}\over{5700}$$

      Q5.
      Calculate 25 × $${3}\over{5}$$ × $${5}\over{6}$$. Give you answer as a mixed number.

      $${25}\over{2}$$
      $${375}\over{30}$$
      Correct answer: $$12 {{1} \over {2}}$$
      $$13 {{1} \over {2}}$$

      Q6.
      Calculate $${28}\over{63}$$ × $${105}\over{1155}$$ by writing each numerator and denominator as a product of its prime factors.

      $${2}\over{33}$$
      $${4}\over{33}$$
      $${2}\over{99}$$
      Correct answer: $${4}\over{99}$$

      Lesson appears in

      UnitMaths / Arithmetic procedures with fractions

      Maths

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