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iGCSE (2021 Edition)

2.07 Order of operations with fractions

Worksheet
Order of operations with fractions
1

Evaluate:

a
\dfrac{4}{19} + \dfrac{9}{19} + \dfrac{2}{19}
b
\dfrac{3}{17} + \dfrac{6}{17} - \dfrac{4}{17}
c
\dfrac{3}{40} + \dfrac{4}{5} \times \dfrac{7}{8}
d
\left(\dfrac{3}{7} + \dfrac{2}{7}\right) \times \dfrac{5}{9}
e
\dfrac{2}{21} + \dfrac{6}{7} \div \dfrac{3}{4}
f
\dfrac{8}{9} - \dfrac{2}{9} - \dfrac{4}{9}
g
\dfrac{8}{21} - \dfrac{3}{7} \times \dfrac{2}{3}
h
\left(\dfrac{7}{9} - \dfrac{2}{9}\right) \div \dfrac{2}{7}
2

Evaluate:

a
\left(\dfrac{4}{7} + \dfrac{2}{5}\right) \div \dfrac{5}{8}
b
\dfrac{4}{16} - \dfrac{2}{16} + \dfrac{12}{16}
c
\dfrac{4}{35} - \left(\dfrac{6}{7} - \dfrac{4}{5}\right)
d
\left(\dfrac{2}{5} - \dfrac{3}{8}\right) \times \dfrac{5}{9}
e
\dfrac{5}{7} - \dfrac{2}{5} \div \dfrac{7}{8}
f
\dfrac{3}{5} \times \dfrac{2}{7} + \dfrac{3}{7}
g
\dfrac{5}{6} \times \left(\dfrac{4}{9} + \dfrac{2}{5}\right)
h
\dfrac{3}{4} \times \dfrac{5}{8} - \dfrac{2}{9}
i
\dfrac{8}{9} \times \dfrac{4}{5} \times \dfrac{2}{7}
j
\dfrac{5}{7} \times \dfrac{3}{4} \div \dfrac{2}{9}
k
\dfrac{2}{3} \div \dfrac{3}{4} + \dfrac{7}{9}
l
\dfrac{2}{9} \div \dfrac{5}{8} - \dfrac{4}{45}
m
\dfrac{5}{7} \div \dfrac{4}{5} \times \dfrac{7}{9}
n
\dfrac{8}{9} \div \left( \dfrac{2}{5} \times \dfrac{3}{7}\right)
o
\dfrac{5}{9} \div \dfrac{3}{4} \div \dfrac{7}{8}
p
\dfrac{3}{5} \div \left( \dfrac{2}{9} \div \dfrac{4}{7}\right)
3

Evaluate:

a
\dfrac{47}{72} - \left(\dfrac{2}{8} + \dfrac{3}{9}\right)
b
\dfrac{6}{7} \times \left(\dfrac{2}{3} - \dfrac{2}{7}\right)
c
\dfrac{7}{8} \div \left(\dfrac{3}{8} + \dfrac{2}{7}\right)
d
\dfrac{5}{8} \div \left(\dfrac{6}{7} - \dfrac{2}{9}\right)
e
\dfrac{3}{8} \times \left(\dfrac{3}{2} + \dfrac{2}{5}\right)
f
\left(\dfrac{3}{4} - \dfrac{2}{9}\right) \div \dfrac{2}{5}
g
\left(\dfrac{2}{5} - \dfrac{3}{8}\right) \times \dfrac{2}{9}
h
\dfrac{3}{10} \div \left(\dfrac{6}{7} - \dfrac{2}{5}\right)
4

Evaluate:

a
\left(\dfrac{1}{4} + \dfrac{3}{8}\right) \times \left(\dfrac{2}{5} + \dfrac{1}{5}\right)
b
\dfrac{5}{7} \times \left(\dfrac{1}{3} + \dfrac{5}{6} - \dfrac{1}{2}\right)
c
\left(\dfrac{2}{5} + \dfrac{3}{10} \times \dfrac{2}{3}\right) \div \dfrac{6}{7}
d
\left(\dfrac{1}{3} + \dfrac{3}{4}\right) \div \left(\dfrac{1}{2} - \dfrac{3}{8} \right)
e
\dfrac{1}{7} \times \dfrac{2}{9} \div \dfrac{4}{27} + \dfrac{7}{2}
f
\left(\dfrac{3}{4} - \dfrac{5}{9}\right) \div \dfrac{2}{3} - \dfrac{1}{24}
g
\dfrac{7}{2} - \left(\dfrac{3}{5} + \dfrac{7}{10} \div \dfrac{9}{30} \right)
h
\left(\dfrac{27}{24} + \dfrac{10}{20}\right) \times \left(\dfrac{7}{8} - \dfrac{3}{4} \right)
5

Evaluate:

a
8\dfrac{1}{4} - 2\dfrac{1}{5} \times 3 \dfrac{1}{2}
b
4\dfrac{1}{5} \times 2\dfrac{1}{4} - 4\dfrac{3}{8}
c
\left(3\dfrac{3}{4} \div 2\dfrac{1}{2}\right) + \dfrac{7}{3}
d
5\dfrac{5}{6} + \left(1\dfrac{1}{3} \times 2 \dfrac{7}{12}\right)
e
2\dfrac{1}{4} + 5\dfrac{5}{8} \times 3\dfrac{1}{3} - 4\dfrac{5}{6}
f
\left(3\dfrac{1}{4} \times 2\dfrac{2}{3}\right) + \left(6\dfrac{3}{4} \div 2\dfrac{3}{12}\right)
g
\left(1\dfrac{1}{3} + 2\dfrac{1}{5} \right) \times \left(3\dfrac{1}{2} - 2\dfrac{3}{4}\right)
h
1\dfrac{7}{8} - \left(3\dfrac{3}{4} \div 2\dfrac{1}{2} - 3\dfrac{3}{16}\right)
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Outcomes

0580C1.8C

Use the four rules for calculations with fractions (including mixed numbers and improper fractions), including correct ordering of operations and use of brackets.

0580E1.8C

Use the four rules for calculations with fractions (including mixed numbers and improper fractions), including correct ordering of operations and use of brackets.

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