Skip to content
Skip to content
Teachers
Go to pupils
View unit
New
New
Lesson 9 of 12

    Rationalising a single term denominator

    I can use the technique of rationalising the denominator to transform a fraction to an equivalent fraction.

    View unit
    Lesson 9 of 12
    New
    New

      Rationalising a single term denominator

      I can use the technique of rationalising the denominator to transform a fraction to an equivalent fraction.

      Lesson details

      Key learning points

      1. Fractions should be given in their simplest term.
      2. The denominator should be written as simply as possible.
      3. Using equivalent fractions, you may be able to write the denominator without a surd.

      Keywords

      • Surd - A surd is an irrational number expressed as the root of a rational number.

      Common misconception

      Pupils may think the simplest form means a simplified surd as a denominator.

      A fraction is not fully simplified if the denominator contains a surd term and must be rationalised as is convention.

      Some pupils may think they scale using the denominator (including coefficient). This will work but it is worth exploring how inefficient and time consuming this is without a calculator.
      Teacher tip

      Equipment

      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

      Skip lesson video

      Loading...

      Prior knowledge starter quiz

      Download quiz pdf

      6 Questions

      Q1.
      Which of these fractions are written in simplest form?

      $${1.2} \over {2.4}$$
      Correct answer: $${3} \over {5}$$
      $${39} \over {102}$$
      $${0.2} \over {10}$$

      Q2.
      Evaluate $$\sqrt {41} \times \sqrt {41}$$

      Correct Answer: 41

      Q3.
      Evaluate $$\sqrt {0.3999} \times \sqrt {0.3999}$$

      Correct Answer: 0.3999

      Q4.
      If the radicand is rational, then squaring the surd results in a number.

      Correct Answer: rational

      Q5.
      Evaluate $$(\sqrt {42})^2$$

      Correct Answer: 42

      Q6.
      True or false? An equivalent fraction can be created by multiplying the denominator by the scale factor.

      True
      Correct answer: False

      Assessment exit quiz

      Download quiz pdf

      6 Questions

      Q1.
      True or false? $$\sqrt {7 {1\over9}}$$ is in its simplest form.

      True
      Correct answer: False

      Q2.
      Simplify $$\sqrt {30 {1\over4}}$$. Write your answer in decimal notation.

      Correct Answer: 5.5

      Q3.
      What should you multiply by to rationalise $$5 \over \sqrt {5}$$ ?

      $$5 \over \sqrt {5}$$
      $$1 \over \sqrt {5}$$
      $$sqrt {5}$$
      Correct answer: $$\sqrt {5} \over \sqrt {5}$$

      Q4.
      What should you multiply by to rationalise $${3 + 2\sqrt {3}} \over \sqrt {7}$$ ?

      Correct answer: $${\sqrt {7}} \over {\sqrt {7}}$$
      $${\sqrt {3}} \over {\sqrt {3}}$$
      $${3 + 2\sqrt {3}} \over \sqrt {7}$$
      $${3 + 2\sqrt {3}} \over {3 + 2\sqrt {3}}$$

      Q5.
      Rationalise the denominator $${3\sqrt {3}} \over {2\sqrt {2}}$$

      $${{27} \over {8}}$$
      $${{6\sqrt {6}} \over {8}}$$
      Correct answer: $${{3\sqrt {6}} \over {4}}$$
      $${{27} \over {6 \sqrt {6}}}$$

      Q6.
      Rationalise the denominator $${36} \over {3\sqrt {4}}$$

      Correct Answer: 6

      Lesson appears in

      UnitMaths / Surds

      Maths

      Show Higher unit