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Year 10
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Rationalising a single term denominator

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

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New
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Year 10
Higher

Rationalising a single term denominator

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

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Share activities with pupils
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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 this is and time consuming without a calculator.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), 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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Starter quiz

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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

Exit quiz

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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