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2. Fractions
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iGCSE (2021 Edition)

2.02 Equivalent and simplified fractions

Lesson
Worksheet
Practice
Worksheet
Equivalent fractions
1

Select the equivalent fractions from the following lists:

a
\dfrac{4}{40}, \quad \dfrac{1}{10}, \quad \dfrac{2}{80}, \quad \dfrac{8}{80}, \quad \dfrac{8}{20}
b
\dfrac{20}{30}, \quad \dfrac{7}{3}, \quad \dfrac{8}{12}, \quad \dfrac{2}{6}, \quad \dfrac{2}{3}
c
\dfrac{1}{4}, \quad \dfrac{16}{64}, \quad \dfrac{4}{8}, \quad \dfrac{128}{256}, \quad \dfrac{32}{64}
d
\dfrac{9}{8}, \quad \dfrac{27}{24}, \quad \dfrac{108}{96}, \quad \dfrac{8}{9}, \quad \dfrac{54}{24}
e
\dfrac{15}{20}, \quad \dfrac{6}{8}, \quad \dfrac{10}{15}, \quad \dfrac{9}{12}, \quad \dfrac{2}{3}
f
\dfrac{6}{9}, \quad \dfrac{3}{4}, \quad \dfrac{10}{15}, \quad \dfrac{17}{24}, \quad \dfrac{4}{6}
g
\dfrac{4}{18}, \quad \dfrac{14}{63}, \quad \dfrac{2}{16}, \quad \dfrac{2}{9}, \quad \dfrac{10}{36}
h
\dfrac{17}{5}, \quad \dfrac{8}{20}, \quad \dfrac{2}{5}, \quad \dfrac{4}{14}, \quad \dfrac{16}{40}
2

Complete the following equivalent fraction statements:

a
\dfrac{1}{2}=\dfrac{⬚}{4}
b
\dfrac{1}{5}=\dfrac{⬚}{75}
c
\dfrac{3}{8}=\dfrac{⬚}{40}
d
\dfrac{9}{5}=\dfrac{⬚}{40}
e
\dfrac{19}{10}=\dfrac{⬚}{90}
f
\dfrac{3}{8}=\dfrac{⬚}{24}
g
\dfrac{5}{16}=\dfrac{20}{⬚}
h
\dfrac{7}{12}=\dfrac{35}{⬚}
i
\dfrac{4}{9}=\dfrac{40}{⬚}
j
\dfrac{4}{3}=\dfrac{48}{⬚}
k
\dfrac{5}{21}=\dfrac{45}{⬚}
l
\dfrac{18}{11}=\dfrac{72}{⬚}
3

Complete the table below:

Mixed numberImproper fractionEquivalent fraction
2 \dfrac{1}{6}
3 \dfrac{4}{5}
4 \dfrac{2}{7}
1 \dfrac{2}{5}
6 \dfrac{1}{8}
2 \dfrac{3}{8}
3 \dfrac{3}{7}
4 \dfrac{2}{9}
5 \dfrac{1}{4}
Simplify fractions
4

Use the diagrams provided to simplify the following fractions:

a

\dfrac{4}{28}

b

\dfrac{20}{32}

c

\dfrac{9}{18}

d

\dfrac{10}{50}

e

\dfrac{20}{35}

f

\dfrac{8}{24}

g

\dfrac{9}{21}

h

\dfrac{3}{27}

5

Simplify the following fractions:

a
\dfrac{3}{9}
b
\dfrac{20}{60}
c
\dfrac{6}{20}
d
\dfrac{27}{45}
e
\dfrac{63}{28}
f
\dfrac{40}{30}
g
\dfrac{26}{50}
h
\dfrac{24}{66}
i
\dfrac{32}{80}
j
\dfrac{64}{92}
k
\dfrac{80}{100}
l
\dfrac{60}{200}
m
\dfrac{2}{10}
n
\dfrac{8}{64}
o
\dfrac{21}{231}
p
\dfrac{150}{270}
Compare fractions
6

For the each of the following pairs of fractions, state which fraction is bigger:

a
\dfrac{1}{3}, \quad \dfrac{3}{15}
b
\dfrac{4}{28}, \quad \dfrac{6}{14}
c
\dfrac{31}{8}, \quad \dfrac{24}{7}
d
\dfrac{3}{8}, \quad \dfrac{1}{2}
e
\dfrac{14}{5}, \quad \dfrac{11}{4}
f
\dfrac{5}{2}, \quad \dfrac{49}{20}
g
1\dfrac{6}{7}, \quad \dfrac{25}{14}
h
3\dfrac{4}{9}, \quad \dfrac{7}{2}
7

For the each of the following pairs of fractions, state which fraction is smaller:

a
\dfrac{2}{9}, \quad \dfrac{7}{8}
b
\dfrac{7}{5}, \quad \dfrac{8}{10}
c
\dfrac{4}{15}, \quad \dfrac{2}{5}
d
\dfrac{4}{7}, \quad \dfrac{4}{8}
e
\dfrac{63}{15}, \quad \dfrac{82}{20}
f
\dfrac{21}{6}, \quad \dfrac{18}{5}
g
\dfrac{27}{45}, \quad \dfrac{5}{8}
h
2\dfrac{5}{9}, \quad 2\dfrac{7}{11}
8

For each of the following groups of fractions:

i

Find the lowest common denominator of the 3 fractions.

ii

Rewrite all 3 fractions with this lowest common denominator.

iii

List the 3 fractions in ascending order.

a

\dfrac{2}{5}, \enspace \dfrac{9}{55}, \enspace \dfrac{7}{11}

b

\dfrac{7}{13}, \enspace \dfrac{8}{65}, \enspace \dfrac{3}{5}

c

\dfrac{5}{7}, \enspace \dfrac{9}{77}, \enspace \dfrac{8}{11}

d

\dfrac{5}{17}, \enspace \dfrac{7}{68}, \enspace \dfrac{3}{4}

9

Arrange the following groups of fractions from smallest to largest:

a
\dfrac{11}{20}, \enspace \dfrac{4}{15}, \enspace \dfrac{2}{5}
b
\dfrac{2}{3}, \enspace \dfrac{3}{7}, \enspace \dfrac{4}{5}
c
\dfrac{21}{9}, \enspace \dfrac{6}{4}, \enspace \dfrac{2}{7}
d
4\dfrac{1}{2}, \enspace \dfrac{31}{4}, \enspace \dfrac{15}{2}
e
\dfrac{39}{4}, \enspace 4\dfrac{5}{10}, \enspace \dfrac{19}{2}
f
1\dfrac{6}{7}, \enspace \dfrac{33}{14}, \enspace \dfrac{16}{7}
g
2\dfrac{2}{5}, \enspace \dfrac{33}{10}, \enspace \dfrac{16}{5}
h
\dfrac{17}{3}, \enspace \dfrac{35}{6}, \enspace 3\dfrac{2}{3}
10

For each of the following groups of fractions:

i

Find the lowest common denominator of the 3 fractions.

ii

Rewrite all 3 fractions with this lowest common denominator.

iii

List the 3 fractions in descending order.

a

\dfrac{1}{4}, \enspace \dfrac{3}{8}, \enspace \dfrac{5}{32}

b

\dfrac{2}{6}, \enspace \dfrac{4}{9}, \enspace \dfrac{1}{54}

c

\dfrac{2}{5}, \enspace \dfrac{6}{7}, \enspace \dfrac{8}{35}

d

2\dfrac{2}{5}, \enspace \dfrac{37}{10}, \enspace \dfrac{18}{5}

11

Arrange the following groups of fractions from largest to smallest:

a
\dfrac{1}{2}, \enspace \dfrac{2}{3}, \enspace \dfrac{5}{8}
b
\dfrac{3}{8}, \enspace \dfrac{9}{16}, \enspace \dfrac{13}{24}
c
2\dfrac{7}{10}, \enspace \dfrac{13}{5}, \enspace \dfrac{7}{2}
d
2\dfrac{1}{7}, \enspace \dfrac{33}{14}, \enspace \dfrac{16}{7}
e
6\dfrac{1}{2}, \enspace \dfrac{35}{4}, \enspace \dfrac{17}{2}
f
\dfrac{33}{10}, \enspace 1\dfrac{4}{5}, \enspace \dfrac{16}{5}
g
\dfrac{17}{4}, \enspace 4\dfrac{3}{4}, \enspace \dfrac{39}{8}
h
\dfrac{21}{2}, \enspace \dfrac{37}{4}, \enspace 9\dfrac{1}{2}
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Outcomes

0580C1.5A

Use the language and notation of simple vulgar and decimal fractions in appropriate contexts.

0580E1.5A

Use the language and notation of simple vulgar and decimal fractions in appropriate contexts.

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