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      Dividing a whole number by a fraction

      Lesson details

      Learning outcome

      I can use the mathematical structures that underpin the division of fractions to divide a whole number by a fraction.

      Key learning points

      1. A diagram can help to show the underlying structure.
      2. The whole number can be split into a number of equal parts equal to the denominator.
      3. The numerator states how many equal parts are wanted.
      4. The value of each part is multiplied by the numerator.

      Keywords

      • Proper fraction - A proper fraction is a fraction where the numerator is less than the denominator

      Common misconception

      Using the unitising method with a remainder, the remainder is not written as a fraction of the unit.

      Drawing bar models, ensure that the unit is subdivided so the remainder can be seen as a fraction of the unit.

      Teacher tip

      Pupils can use MWB or go to the board and draw bar models to show each step of dividing a whole number by a fraction. This should be completed in steps and each step should be checked; bar models are drawn, sub dividing and correct units used.

      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.
      How many halves are in 3 wholes? (You can use a bar model if it helps.)

      3
      Correct answer: 6
      1.5
      0

      Q2.
      How many quarters are in 5?

      4
      5
      10
      Correct answer: 20
      25

      Q3.
      The bar model shows that there are lots of a $${1} \over {3}$$ in 4.

      An image in a quiz
      Correct Answer: 12

      Q4.
      The bar model shows that there are lots of a $${1} \over {5}$$ in 3.

      An image in a quiz
      Correct Answer: 15

      Q5.
      The Oak teacher gave 4 pupils a question, "How many tenths are there in 5?" Select the correct answer and explanation.

      Laura says "There are 500 tenths because $$ 5\times 100$$ = 500"
      Correct answer: Andeep says "There are 50 tenths because $$ 5\times 10$$ = 50"
      Jun says "There are 50 tenths because each 10 wholes has five fifths."
      Alex says "There are 2 tenths because $$ 10\div5 $$ = 2"

      Q6.
      Sort the following from largest to smallest.

      1 - $$ 10\div \frac{1}{3}$$
      2 - $$ 2\div \frac{1}{9}$$
      3 - $$ 1\div \frac{1}{11}$$
      4 - $$ 1\div \frac{1}{3}$$
      5 - $$ 1\div \frac{1}{2}$$

      6 Questions

      Q1.
      Using the bar model, work out $$ 4\div \frac{2}{3} = $$ .

      An image in a quiz
      Correct Answer: 6, six

      Q2.
      Using the bar model, work out $$ 3\div \frac{3}{4} = $$ .

      An image in a quiz
      Correct Answer: 4, four

      Q3.
      What does this bar model represent?

      An image in a quiz
      $$4 \div \frac{2}{3}$$
      $$4 \div \frac{2}{7}$$
      Correct answer: $$4 \div \frac{2}{5}$$
      $$4 \div \frac{5}{2}$$
      $$4 \div \frac{3}{5}$$

      Q4.
      Match the question on the left with the calculation on the right.

      Correct Answer:$$ 6\div \frac{2}{5}$$,$$\frac{30}{5} \div \frac{2}{5}$$

      $$\frac{30}{5} \div \frac{2}{5}$$

      Correct Answer:$$ 4\div \frac{2}{5}$$,$$\frac{20}{5} \div \frac{2}{5}$$

      $$\frac{20}{5} \div \frac{2}{5}$$

      Correct Answer:$$ 10\div \frac{2}{5}$$,$$\frac{50}{5} \div \frac{2}{5}$$

      $$\frac{50}{5} \div \frac{2}{5}$$

      Correct Answer:$$ 5\div \frac{2}{5}$$,$$\frac{25}{5} \div \frac{2}{5}$$

      $$\frac{25}{5} \div \frac{2}{5}$$

      Q5.
      What does this bar model represent?

      An image in a quiz
      $$4 \div \frac{2}{3}$$
      $$4 \div \frac{3}{2}$$
      Correct answer: $$4 \div \frac{3}{5}$$
      $$6 \div \frac{3}{5}$$

      Q6.
      By drawing your own bar models or otherwise, match the calculations on the left with the answers on the right.

      Correct Answer:$$4 \div \frac{3}{5}$$,$$6 {{2} \over {3}}$$

      $$6 {{2} \over {3}}$$

      Correct Answer:$$5 \div \frac{2}{3}$$,$$7{{1} \over {2}}$$

      $$7{{1} \over {2}}$$

      Correct Answer:$$2 \div \frac{3}{5}$$,$$3 {{1} \over {3}}$$

      $$3 {{1} \over {3}}$$

      Correct Answer:$$1 \div \frac{2}{3}$$,$$1 {{1} \over {2}}$$

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


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