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      Simplifying algebraic fractions

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      Lesson details

      Learning outcome

      I can simplify expressions involving algebraic fractions.

      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 $$\\frac{4}{5}$$

      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.

      Teacher tip

      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.

      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

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      Prior knowledge starter quiz

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      6 Questions

      Q1.
      Which fractions simplify to $$4\over 5$$?

      $$8\over 12$$
      Correct answer: $$24\over 30$$
      $$36\over 40$$
      $$404\over 515$$
      Correct answer: $$720\over 900$$

      Q2.
      Which of these is the highest common factor of $$12a^2b$$ and $$6a^3b^2$$?

      $$3a^2b^2$$
      $$6ab$$
      Correct answer: $$6a^2b$$
      $$12a^2b$$
      $$12a^3b^2$$

      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 $$12x^2 + 18x$$.

      $$2x(6x+9)$$
      $$6(x^2+3x)$$
      Correct answer: $$6x(2x+3)$$
      $$12x(x+3)$$
      $$12x(x^2+6)$$

      Q5.
      Factorise $$x^2 + 5x -6$$

      $$(x-3)(x-2)$$
      $$(x+3)(x-2)$$
      Correct answer: $$(x+6)(x-1)$$
      $$(x+1)(x-6)$$

      Q6.
      Factorise $$6x^2-5x -4$$

      Correct answer: $$(2x+1)(3x-4)$$
      $$(2x-1)(3x+4)$$
      $$(6x+1)(x-4)$$
      $$(6x-4)(x+1)$$

      Assessment exit quiz

      Download exit quiz questions (PDF)

      6 Questions

      Q1.
      What is the simplest form of the fraction $$18x^2y^6\over 12x^5y^2$$?

      $$3y^3\over 4x$$
      $${3\over 2}x^3y^4$$
      Correct answer: $${3y^4\over 2x^3}$$
      $${3xy^5\over 2x^4y}$$
      $${9xy^3\over 6x^3}$$

      Q2.
      Simplify fully $$4a+8\over 6a+2$$.

      $$1\over 2$$
      $$2$$
      $$a+2\over 3a+1$$
      Correct answer: $$2a+4\over 3a+1$$
      $$4a+8\over 6a+2$$

      Q3.
      Write the fraction $$8a + 24\over 4a + 12$$ in its simplest form.

      Correct Answer: 2

      Q4.
      Simplify $$3x^2 -6x\over x^2 - 7x + 10$$.

      $$3\over x-5$$
      $$3x\over x-2$$
      $$x+3\over x-2$$
      Correct answer: $$3x\over x-5$$
      $$3\over x+10$$

      Q5.
      Simplify $$x^2 -16\over x^2 - x - 12$$.

      $$16\over x+12$$
      $$x\over x-3$$
      $$x-4\over x-3$$
      Correct answer: $$x+4\over x+3$$

      Q6.
      Simplify $$3x^2 +17x + 10\over 6x^2 + 25x + 14$$.

      Correct answer: $$x+5\over 2x+7$$
      $$x+10\over 3x+2$$
      $$3x+2\over 2x+5$$
      $$3x+5\over 6x+7$$

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