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Year 11

Higher

Solving equations with algebraic fractions

I can manipulate and solve equations involving algebraic fractions.

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New

Year 11

Higher

Solving equations with algebraic fractions

I can manipulate and solve equations involving algebraic fractions.

Download all resources

Share activities with pupils

Link copied to clipboard

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

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Lesson details

Key learning points

Before performing any operation, equivalent fractions should be considered.
Algebraic fractions follow the same rules as fractions.
It is important to maintain equivalence between two algebraic statements.
Multiplying both connected statements by the reciprocal can simplify.

Keywords

Factorise - To factorise is to express a term as the product of its factors.
Quadratic formula - The quadratic formula is a formula for finding the solutions to any quadratic equation of the form $a x^{2} + b x + c = 0$

Common misconception

Assuming that 'cross multiplying' is always the best way to solve equations with fractions on both sides.

Examples are included in the lesson where this results in unnecessary quadratic equations. Factorising and looking for common factors allows pupils to spot efficient methods. This also links with fraction skills of finding a common denominator.

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

Solving quadratics is an essential skill for this lesson. This is a good opportunity to review choices of methods to solve quadratics as well as the use of technology to check answers. Some pupils may wish to use the equation tool on their calculators to solve quadratic equations.

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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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Worksheet

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Starter quiz

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6 Questions

Q1.

The solution to the equation

\frac{2 x}{5} = 4

is when

x =

Correct Answer: 10

Q2.

Solve

\frac{12}{5 x} = 8

\frac{2}{15}

Correct answer:

\frac{3}{10}

\frac{4}{5}

\frac{10}{3}

\frac{15}{2}

Q3.

Factorise

x^{2} + 3 x - 4

(x - 2) (x - 2)

(x - 1) (x + 3)

Correct answer:

(x - 1) (x + 4)

(x - 4) (x + 3)

Q4.

Find all the solutions to the equation

x^{2} + 5 x + 6 = 2

x = - 2

x = - 2

and

x = - 3

Correct answer:

x = - 1

and

x = - 4

x = 1

and

x = 4

x = 2

and

x = 3

Q5.

Which of these is equivalent to

\frac{x + 3}{2} \times \frac{4}{x + 4}

\frac{2 x + 12}{8}

Correct answer:

\frac{2 x + 6}{x + 4}

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

\frac{4 x + 3}{2 x + 4}

\frac{x^{2} + 7 x + 12}{8}

Q6.

Simplify

\frac{x + 1}{3 x} + \frac{x + 2}{6 x}

\frac{2 x + 3}{6 x}

\frac{2 x + 3}{9 x}

\frac{3 x + 3}{18 x}

Correct answer:

\frac{3 x + 4}{6 x}

\frac{3 x^{2} + 1}{6 x^{2}}

Exit quiz

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6 Questions

Q1.

What would be the most efficient first step to solve

\frac{x + 2}{4 x} + \frac{3}{6 x} = 4

Correct answer: Convert to fractions over a common denominator.

Factorise all expressions.

Multiply all terms by

6 x

Subtract 2 from both sides.

Subtract 4 from both sides.

Q2.

Which of these show all the solutions to the equation

\frac{x + 2}{4 x} + \frac{3}{6 x} = 4

x = - \frac{8}{3}

x = 0

x = \frac{4}{7}

x = \frac{5}{39}

Correct answer:

x = \frac{4}{15}

x = \frac{1}{3}

Q3.

Which of these is a correct step when solving

\frac{4}{x - 2} - \frac{6}{x - 4} = - 2

\frac{4}{x - 4} = - 2

\frac{4}{x - 2} - \frac{4}{x - 4} = 0

\frac{- 2 x - 28}{(x - 4) (x - 2)} = - 2

\frac{- 2 x - 6}{(x - 4) (x - 2)} = - 2

Correct answer:

\frac{- 2 x - 4}{(x - 4) (x - 2)} = - 2

Q4.

Find all the solutions to

\frac{4}{x - 2} - \frac{6}{x - 4} = - 2

x = - 6

x = 1

x = - 2

x = 5

x = 2

x = 3

x = 2

x = 5

Correct answer:

x = 6

x = 1

Q5.

Which of these is a correct step when solving

\frac{x + 3}{2 x - 3} = \frac{5}{x - 1}

x^{2} - 3 = 10 x - 15

\frac{- 1 (x - 3)}{2 (x - 3)} = \frac{5}{x - 1}

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

Correct answer:

\frac{x^{2} + 2 x - 3}{(2 x - 3) (x - 1)} = \frac{10 x - 15}{(2 x - 3) (x - 1)}

\frac{(x + 3) (x - 1)}{2 (x - 3) (x - 1)} = \frac{10 (x - 3)}{2 (x - 3) (x - 1)}

Q6.

Find all the solutions to

\frac{x + 3}{2 x - 3} = \frac{5}{x - 1}

Correct answer:

x = 2

x = 6

x = 2

x = - 6

x = - 2

x = 6

x = - 2

x = - 6

Solving equations with algebraic fractions

Link copied to clipboard

Solving equations with algebraic fractions

Link copied to clipboard

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