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      Solve problems involving converting between mixed numbers and improper fractions

      I can solve problems involving converting between mixed numbers and improper fractions.

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      Lesson 5 of 5
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      • Year 4

      Solve problems involving converting between mixed numbers and improper fractions

      I can solve problems involving converting between mixed numbers and improper fractions.

      Lesson details

      Key learning points

      1. Mixed numbers can be converted into improper fractions and vice versa.
      2. Times table knowledge can help to convert between mixed numbers and improper fractions.
      3. To solve problems comparing amounts with different types of fractions, convert to the same type of fraction.

      Keywords

      • Mixed number - A mixed number is a whole number and a fraction combined.

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

      Common misconception

      Children may make mistakes when using the generalisations if they are unaware of the structure behind them.

      Check your answers using the corresponding stem sentences or by representing the number. Ensure that, when you compare amounts that are presented as different fraction types, you convert to the same fraction type.

      A secure recall of multiplication facts is beneficial in this lesson. If pupils are less secure consider providing a multiplication square to allow them to focus on the concept of converting. Children should start by identifying the unit that they are working with by looking at the 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.
      Which symbol would make this inequality correct?

      An image in a quiz
      Correct answer: <
      >
      =

      Q2.
      Starting with the smallest, put these fractions in order.

      1 - $$ {3} \over {10}$$
      2 - $$ {4} \over {10}$$
      3 - $$ {5} \over {10}$$
      4 - $$ {8} \over {10}$$
      5 - $$ {9} \over {10}$$

      Q3.
      If we want to express $$ {21} \over {3}$$ as a mixed number, the unit we need to think about is .

      Correct Answer: thirds

      Q4.
      Match the calculation to its result.

      Correct Answer:4 × 10 + 1 = ,41
      Correct Answer:6 × 7 + 3 = ,45
      Correct Answer:20 ÷ 5 = ,4
      Correct Answer:3 × 5 + 4 = ,19
      Correct Answer:45 ÷ 5 = ,9

      Q5.
      Express $$ {9} \over {7}$$ as a mixed number.

      $$ 1{{1} \over {7}}$$
      Correct answer: $$ 1{{2} \over {7}}$$
      $$ 1{{3} \over {7}}$$
      $$ 2{{1} \over {7}}$$
      $$ 2{{2} \over {7}}$$

      Q6.
      Express $$3{{1} \over {10}}$$ as an improper fraction.

      $$ {31} \over {10}$$
      $$ {1} \over {10}$$
      $$ {3} \over {10}$$
      $$ {30} \over {10}$$
      Correct answer: $$ {31} \over {10}$$

      Assessment exit quiz

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      6 Questions

      Q1.
      Convert this improper fraction into a mixed number.

      An image in a quiz
      $$ 1 {{2} \over {4}} $$
      Correct answer: $$ 2 {{2} \over {4}} $$
      $$ 2 {{1} \over {4}} $$
      $$ {10} \over {4} $$

      Q2.
      Convert this mixed fraction into an improper fraction. $$ 3 {{1} \over {5}} $$

      $$ {1} \over {5} $$
      $$ {4} \over {5} $$
      $$ {11} \over {5} $$
      Correct answer: $$ {16} \over {5} $$
      $$ {31} \over {5} $$

      Q3.
      Compare these fractions using < > or =

      An image in a quiz
      Correct answer: <
      >
      +

      Q4.
      True or false?

      An image in a quiz
      Correct answer: True
      False

      Q5.
      Aisha has three and two-quarters oranges. Jun has 13 quarters of oranges. Which statement is correct?

      Three and two-quarters = 13 quarters
      Correct answer: Three and two-quarters > 13 quarters
      Three and two-quarters < 13 quarters

      Q6.
      Aisha runs two and four-fifths of a kilometre. Jun runs 14 fifths of a kilometre. Who has run the furthest?

      Aisha has run the furthest.
      Jun has run the furthest.
      Correct answer: They have both run the same distance.

      Lesson appears in

      UnitMaths / Convert improper fractions to mixed numbers and vice versa

      Maths

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