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Year 7

2.03 Adding and subtracting fractions

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

State the lowest common denominator of the following sets of fractions:

a

\dfrac{1}{3}, \, \dfrac{1}{2}

b

\dfrac{1}{4}, \, \dfrac{1}{9}

c

\dfrac{1}{2}, \, \dfrac{1}{4}, \, \dfrac{2}{5}

d

\dfrac{5}{12}, \, \dfrac{1}{6}, \, \dfrac{2}{3}

3

Complete the following statements:

a
\displaystyle \frac{2}{3} + \frac{1}{9} \displaystyle =\displaystyle \frac{6}{⬚} + \frac{1}{⬚}Rewrite with a common denominator
\displaystyle =\displaystyle \dfrac{7}{⬚}Evaluate the sum
b
\displaystyle \frac{1}{2} + \frac{2}{3} \displaystyle =\displaystyle \frac{⬚}{6} + \frac{⬚}{6} Rewrite with a common denominator
\displaystyle =\displaystyle \frac{⬚}{6}Evaluate the sum
\displaystyle =\displaystyle 1 \frac{⬚}{6}Rewrite as a mixed number
c
\displaystyle \frac{7}{8} - \frac{3}{16} \displaystyle =\displaystyle \frac{⬚}{⬚} - \frac{3}{⬚} Rewrite with a common denominator
\displaystyle =\displaystyle \frac{⬚}{⬚}Evaluate the difference
d
\displaystyle \frac{11}{4} - \frac{7}{6} \displaystyle =\displaystyle \frac{⬚}{⬚} - \frac{⬚}{⬚} Rewrite with a common denominator
\displaystyle =\displaystyle \frac{19}{⬚}Evaluate the difference
\displaystyle =\displaystyle 1 \frac{⬚}{⬚}Rewrite as a mixed number
4

Simplify the following, writing your answer as a mixed number 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}
5

Consider the expression 2 \dfrac{1}{4} + 5 \dfrac{1}{2}.

a

Find the sum of the whole number part of each mixed number.

b

Find the sum of the fraction part of each mixed number.

c

Simplify 2 \dfrac{1}{4} + 5 \dfrac{1}{2}.

6

Fill in the boxes to complete the working out:

\displaystyle 1 \frac{1}{4} + 2 \frac{2}{4} \displaystyle =\displaystyle 1 + ⬚ + \frac{1}{⬚} + \frac{2}{⬚} Group the whole number parts and fraction parts
\displaystyle =\displaystyle ⬚ + \frac{⬚}{⬚}Add the whole number parts and fraction parts
\displaystyle =\displaystyle ⬚ \frac{⬚}{⬚}Evaluate the sum
7

Consider the expression 3 \dfrac{1}{3} - 2 \dfrac{1}{6}.

a

Rewrite the mixed numbers as improper fractions.

b

Using part (a), rewrite the improper fractions with the same denominator.

c

Simplify 3 \dfrac{1}{3} - 2 \dfrac{1}{6}.

8

Fill in the boxes to complete the working out:

\displaystyle 2 \frac{1}{3} - 1 \frac{5}{9}\displaystyle =\displaystyle \frac{⬚}{3} - \frac{⬚}{9}Rewrite as improper fractions
\displaystyle =\displaystyle \frac{⬚}{⬚} - \frac{⬚}{9}Rewrite with a common denominator
\displaystyle =\displaystyle \frac{⬚}{⬚}Evaluate the difference
9
Simplify the following, writing your answer as a mixed number 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}
10

Simplify the following, writing your answer as a mixed number 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}
11

Simplify the following, writing your answer as a mixed number 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
12

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?

13

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?

14

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?

15

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?

16

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?

17

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?

18

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?

19

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?

20

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?

21

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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ACMNA153

Solve problems involving addition and subtraction of fractions, including those with unrelated denominators

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