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      Use knowledge of common equivalents to compare fractions and decimals

      Lesson details

      Learning outcome

      I can use knowledge of common equivalents to compare fractions and decimals.

      Key learning points

      1. 0.1 is equal to 1/10
      2. 0.2 is equal to 1/5
      3. 0.25 is equal to 1/4
      4. 0.5 is equal to 1/2
      5. 0.75 is equal to 3/4

      Keywords

      • Equivalent - Numbers are equivalent if they have exactly the same value.

      • Tenth - When one whole is divided into 10 equal parts, each part is one tenth. This can be expressed as a fraction or as a decimal.

      • Hundredth - When one whole is divided into 100 equal parts, each part is one hundredth. This can be expressed as a fraction or as a decimal.

      Common misconception

      The numbers in a decimal can be rewritten as a fraction so one-fifth becomes 1.5 as a decimal and that fractions and decimals do not represent equivalent values.

      Read decimals as a number of tenths and hundredths to make the link to fractions.

      Teacher tip

      Give pupils time to rehearse the fraction-decimal equivalences that are useful to have as known facts. Make the link to equivalent fractions and fractions in their simplest form when using tenths and hundredths to convert fractions into decimals.

      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

      6 Questions

      Q1.
      What is 100 divided into four equal parts? Each part is equal to

      Correct Answer: 25, twenty five

      Q2.
      What is 1,000 divided into five equal parts? Each part is equal to

      Correct Answer: 200

      Q3.
      What is 10 divided into five equal parts? Each part is equal to

      Correct Answer: 2, two

      Q4.
      10 divided into five equal parts is the same as saying ___

      Five times ten
      Correct answer: One fifth of 10
      Correct answer: 10 divided by 5
      One fifth divided by 10
      Correct answer: One fifth multiplied by 10

      Q5.
      Which equation would you use to calculate 1,000 divided into four equal parts?

      $${1}\over{4}$$ ÷ 1,000
      Correct answer: $${1}\over{4}$$ × 1,000
      $${1}\over{5}$$ ÷ 1,000
      $${1}\over{5}$$ × 1,000

      Q6.
      Match the statements to the equations they represent.

      Correct Answer:$${1}\over{5}$$ × 10,One fifth of 10

      One fifth of 10

      Correct Answer:$${1}\over{4}$$ × 10,One quarter of 10

      One quarter of 10

      Correct Answer:$${1}\over{2}$$ × 10,One half of 10

      One half of 10

      Correct Answer:$${1}\over{10}$$ × 10,One tenth of 10

      One tenth of 10

      6 Questions

      Q1.
      How could you write this decimal as a fraction? The decimal is 0.04

      $${1}\over{10}$$
      $${1}\over{100}$$
      $${2}\over{100}$$
      Correct answer: $${4}\over{100}$$
      Correct answer: $${2}\over{50}$$

      Q2.
      How could you write this decimal as a fraction? The decimal is 0.75

      Correct answer: $${75}\over{100}$$
      $${7}\over{10}$$
      Correct answer: $${3}\over{4}$$
      $${5}\over{100}$$

      Q3.
      Match the fraction with the equivalent decimal.

      Correct Answer:$${3} \over {100}$$,0.03

      0.03

      Correct Answer:$${3} \over {4}$$,0.75

      0.75

      Correct Answer:$${3} \over {5}$$,0.6

      0.6

      Correct Answer:$${3} \over {10}$$,0.3

      0.3

      Q4.
      Why is $${1}\over{3}$$ more difficult to convert to a decimal?

      Correct answer: It is because 3 is not a factor of 10 or 100
      It is because 3 is a prime number.

      Q5.
      Which pair of fractions and decimals is equivalent?

      An image in a quiz
      An image in a quiz
      Correct Answer: An image in a quiz
      An image in a quiz

      Q6.
      Which symbol would go between this fraction and decimal?

      An image in a quiz
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      =
      Correct answer: >

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