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1.04 Operations with fractions

Worksheet
Operations with fractions
1

Evaluate the following, writing your answers in simplest form:

a

\dfrac{5}{9} + \dfrac{3}{9}

b
\dfrac{1}{5} + \dfrac{2}{4}
c
\dfrac{6}{5} + \dfrac{5}{3}
d
\dfrac{1}{3} - \dfrac{1}{10}
e
\dfrac{4}{7} - \dfrac{1}{2}
f
\dfrac{8}{9} \times \dfrac{9}{56}
g
\dfrac{8}{15} \times \dfrac{9}{7}
h
\dfrac{9}{10} \times \dfrac{10}{9}
i

\dfrac{11}{9} \times \dfrac{2}{99}

j

- \dfrac{3}{7} \times \dfrac{2}{3}

k

\left(\dfrac{4}{9}\right)^{2}

l
\dfrac{2}{7} \div \dfrac{5}{3}
m
\dfrac{9}{10} \div \dfrac{10}{9}
n
\dfrac{2}{7} \div \dfrac{7}{18}
o
\dfrac{3}{15} \div \dfrac{4}{3}
p

\dfrac{3}{8} \div \dfrac{3}{4}

2

Evaluate the following, writing your answers as mixed numbers in simplest form:

a
2\dfrac{3}{11} + 4\dfrac{7}{11}
b
3\dfrac{2}{6} + 4\dfrac{4}{5}
c
3\dfrac{1}{3} + 4\dfrac{11}{12}
d
3\dfrac{1}{3} + 4\dfrac{11}{12}
e
2\dfrac{2}{3} + 3\dfrac{11}{15}
f
6+ 1\dfrac{4}{5}
g
7 + 3\dfrac{3}{4}
h
4\dfrac{3}{7} - 7\dfrac{4}{7}
i
4\dfrac{4}{7} - \left( - 8\dfrac{2}{7} \right)
j
- 8\dfrac{4}{7} + 3\dfrac{3}{7}
k
6\dfrac{3}{11} - 9\dfrac{6}{11}
l
- 5\dfrac{4}{11} - 7\dfrac{6}{11}
m
2\dfrac{2}{3} - 7
n
2\dfrac{3}{8} - 8\dfrac{3}{4}
o
- 2\dfrac{3}{8} - 7\dfrac{2}{7}
p
6\dfrac{5}{6} - 9\dfrac{8}{9}
q
5\dfrac{3}{14}-\left(- 9\dfrac{2}{7}\right)
r
3\dfrac{2}{5} - \left( - 7\dfrac{3}{7} \right)
s
- 3\dfrac{5}{6} + 8\dfrac{4}{9}
t
2 - 9\dfrac{2}{3}
3

Evaluate the following, writing your answers as mixed numbers in simplest form:

a
2\dfrac{2}{3} \times \left( - 8 \right)
b
- 10 \times \left( - 2\dfrac{1}{4} \right)
c
- 8 \times \left( - 2\dfrac{2}{5} \right)
d
\dfrac{1}{2} \times \left( - 3\dfrac{1}{2} \right)
e
- 2\dfrac{1}{5} \times \left( - \dfrac{1}{2} \right)
f
3\dfrac{1}{7} \times \left( - \dfrac{1}{4} \right)
g
- \dfrac{3}{5} \times 2\dfrac{1}{5}
h
\dfrac{3}{4} \times \left( - 3\dfrac{3}{5} \right)
i
- 1\dfrac{1}{6} \times \left( - \dfrac{9}{2} \right)
j
- 2\dfrac{3}{4} \times \left( - 1\dfrac{1}{6} \right)
k
- 2\dfrac{3}{4} \times 3\dfrac{1}{3}
l
-2\dfrac{1}{4} \times 3\dfrac{1}{3}
4

Evaluate the following, writing your answers as mixed numbers in simplest form:

a
3\dfrac{1}{3} \div 2\dfrac{1}{2}
b
\left( - 5 \right) \div 2\dfrac{2}{3}
c
\left( - 7\dfrac{1}{2} \right) \div \left( - 12 \right)
d
\dfrac{1}{5} \div \left( - 2\dfrac{1}{3} \right)
e
2\dfrac{1}{4} \div \left( - \dfrac{1}{6} \right)
f
\left( - 1\dfrac{2}{9} \right) \div \dfrac{1}{9}
g
\left( - 1\dfrac{4}{7} \right) \div \left( - \dfrac{1}{7} \right)
h
\left( - \dfrac{3}{7} \right) \div \left( - 3\dfrac{1}{3} \right)
i
\left( - \dfrac{7}{8} \right) \div 1\dfrac{3}{8}
j
\left( - \dfrac{3}{5} \right) \div \left( - 1\dfrac{2}{5} \right)
k
\left( - 1\dfrac{1}{2} \right) \div \left( - \dfrac{3}{5} \right)
l
\left( - 2\dfrac{4}{7} \right) \div \left( - \dfrac{9}{2} \right)
m
3\dfrac{1}{2} \div \left( - 2\dfrac{2}{5} \right)
n
\left( - 6\dfrac{9}{10} \right) \div 6\dfrac{9}{10}
o
\left( - 3\dfrac{9}{10} \right) \div \left( - 3\dfrac{9}{10} \right)
p
\left( - 4\dfrac{1}{8} \right) \div \left( - 2\dfrac{5}{8} \right)
q
\left( - 2\dfrac{1}{7} \right) \div 1\dfrac{3}{7}
r
4\dfrac{2}{3} \div \left( - 1\dfrac{2}{5} \right)
5

Evaluate the following, writing your answers in simplest form:

a
3 + 4 - \left( - \dfrac{4}{5} \right)
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{47}{72} - \left(\dfrac{2}{8} + \dfrac{3}{9}\right)
f
\dfrac{6}{7} \times \left(\dfrac{2}{3} - \dfrac{2}{7}\right)
g

\dfrac{3}{5} \times \dfrac{2}{3} + \dfrac{5}{15}

h

\left(\dfrac{2}{3} + \dfrac {3}{5}\right) \times \dfrac{3}{7}

i
-\dfrac{2}{5} \times \dfrac{4}{5} + \dfrac{2}{25}
j
-\dfrac{3}{5} \times \dfrac{4}{5} - \dfrac{1}{25}
k
\dfrac{2}{5} \times -\dfrac{ 4}{3} - \dfrac{3}{15}
l
-\dfrac{3}{10} \times -\dfrac{1}{2} + \dfrac{5}{20}
m
\left(\dfrac{4}{7} + \dfrac{2}{5}\right) \div \dfrac{5}{8}
n
- \left(\dfrac{2}{3}\right)^{2} + \dfrac{3}{8}
o
\left(\dfrac{2}{5} + \dfrac{3}{10} \times \dfrac{2}{3}\right) \div \dfrac{6}{7}
p
\left(\dfrac{1}{3} + \dfrac{3}{4}\right) \div \left(\dfrac{1}{2} - \dfrac{3}{8} \right)
Applications
6

A class has 40 students. \dfrac{2}{5} of the class are boys.

a

What fraction of the class are not boys?

b

How many boys are in the class?

7

At the end of last month, a dam was \dfrac{5}{7} full. Over the current month, \dfrac{52}{63} of the dam's capacity was used up by the town. Meanwhile, rain filled \dfrac{5}{9} of the dam's capacity. What fraction of the dam is full at end of this month?

8

In a survey of 270 people, \dfrac{1}{10} said their favorite sport was football, and \dfrac{1}{9} said their favorite sport was tennis.

a

Find the total fraction of people who said their favorite sport was football or tennis.

b

Find the fraction of people who did not put football or tennis as their favorite sport.

c

How many people did not put football or tennis as their favorite sport?

9

Victoria borrows a 360-page novel from the library. She reads \dfrac{3}{4} of the novel.

a

How many pages did she read?

b

How many more pages does she have to read to finish her novel?

10

Luke has a dice tin that is \dfrac{1}{4} full. He puts 8 extra dice in and the tin is now \dfrac{1}{3} full.

a

What fraction of the tin do the 8 extra dice take up?

b

How many dice can fit inside the tin?

11

After an earthquake, \dfrac{3}{7} of all claims were paid within a month. Of the remaining claims that had not yet been paid, \dfrac{5}{7} of them were paid within the second month. What fraction of all claims were paid in the second month?

12

A family drinks \dfrac{3}{4} of a carton of milk per day. How many days will 6 cartons of milk last the family?

13

Christine has 1\dfrac{3}{4} meters of ribbon. She uses \dfrac{7}{20} to wrap a present. How many presents can she wrap with her ribbon?

14

During a sale, 89 computers were up for sale but only some of them were sold. Six computers were sold at a loss, which represents \dfrac{1}{6} of the total number of computers that were sold. How many computers weren't sold?

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Outcomes

MA.7.NSO.2.2

Add, subtract, multiply and divide rational numbers with procedural fluency.

MA.7.NSO.2.3

Solve real-world problems involving any of the four operations with rational numbers.

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