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Year 11
Higher

Operations with algebraic fractions

I can multiply, divide, add and subtract with algebraic fractions.

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New
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Year 11
Higher

Operations with algebraic fractions

I can multiply, divide, add and subtract with algebraic fractions.

Download all resources
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Share activities with pupils
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These resources will be removed by end of Summer Term 2025.

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

These resources were created for remote use during the pandemic and are not designed for classroom teaching.

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Lesson details

Key learning points

  1. When multiplying/dividing, it can be easier to fully factorise every expression first.
  2. When dividing by an expression, it is equivalent to multiplying by the reciprocal of that expression.
  3. When adding/subtracting with algebraic fractions, a common denominator is required.

Keywords

  • Reciprocal - The reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1

  • Factorise - To factorise is to express a term as the product of its factors.

Common misconception

Trying to simplify a division calculation by identifying common factors before calculating.

Pupils need to understand why this works with multiplication questions to understand why this does not work with division. Encourage pupils to write their division as a multiplication of the reciprocal before identifying common factors.


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

A reminder of operations with numerical fractions before starting this lesson will help pupils see that operations with algebraic fractions are exactly the same.
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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

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Starter quiz

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6 Questions

Q1.
Calculate $${3\over 5} \times {2\over 3}$$.
Correct answer: $$2\over 5$$
$$3\over 4$$
$$5\over 8$$
$$7\over 15$$
$$6$$
Q2.
Calculate $${9\over 10} \div {12\over 5}$$.
$$1\over 2$$
$$1\over 3$$
$$3\over 2$$
Correct answer: $$3\over 8$$
$$54\over 25$$
Q3.
Calculate $${3\over 8}-{1\over 6}$$.
Correct answer: $$5\over 24$$
$$13\over 24$$
$$2\over 48$$
$$11\over 48$$
Q4.
Which of these is the fully factorised form of $$24-36x$$?
$$2(-18x+12)$$
$$4(-9x+6)$$
$$6(-6x+4)$$
Correct answer: $$12(-3x+2)$$
$$24(1-3x)$$
Q5.
Factorise $$x^2 - 2x -24$$.
$$(x-3)(x+8)$$
$$(x-4)(x+6)$$
Correct answer: $$(x-6)(x+4)$$
$$(x-8)(x+3)$$
$$(x-12)(x+2)$$
Q6.
What is the simplest form of the fraction $$14x^3y^6\over 15x^4y^3$$?
$$14y^2\over 15x$$
$$14y^2\over 15x^3$$
$$14xy^3\over 15$$
$$14x^3\over 15y^3$$
Correct answer: $$14y^3\over 15x$$

Exit quiz

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6 Questions

Q1.
Simplify $${5x\over 6x}\times {4x\over 3x}$$.
$$5\over 2$$
Correct answer: $$10\over 9$$
$$9x\over 10$$
$$20x^2\over 18x$$
$$20x^2\over 21x^2$$
Q2.
Simplify $${2\over a}\div {3a\over 4}$$.
$$2\over 3$$
$$3\over 2$$
$$8\over 3a$$
$$2\over 3a^2$$
Correct answer: $$8\over 3a^2$$
Q3.
Write $${3\over a}+{2a\over 5}$$ in its simplest form.
$$6\over 5$$
$$15\over2a^2$$
$$3 + 2a\over 5a$$
$$2a + 15\over 10a$$
Correct answer: $$2a^2 + 15\over 5a$$
Q4.
Which of these are equivalent to $${2x+10\over 5}\times {x\over x^2 +8x + 15}$$?
$$2\over x+3$$
$$x\over 5x+10$$
Correct answer: $$2x\over 5x+15$$
$$2x\over 5x+50$$
$$4x+2\over 8x+15$$
Q5.
Which of these are equivalent to $${x^2-x -6\over 2x}\div {x^2+x-12\over x}$$?
$$x+2\over x+4$$
$$x-3\over x-4$$
Correct answer: $$x+2\over 2x+8$$
$$x^2+6x+8\over 2x^2$$
Q6.
Write $${5\over 3x+12}+{x\over 5x+20}$$ in its simplest form.
$$x+5\over 8x+32$$
$$28x\over 5x+20$$
$$13x+40\over 5x+20$$
Correct answer: $$3x+25\over 15x+60$$
$$5x+15\over 15x+60$$