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      The identity property of multiplication and division

      Lesson details

      Learning outcome

      I can use the fact that 1 can be written in the form n/n and vice versa.

      Key learning points

      1. Anything multiplied by one is itself.
      2. Anything divided by one is itself.
      3. One can be written in infinitely many ways using fractions because anything divided by itself is one.
      4. When a fraction is multiplied by 1 it remains the same but may look different.
      5. When a fraction is divided by 1 it remains the same but may look different.

      Keywords

      • Equivalent fractions - Two fractions are equivalent if they have the same value

      Common misconception

      As the denominator is larger the value of the fraction is larger.

      An analogy of sharing pizza helps students understand. Would pupils get a bigger slice of pizza if it was shared between more people?

      Teacher tip

      Using MWB or drawing in their books, draw a 6 by 4 grid and ask pupils how many different ways can they show 1/4? Ensuring they subdivide so there are equal parts or equal areas. 1/4=2/8=3/12=6/24=12/48 etc

      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 fraction of the whole rectangle is unshaded?

      An image in a quiz
      $$1 \over2$$
      $$1 \over9$$
      Correct answer: $$1 \over10$$
      $$9\over10$$
      $$10\over1$$

      Q2.
      In the fraction $$2 \over5$$, 5 is called the .

      Correct Answer: denominator

      Q3.
      In these cuisenaire rods, the yellow rod (y) represents 1. What fraction does the light green rod (g) represent?

      An image in a quiz
      $$1 \over 2$$
      $$2 \over 5$$
      Correct answer: $$3 \over 5$$
      $$5 \over 2$$
      $$5 \over 3$$

      Q4.
      What fraction of this diagram is shaded?

      An image in a quiz
      $$3\over 5$$
      $$3\over 5$$
      Correct answer: $$3\over 8$$
      $$5\over 8$$
      $$8\over 3$$

      Q5.
      What fraction is the arrow pointing to?

      An image in a quiz
      $$1\over 4$$
      $$5\over 8$$
      $$3\over 7$$
      Correct answer: $$3\over 8$$
      $$3\over 9$$

      Q6.
      Match each label to the correct fraction.

      An image in a quiz
      Correct Answer:Label a points to,$$1\over 5$$

      $$1\over 5$$

      Correct Answer:Label b points to,$$6\over 5$$

      $$6\over 5$$

      Correct Answer:Label c points to,$$1 \frac{2}{5}$$

      $$1 \frac{2}{5}$$

      Correct Answer:Label d points to,$$2$$

      $$2$$

      6 Questions

      Q1.
      Two fractions are if they have the same value.

      Correct Answer: equivalent

      Q2.
      Use the diagram to help you find two more fractions that are equivalent to $$2 \over 5$$.

      An image in a quiz
      $$1 \over 5$$
      Correct answer: $$4 \over 10$$
      $$2 \over 10$$
      $$6 \over 20$$
      Correct answer: $$8 \over 20$$

      Q3.
      Andeep writes: $$\frac{3\times \square}{4\times \square} = \frac{9}{12}$$. What number should Andeep write in each box?

      Correct Answer: 3, three

      Q4.
      Select all the fractions that are equivalent to $$1 \over 3$$.

      Correct answer: $$2 \over 6$$
      $$3 \over 5$$
      $$4 \over 6$$
      Correct answer: $$3 \over 9$$
      $$4 \over 9$$

      Q5.
      Select all the fractions that are equivalent to $$4 \over 9$$.

      $$6 \over 11$$
      Correct answer: $$8 \over 18$$
      $$2 \over 7$$
      $$16 \over 45$$
      Correct answer: $$20 \over 45$$

      Q6.
      Match each fraction to an equivalent fraction.

      Correct Answer:$$1 \over 5$$,$$3 \over 15$$

      $$3 \over 15$$

      Correct Answer:$$2 \over 7$$,$$6 \over 21$$

      $$6 \over 21$$

      Correct Answer:$$4 \over 11$$,$$20 \over 55$$

      $$20 \over 55$$

      Correct Answer:$$3 \over 8$$,$$12 \over 32$$

      $$12 \over 32$$

      Correct Answer:$$5 \over 6$$,$$20 \over 24$$

      $$20 \over 24$$


      To help you plan your 7 maths lesson on: The identity property of multiplication and division, download all teaching resources for free and adapt to suit your pupils' needs...