CAIE IGCSE Mathematics Extended E2.3 Algebraic fractions Question Bank

Practise simplifying algebraic fractions by factorising, cancelling common factors and combining terms over a common denominator.

Exam points

combine algebraic fractions into one simplified fraction using a common denominator
factorise numerator and denominator before cancelling shared brackets
multiply or divide algebraic fractions, cancelling variables or brackets correctly

[Maximum number: 3]

Write as a single fraction in its simplest form.
$\frac{4a}{5}\div\frac{3ad}{10c}$

$\frac{8c}{3d}$ final answer
B2 for $\frac{8ac}{3ad}$ or $\frac{40c}{15d}$
or M1 for $\frac{4a}{5}\times\frac{10c}{3ad}$ oe

[Maximum number: 4]

Simplify.
$\frac{2x-1-4ax+2a}{2x^2-x}$

$\frac{1-2a}{x}$
oe final answer

B2 for (2x-1)(1-2a) oe
or B1 for 2x-1-2a(2x-1) or 2x(1-2a)-(1-2a)
B1 for x(2x-1)

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