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Year 11

Higher

Simplifying algebraic fractions

I can simplify expressions involving algebraic fractions.

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New

Year 11

Higher

Simplifying algebraic fractions

I can simplify expressions involving algebraic fractions.

Download all resources

Share activities with pupils

These resources will be removed by end of Summer Term 2025.

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Lesson details

Key learning points

An algebraic fraction can have more than one term in the denominator.
Your equivalent fraction knowledge can be used to simplify the fraction.

Keywords

Simplify - To simplify an expression is to write it in a more efficient form without affecting the value of the original expression. Fully simplifying means the expression cannot be simplified further.
Factorise - To factorise is to express a term as the product of its factors.

Common misconception

Simplifying $f r a c (x + 4) (x + 5)$ by crossing out the $x$ terms and getting $f r a c 45$

Refrain from crossing out factors. Instead pupils should write the numerator and denominator as products of the hightest common factor and see that HCF/HCF = 1.

To help you plan your year 11 maths lesson on: Simplifying algebraic fractions, download all teaching resources for free and adapt to suit your pupils' needs...

This is an excellent opportunity to practise expanding and factorising skills. Pupils could write their own algebraic fractions which simplify when factorised and challenge each other. This can be tailored to their own ability level and could include coefficients greater than 1 as necessary.

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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).

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Starter quiz

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6 Questions

Q1.

Which fractions simplify to

\frac{4}{5}

\frac{8}{12}

Correct answer:

\frac{24}{30}

\frac{36}{40}

\frac{404}{515}

Correct answer:

\frac{720}{900}

Q2.

Which of these is the highest common factor of

12 a^{2} b

and

6 a^{3} b^{2}

3 a^{2} b^{2}

6 a b

Correct answer:

6 a^{2} b

12 a^{2} b

12 a^{3} b^{2}

Q3.

Which of these is equivalent to

a^{6} \div a^{3}

a

a^{2}

Correct answer:

a^{3}

a^{9}

a^{18}

Q4.

Fully factorise

12 x^{2} + 18 x

2 x (6 x + 9)

6 (x^{2} + 3 x)

Correct answer:

6 x (2 x + 3)

12 x (x + 3)

12 x (x^{2} + 6)

Q5.

Factorise

x^{2} + 5 x - 6

(x - 3) (x - 2)

(x + 3) (x - 2)

Correct answer:

(x + 6) (x - 1)

(x + 1) (x - 6)

Q6.

Factorise

6 x^{2} - 5 x - 4

Correct answer:

(2 x + 1) (3 x - 4)

(2 x - 1) (3 x + 4)

(6 x + 1) (x - 4)

(6 x - 4) (x + 1)

Exit quiz

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6 Questions

Q1.

What is the simplest form of the fraction

\frac{18 x^{2} y^{6}}{12 x^{5} y^{2}}

\frac{3 y^{3}}{4 x}

\frac{3}{2} x^{3} y^{4}

Correct answer:

\frac{3 y^{4}}{2 x^{3}}

\frac{3 x y^{5}}{2 x^{4} y}

\frac{9 x y^{3}}{6 x^{3}}

Q2.

Simplify fully

\frac{4 a + 8}{6 a + 2}

\frac{1}{2}

2

\frac{a + 2}{3 a + 1}

Correct answer:

\frac{2 a + 4}{3 a + 1}

\frac{4 a + 8}{6 a + 2}

Q3.

Write the fraction

\frac{8 a + 24}{4 a + 12}

in its simplest form.

Correct Answer: 2

Q4.

Simplify

\frac{3 x^{2} - 6 x}{x^{2} - 7 x + 10}

\frac{3}{x - 5}

\frac{3 x}{x - 2}

\frac{x + 3}{x - 2}

Correct answer:

\frac{3 x}{x - 5}

\frac{3}{x + 10}

Q5.

Simplify

\frac{x^{2} - 16}{x^{2} - x - 12}

\frac{16}{x + 12}

\frac{x}{x - 3}

\frac{x - 4}{x - 3}

Correct answer:

\frac{x + 4}{x + 3}

Q6.

Simplify

\frac{3 x^{2} + 17 x + 10}{6 x^{2} + 25 x + 14}

Correct answer:

\frac{x + 5}{2 x + 7}

\frac{x + 10}{3 x + 2}

\frac{3 x + 2}{2 x + 5}

\frac{3 x + 5}{6 x + 7}

Simplifying algebraic fractions

Simplifying algebraic fractions

These resources will be removed by end of Summer Term 2025.

Slide deck

Lesson details

Key learning points

Keywords

Common misconception

How to plan a lesson using our resources

Licence

Lesson video

Worksheet

Starter quiz

6 Questions

Exit quiz

6 Questions