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2. Fractions
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Middle Years

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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