Look for a common factor: (2x)/(6) Divide top and bottom by 2: (2x)/(6) = (x)/(3) State the answer: (x)/(3) Answer: (x)/(3)

Look for a common factor: (6x)/(9) Divide top and bottom by 3: (6x)/(9) = (2x)/(3) State the answer: (2x)/(3) Answer: (2x)/(3)

Simplify (10ab)/(5a).

Identify the common factor: (10ab)/(5a) Cancel 5a: (10ab)/(5a) = (2b)/(1) State the answer: 2b Answer: 2b

Write out the powers: (x × x)/(x) Cancel one x: (x × x)/(x) = x State the answer: x Answer: x

Simplify (4x^2)/(2x).

Split the number and letter parts: (4)/(2) × (x^2)/(x) Cancel each part: 2 × x = 2x State the answer: 2x Answer: 2x

Algebraic fractions Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Algebraic fractions questions. See exactly how to solve problems on simplifying, cancelling, index laws, factorising.

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GCSE Higher70 questionsStep-by-step solutions

Question 1

1 markeasy

Simplify

\frac{2x}{6}

Worked solution

Look for a common factor
$\frac{2x}{6}$
The top $2x$ and the bottom $6$ share a factor of $2$ .
Divide top and bottom by $2$
$\frac{2x}{6} = \frac{x}{3}$
Cancelling the 2 leaves x over 3.
State the answer
$\frac{x}{3}$
The fraction is now in its simplest form.

Answer

\frac{x}{3}

Question 2

1 markeasy

Simplify

\frac{6x}{9}

Worked solution

Look for a common factor
$\frac{6x}{9}$
Both $6$ and $9$ are multiples of $3$ .
Divide top and bottom by $3$
$\frac{6x}{9} = \frac{2x}{3}$
Six divided by $3$ is $2$ and $9$ divided by $3$ is $3$ .
State the answer
$\frac{2x}{3}$
No further factor is common to $2x$ and $3$ .

Answer

\frac{2x}{3}

Question 3

1 markeasy

Simplify

\frac{10ab}{5a}

Worked solution

Identify the common factor
$\frac{10ab}{5a}$
Top and bottom both contain a factor of $5a$ .
Cancel $5a$
$\frac{10ab}{5a} = \frac{2b}{1}$
Ten divided by $5$ is $2$ and one a cancels.
State the answer
$2b$
The simplified expression is $2b$ .

Answer

2b

Question 4

1 markeasy

Simplify

\frac{x^2}{x}

Worked solution

Write out the powers
$\frac{x \times x}{x}$
x squared means x times x.
Cancel one x
$\frac{x \times x}{x} = x$
One factor of x on top cancels the x on the bottom.
State the answer
x
The simplified expression is x, provided x is not 0.

Answer

Question 5

1 markeasy

Simplify

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

Worked solution

Split the number and letter parts
$\frac{4}{2} \times \frac{x^2}{x}$
Deal with the coefficients and the powers of x separately.
Cancel each part
$2 \times x = 2x$
Four over 2 is 2, and x squared over x is x.
State the answer
$2x$
The simplified expression is $2x$ .

Answer

2x

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