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iGCSE (2021 Edition)

13.05 Multiplying and dividing algebraic fractions

Worksheet
Multiplication of algebraic fractions
1

Simplify the following expressions:

a

\dfrac{1}{a} \times \dfrac{1}{b}

b

\dfrac{a}{3} \times \dfrac{a}{7}

c

\dfrac{b}{q} \times \dfrac{k}{u}

d

\dfrac{c}{3} \times \dfrac{d}{2}

e

\dfrac{9 x}{2} \times \dfrac{5 y}{7}

f

\dfrac{4 x}{5} \times \dfrac{3 y}{7}

g

\dfrac{11 s}{7 t} \times \dfrac{3 r}{5 q}

h

\dfrac{9 u}{7 v} \times \dfrac{8 w}{11 y}

i

\dfrac{ y}{8} \times \dfrac{5 y}{9}

j

\dfrac{u}{3 a} \times \dfrac{ v}{5 b}

k

\dfrac{5 a}{ b} \times \dfrac{3 }{8 }

l

\dfrac{8 a}{7 y} \times \dfrac{9 b}{5 x}

m
\dfrac{m}{3} \times \dfrac{5 m}{9}
n
\dfrac{2 p}{ m} \times \dfrac{7 q}{5 n}
o
\dfrac{2a}{9b} \times \dfrac{a^2}{7}
p
\dfrac{6b}{ 11m} \times \dfrac{9c}{5 n}
2

Complete the following:

\dfrac{⬚}{3a^2}\times\dfrac{7b}{⬚}=\dfrac{14bc}{9a^2 d}
3

The product of two fractions is 1. If one of the fractions is \dfrac{3x}{4yz}, what is the other fraction?

Multiplication of algebraic fractions (Extended)
4

Simplify the following expressions:

a

\dfrac{3 y}{8} \times \dfrac{4 y}{9}

b

\dfrac{5 u}{3 a} \times \dfrac{3 v}{5 b}

c

\dfrac{9 a}{10 b} \times \dfrac{3 b}{8 a}

d

\dfrac{8 x}{7 y} \times \dfrac{9 y}{5 x}

e

\dfrac{14 u}{15 v} \times \dfrac{40 v}{24 q}

f

\dfrac{9 u}{77 v} \times \dfrac{110 v}{24 q}.

g

\dfrac{x^{2}}{3} \times \dfrac{6}{x}

h

\dfrac{p^{2}}{q} \times \dfrac{q^{2}}{p}

i

\dfrac{r^{2}}{n} \times \dfrac{n^{2}}{r}

j

\dfrac{5 y^{2}}{9} \times 27 y^{2}

k

\dfrac{5 y}{2} \times 6 y^{5}.

l

\dfrac{4 m^{2}}{20} \times \dfrac{3 y^{2}}{7 m}

m

\dfrac{7 a^{2}}{15 b^{2}} \times \dfrac{10 b}{11 a}.

n

\dfrac{11 a^{2}}{4 b^{2}} \times \dfrac{10 b}{3 a}

o

\left( - \dfrac{10}{21 x} \right) \times \dfrac{3 x^{2}}{110}

p

\dfrac{2 n^{2}}{6} \times \dfrac{- 2 y^{2}}{3 n}

5

Simplify:

a
\dfrac{m}{3} \times \dfrac{5 m}{9} \times 81 q
b
\dfrac{2 n}{3 m} \times \dfrac{21 q}{4 n} \times \dfrac{10 m}{49 p}
6

Simplify \left(\dfrac{x}{3y}\right)^2\times\dfrac{5x^2}{2y}.

Division of algebraic fractions
7

Simplify the following expressions:

a

\dfrac{r}{3} \div \dfrac{2}{m}

b

\dfrac{u}{3} \div \dfrac{4}{v}

c

\dfrac{3 y}{5} \div \dfrac{4 }{7}

d

\dfrac{2 x}{9} \div \dfrac{7}{5 y}

e

\dfrac{y^{2}}{4} \div \dfrac{12}{29 y^{6}}

f

\dfrac{4 u}{11 } \div \dfrac{7 q}{50 y}

g

\dfrac{- 2 x}{11} \div \dfrac{5y}{3}

h

\dfrac{9 u}{11 v} \div \dfrac{7 v}{10 u}

i

\dfrac{- 9 m}{5} \div \dfrac{11 n}{8}

j

\dfrac{u^{2}}{12} \div \dfrac{v}{11}

k

\dfrac{u^{2}}{9} \div \dfrac{v}{20}

l

\dfrac{2 u^{3}}{13 v} \div \dfrac{5 v^{3}}{23 u}

8

Complete the following:

\dfrac{⬚}{4p^2}\div\frac{2q^2}{3r}=\frac{27r^3}{⬚}
9

A rectangle has an area of \dfrac{5 x^{3} y^{4}}{3 p q} and a length of \dfrac{4 x y}{p}. Find an expression for the width of the rectangle.

Division of algebraic fractions (Extended)
10

Simplify the following expressions:

a

\dfrac{m}{4} \div \dfrac{m}{3}

b

\dfrac{m}{28} \div \dfrac{23}{20}

c

\dfrac{3 y}{6} \div \dfrac{4 y}{7}

d

\dfrac{3 y^{2}}{4} \div \dfrac{12}{29 y^{6}}

e

\dfrac{4 u}{35 y} \div \dfrac{14 q}{50 y}

f

\dfrac{- 2 x}{11} \div \dfrac{2 x}{3}.

g

\dfrac{9 u}{36 v} \div \dfrac{7 v}{36 u}

h

\dfrac{- 9 n}{4} \div \dfrac{11 n}{8}.

i

\dfrac{u^{2}}{12} \div \dfrac{u}{9}

j
\dfrac{4x^2 y}{9z^4}\div \dfrac{6xy^5}{15z}
k

\dfrac{u^{2}}{9} \div \dfrac{u}{6}.

l

\dfrac{8 u^{3}}{32 v} \div \dfrac{5 v^{3}}{96 u}

m

\dfrac{3 w^{3}}{7} \div 9 w^{6}

n

\dfrac{16 u}{17 v} \div \left( - 14 u v \right)

o

\dfrac{45 x^{2} y z}{10} \div \dfrac{9 y^{2}}{5 x}

p

\dfrac{35 t^{2} u^{2}}{12 v^{2} w^{2}} \div \dfrac{35 t^{3} u}{12 w^{2} y^{2}}

q

\dfrac{10 t^{2} u^{3}}{35 v^{3} w^{3}} \div \dfrac{10 t^{3} u^{2}}{20 w^{3} y}

11

Simplify \left(\dfrac{2x}{y}\right)^4\div\left(\dfrac{z}{3x^2 y}\right)^2.

12

Simplify \dfrac{3 x y}{12 y} \times \dfrac{4 y^{2}}{3 w x} \div \dfrac{15 w x}{3 w^{2}}.

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Outcomes

0607C2.9

Algebraic fractions: simplification, addition or subtraction of fractions with integer denominators, multiplication or division of two simple fractions.

0607E2.9

Algebraic fractions: simplification, including use of factorisation, addition or subtraction of fractions with linear denominators or single term, multiplication or division and simplification of two fractions.

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