Topics
2. Fractions
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Middle Years

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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