New
New
Year 10
Higher

Rationalising a single term denominator

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

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New
New
Year 10
Higher

Rationalising a single term denominator

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

Link copied to clipboard

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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.


To help you plan your year 10 maths lesson on: Rationalising a single term denominator, download all teaching resources for free and adapt to suit your pupils' needs...

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

6 Questions

Q1.
Which of these fractions are written in simplest form?
1.22.4
Correct answer: 35
39102
0.210
Q2.
Evaluate 41×41
Correct Answer: 41
Q3.
Evaluate 0.3999×0.3999
Correct Answer: 0.3999
Q4.
If the radicand is rational, then squaring the surd results in a number.
Correct Answer: rational
Q5.
Evaluate (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

6 Questions

Q1.
True or false? 719 is in its simplest form.
True
Correct answer: False
Q2.
Simplify 3014. Write your answer in decimal notation.
Correct Answer: 5.5
Q3.
What should you multiply by to rationalise 55 ?
55
15
sqrt5
Correct answer: 55
Q4.
What should you multiply by to rationalise 3+237 ?
Correct answer: 77
33
3+237
3+233+23
Q5.
Rationalise the denominator 3322
278
668
Correct answer: 364
2766
Q6.
Rationalise the denominator 3634
Correct Answer: 6
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