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      Use the relationship between the numerator and denominator to simplify fractions

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      Lesson details

      Learning outcome

      I can use the relationship between the numerator and denominator to simplify fractions.

      Key learning points

      1. If the multiplicative relationship between the numerator and denominator is the same, the fractions will be equivalent.
      2. If a fraction has been simplified, the numerator and denominator are as small as they can be to keep the relationship.
      3. Create an equivalent fraction in a simpler form with lower values of the numerator and denominator.
      4. Use common factors of the numerator and denominator to simplify fractions.

      Keywords

      • Common factor - When you are comparing the factors of two numbers, a common factor is one shared by both numbers.

      • Simplest form - When a fraction is in its simplest form, the numerator and denominator only share a common factor of one.

      • Simplify - To simplify a fraction is to identify the highest common factor shared by the numerator and denominator and to scale down both by that factor.

      • Scale up/down - To scale up or down is to multiply or divide by a given number or factor.

      Common misconception

      Pupils may not see that the fraction and its simplified version are equivalent. Pupils may not have a deep understanding of how factors relate to fractions.

      Stress the equivalence of fractions when simplifying and make use of representations to show that fractions are equivalent using parts of a whole and position on a number line. Discuss the language of factors, common factors and prime numbers.

      Teacher tip

      Include opportunities for pupils to discuss, reason and explain their thinking about the fractions they are exploring in the lesson, using the language of factors and scaling. Encourage them to sketch or use representations to reinforce the understanding of equivalence when simplifying fractions.

      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

      Download starter quiz questions (PDF)

      6 Questions

      Q1.
      Which of the numbers are factors of 8?

      Correct answer: 1
      Correct answer: 2
      Correct answer: 4
      6
      Correct answer: 8

      Q2.
      1, 2, 3, 4, 6 and 12 are all factors of which number in this list?

      6
      10
      Correct answer: 12
      16

      Q3.
      Which number would be a factor of both 9 and 12?

      2
      Correct answer: 3
      4
      6

      Q4.
      What number do you get if 6 is scaled up by a factor of 3?

      Correct Answer: 18, eighteen

      Q5.
      What number do you get if 18 is scaled down by a factor of 2?

      Correct Answer: 9, nine

      Q6.
      Which of these expressions have the same value?

      Correct answer: 12 ÷ 3
      20 ÷ 4
      12 ÷ 4
      Correct answer: 20 ÷ 5
      Correct answer: 100 ÷ 25

      Assessment exit quiz

      Download exit quiz questions (PDF)

      6 Questions

      Q1.
      What is the highest factor which is common to the numerator and denominator in the fraction $${6}\over{12}$$

      Correct Answer: 6, six

      Q2.
      Is the fraction $${3}\over{6}$$ written in its simplest form?

      Yes because the numerator and denominator are both one digit numbers
      Correct answer: No because the numerator and denominator both share a factor greater than 1

      Q3.
      What is $${3}\over{6}$$ written in its simplest form?

      $${1}\over{6}$$
      $${1}\over{3}$$
      Correct answer: $${1}\over{2}$$
      $${6}\over{12}$$

      Q4.
      Is Jun's statement always, sometimes or never true?

      An image in a quiz
      Always
      Correct answer: Sometimes
      Never

      Q5.
      Which of these fractions are in their simplest form?

      $${6}\over{9}$$
      Correct answer: $${6}\over{13}$$
      Correct answer: $${1}\over{6}$$
      $${6}\over{14}$$
      Correct answer: $${7}\over{12}$$

      Q6.
      Match the fractions to the equivalent in its simplest form.

      Correct Answer:$${6}\over{9}$$,$${2}\over{3}$$

      $${2}\over{3}$$

      Correct Answer:$${6}\over{14}$$,$${3}\over{7}$$

      $${3}\over{7}$$

      Correct Answer:$${7}\over{14}$$,$${1}\over{2}$$

      $${1}\over{2}$$

      Correct Answer:$${9}\over{12}$$,$${3}\over{4}$$

      $${3}\over{4}$$

      Correct Answer:$${12}\over{15}$$,$${4}\over{5}$$

      $${4}\over{5}$$


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