Topics
2. Fractions
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iGCSE (2021 Edition)

2.03 Adding and subtracting fractions

Lesson
Worksheet
Practice
Worksheet
Adding and subtracting fractions
1

Simplify:

a
\dfrac{1}{11} + \dfrac{9}{11}
b
\dfrac{2}{6} + \dfrac{2}{6}
c
\dfrac{4}{7} - \dfrac{2}{7}
d
\dfrac{5}{6} - \dfrac{3}{6}
e
\dfrac{7}{9} + \dfrac{4}{9}
f
\dfrac{8}{9} - \dfrac{7}{9}
g
\dfrac{7}{25} + \dfrac{3}{25}
h
\dfrac{9}{22} - \dfrac{5}{22}
2

Simplify the following, writing your answer as a mixed numeral where necessary:

a
\dfrac{1}{4} + \dfrac{1}{9}
b
\dfrac{6}{7} + \dfrac{1}{14}
c
\dfrac{1}{4} + \dfrac{1}{6}
d
\dfrac{1}{5} + \dfrac{2}{4}
e
\dfrac{7}{8} + \dfrac{5}{6}
f
\dfrac{6}{5} + \dfrac{5}{3}
g
\dfrac{1}{3} - \dfrac{1}{10}
h
\dfrac{3}{4} - \dfrac{1}{8}
i
\dfrac{1}{9} - \dfrac{1}{12}
j
\dfrac{2}{8} - \dfrac{1}{9}
k
\dfrac{4}{7} + \dfrac{1}{3}
l
\dfrac{2}{9} - \dfrac{1}{18}
3
Simplify the following, writing your answer as a mixed numeral where necessary:
a
\dfrac{8}{5} + \dfrac{11}{5}
b
\dfrac{7}{6} + \dfrac{13}{10}
c
\dfrac{5}{2} + 3
d
2\dfrac{3}{11} + 4\dfrac{7}{11}
e
3\dfrac{2}{6} + 4\dfrac{4}{5}
f
\dfrac{46}{22} - \dfrac{16}{22}
g
\dfrac{9}{4} - \dfrac{6}{14}
h
\dfrac{7}{4} - \dfrac{5}{3}
i
\dfrac{10}{8} - \dfrac{7}{6}
j
4 - \dfrac{7}{9}
k
5\dfrac{10}{11} - 4\dfrac{8}{11}
l
4\dfrac{6}{7} - 3\dfrac{6}{8}
m
3\dfrac{1}{3} + 4\dfrac{11}{12}
n
6\dfrac{1}{2} - 4\dfrac{1}{10}
o
6\dfrac{1}{2} - \dfrac{3}{8}
p
2\dfrac{2}{3} + 3\dfrac{11}{15}
4

Simplify the following, writing your answer as a mixed numeral where necessary:

a
1 + \dfrac{1}{2}
b
2 - \dfrac{3}{4}
c
6+ 1\dfrac{4}{5}
d
8 - 2\dfrac{1}{2}
e
7 + 3\dfrac{3}{4}
f
10 - 5\dfrac{1}{3}
g
9-2\dfrac{5}{7}
h
11 + 4\dfrac{3}{8}
5

Simplify the following, writing your answer as a mixed numeral where necessary:

a
\dfrac{3}{4} + \dfrac{1}{8} - \dfrac{1}{4}
b
\dfrac{5}{9} + \dfrac{2}{3} + \dfrac{5}{6}
c
\dfrac{10}{12} - \dfrac{1}{6} - \dfrac{1}{4}
d
\dfrac{8}{10} + \dfrac{2}{5} - \dfrac{7}{20}
e
\dfrac{2}{5} + \dfrac{1}{10} - \dfrac{7}{30}
f
\dfrac{7}{45} + \dfrac{2}{9} - \dfrac{8}{9}
g
\dfrac{4}{45} + \dfrac{7}{5} - \dfrac{8}{5}
h
\dfrac{3}{4} + \dfrac{7}{8} - \dfrac{5}{24}
i
\dfrac{6}{35} - \dfrac{1}{7} + \dfrac{3}{14}
j
\dfrac{2}{45} + \dfrac{7}{9} + \dfrac{2}{3}
k
\dfrac{1}{2} - \dfrac{1}{3} - \dfrac{1}{9}
l
\dfrac{8}{21} - \dfrac{2}{7} + \dfrac{9}{14}
Applications
6

Marge ran three ninths of a kilometre. She took a 5-minute rest, then ran another three thirds of a kilometre. How many kilometres did she run in total?

7

Jack felt dehydrated. He drank one third of a litre at first, then drank another one ninth of a litre. How many litres did he drink in total?

8

Valerie walks eight sixths of a kilometre to school while Fred walks one half of a kilometre to school. How much farther does Valerie walk than Fred?

9

A bridge is being built to span \dfrac{3}{4} \text{ km}. After a month, the engineer reported that \dfrac{3}{8} \text{ km} has been completed so far. What part of the bridge has not yet been completed?

10

Jane eats \dfrac{1}{4} of a cake and Joshua eats \dfrac{1}{3} of the cake. What fraction of the cake did they eat altogether?

11

During a blizzard it snowed 10\dfrac{1}{2} \text{ cm}. When the sun came out the next day, 5 \dfrac{3}{4} \text{ cm} of show melted. How much snow was left on the ground?

12

A market stall is open for 3 \dfrac{1}{2} hours in the morning and 2 \dfrac{3}{4} hours in the evening. How many hours is the stall open altogether?

13

Georgio buys 3 cups of sugar to use in his baking. He uses \dfrac{3}{4} of a cup in his cake, 1 \dfrac{1}{5} of a cup in his pastries and accidentally spilled \dfrac{1}{2} of a cup. How much sugar does he have left?

14

Mr. Pemberton, the president of Zoom Motors, owns \dfrac{1}{3} of the stock of the company. His wife owns \dfrac{1}{4} of the stock. What fractional part of the stock will his daughter need to purchase in order for the family to own \dfrac{3}{4} of the stock?

15

Missy mailed 4 letters that have a total weight of 3 grams. One letter weighed \dfrac{1}{2} of a gram, another weighed \dfrac{3}{4} of a gram, and a third weighed \dfrac{7}{8} of a gram. How much did the fourth letter weigh?

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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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