Skip to content
Oak National Academy
Oak National Academy
View my library
0
Teachers
Pupils
View unit
New
New
Lesson 9 of 12
  • 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.

Download all
View unit
Lesson 9 of 12
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.

Download all

These resources were made for remote use during the pandemic, not classroom teaching.

Switch to our new teaching resources now - designed by teachers and leading subject experts, and tested in classrooms.

View new resources

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

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