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Year 11
Higher

Simplifying algebraic fractions

I can simplify expressions involving algebraic fractions.

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New
New
Year 11
Higher

Simplifying algebraic fractions

I can simplify expressions involving algebraic fractions.

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Lesson details

Key learning points

  1. An algebraic fraction can have more than one term in the denominator.
  2. 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 frac(x+4)(x+5) by crossing out the x terms and getting frac45

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).

Lesson video

6 Questions

Q1.
Which fractions simplify to 45?
812
Correct answer: 2430
3640
404515
Correct answer: 720900
Q2.
Which of these is the highest common factor of 12a2b and 6a3b2?
3a2b2
6ab
Correct answer: 6a2b
12a2b
12a3b2
Q3.
Which of these is equivalent to a6÷a3?
a
a2
Correct answer: a3
a9
a18
Q4.
Fully factorise 12x2+18x.
2x(6x+9)
6(x2+3x)
Correct answer: 6x(2x+3)
12x(x+3)
12x(x2+6)
Q5.
Factorise x2+5x6
(x3)(x2)
(x+3)(x2)
Correct answer: (x+6)(x1)
(x+1)(x6)
Q6.
Factorise 6x25x4
Correct answer: (2x+1)(3x4)
(2x1)(3x+4)
(6x+1)(x4)
(6x4)(x+1)

6 Questions

Q1.
What is the simplest form of the fraction 18x2y612x5y2?
3y34x
32x3y4
Correct answer: 3y42x3
3xy52x4y
9xy36x3
Q2.
Simplify fully 4a+86a+2.
12
2
a+23a+1
Correct answer: 2a+43a+1
4a+86a+2
Q3.
Write the fraction 8a+244a+12 in its simplest form.
Correct Answer: 2
Q4.
Simplify 3x26xx27x+10.
3x5
3xx2
x+3x2
Correct answer: 3xx5
3x+10
Q5.
Simplify x216x2x12.
16x+12
xx3
x4x3
Correct answer: x+4x+3
Q6.
Simplify 3x2+17x+106x2+25x+14.
Correct answer: x+52x+7
x+103x+2
3x+22x+5
3x+56x+7
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