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

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.

Keywords

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

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).

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Worksheet

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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