Exercise 1

Associate the following fractions with the corresponding amount of minutes in an hour:

\frac{1}{2},   \frac{1}{4},     \frac{3}{4},       \frac{1}{10},       \frac{1}{12},       \frac{1}{3}

 

The best Maths tutors available
1st lesson free!
Intasar
4.9
4.9 (23 reviews)
Intasar
£42
/h
1st lesson free!
Matthew
5
5 (17 reviews)
Matthew
£25
/h
1st lesson free!
Dr. Kritaphat
4.9
4.9 (6 reviews)
Dr. Kritaphat
£49
/h
1st lesson free!
Paolo
4.9
4.9 (11 reviews)
Paolo
£25
/h
1st lesson free!
Ayush
5
5 (28 reviews)
Ayush
£60
/h
1st lesson free!
Petar
4.9
4.9 (9 reviews)
Petar
£27
/h
1st lesson free!
Rajan
4.9
4.9 (11 reviews)
Rajan
£15
/h
1st lesson free!
Farooq
5
5 (13 reviews)
Farooq
£35
/h
1st lesson free!
Intasar
4.9
4.9 (23 reviews)
Intasar
£42
/h
1st lesson free!
Matthew
5
5 (17 reviews)
Matthew
£25
/h
1st lesson free!
Dr. Kritaphat
4.9
4.9 (6 reviews)
Dr. Kritaphat
£49
/h
1st lesson free!
Paolo
4.9
4.9 (11 reviews)
Paolo
£25
/h
1st lesson free!
Ayush
5
5 (28 reviews)
Ayush
£60
/h
1st lesson free!
Petar
4.9
4.9 (9 reviews)
Petar
£27
/h
1st lesson free!
Rajan
4.9
4.9 (11 reviews)
Rajan
£15
/h
1st lesson free!
Farooq
5
5 (13 reviews)
Farooq
£35
/h
First Lesson Free>

Exercise 2

Find the pairs of equivalent fractions and place them in pairs:

\frac{4}{3},   \frac{5}{7},     \frac{8}{3},       \frac{2}{11},       \frac{6}{9}

\frac{16}{6},   \frac{15}{21},     \frac{4}{22},       \frac{2}{3},       \frac{12}{9}

 

Exercise 3

Write the reciprocals of the following fractions:

\frac{2}{3},   \frac{5}{2},     -\frac{3}{7},     5,     \frac{4}{11},       \frac{1}{8}

 

Exercise 4

Write the sign > or <, to create a correct statement.

\frac{3}{7} \square \frac{3}{9},    \frac{2}{5} \square \frac{6}{5},           \frac{3}{9} \square \frac{3}{4},           \frac{2}{7} \square \frac{5}{7}

 

Exercise 5

Write the sign > or <, to create a correct statement.

\frac{2}{3} \square \frac{3}{5},      \frac{2}{5} \square \frac{3}{7}\frac{5}{7} \square \frac{6}{8},      \frac{4}{3} \square \frac{5}{4}

 

Exercise 6

Order the following fractions from smallest to largest:

\frac{5}{12}\frac{2}{15}\frac{5}{4}\frac{7}{5}

 

Exercise 7

Classify the following fractions as either proper or improper fraction:

\frac{2}{3}\frac{5}{6}\frac{8}{5}\frac{7}{9}\frac{5}{2}\frac{5}{12}\frac{3}{4}\frac{7}{5}

 

 

Exercise 8

Solve:

5\frac{1}{4} + 1 \frac{1}{6}

 

Exercise 9

Solve using two different methods:

\frac{1}{2} \cdot (\frac{3}{4} + \frac{1}{8})

 

Exercise 10

Solve:
1.  (3 + \frac{1}{4}) - (2 + \frac{1}{6})

2. \frac{1}{2}: (\frac{1}{4} + \frac{1}{3})

3.   (\frac{5}{3} - 1) \cdot (\frac{7}{2} - 2)

4.  (\frac{3}{4} + \frac{1}{2}) : (\frac{5}{3} + \frac{1}{6})

 

 

Exercise 11

Solve:

\frac{2}{3} : [5 : (\frac{2}{4} + 1) - 3 (\frac{1}{2} - \frac{1}{4})]

 

 

Exercise 12

Perform the divisions:

1 : \frac{2}{3}

3 : \frac {1}{2}

\frac{3}{5} : \frac{1}{2}

 

Solution of exercise 1

Associate the following fractions with the corresponding amount of minutes in an hour:

\frac{1}{2}\cdot 60 = 30 minutes

\frac{1}{4}\cdot 60 = 15 minutes

\frac{3}{4}\cdot 60 = 45 minutes

\frac{1}{10}\cdot 60 = 6 minutes

\frac{1}{12}\cdot 60 = 5 minutes

\frac{1}{3}\cdot 60 = 20 minutes

Solution of exercise 2

Find the pairs of equivalent fractions and place them in pairs:

\frac{4}{3},   \frac{5}{7},     \frac{8}{3},       \frac{2}{11},       \frac{6}{9}

\frac{16}{6},   \frac{15}{21},     \frac{4}{22},       \frac{2}{3},       \frac{12}{9}

\frac{2}{3} = \frac{12}{9}      4 \cdot 9 = 3 \cdot 12    36 = 36

\frac{5}{7} = \frac{15}{21}      5 \cdot 21 = 7 \cdot 15        105 = 105

\frac{8}{3} = \frac{16}{6}       8 \cdot 6 = 3 \cdot 16       48 = 48

\frac{2}{11} = \frac{4}{22}    2 \cdot 22 = 4 \cdot 11        44 = 44

\frac{6}{9} = \frac{2}{3}         6 \cdot 3 = 9 \cdot 2           18 = 18

 

Solution of exercise 3

Write the reciprocals of the following fractions:

\frac{2}{3},   \frac{5}{2},     -\frac{3}{7},     5,     \frac{4}{11},       \frac{1}{8}

\frac{3}{2},   \frac{2}{5},     -\frac{7}{3},     \frac{1}{5},     \frac{11}{4},      8

 

Solution of exercise 4

Write the sign > or <, to create a correct statement.

\frac{3}{7} \square \frac{3}{9},    \frac{2}{5} \square \frac{6}{5},        \frac{3}{9} \square \frac{3}{4}\frac{2}{7} \square \frac{5}{7}

\frac{3}{7} > \frac{3}{9},    \frac{2}{5} < \frac{6}{5},        \frac{3}{9} < \frac{3}{4}\frac{2}{7} <\frac{5}{7}

 

Solution of exercise 5

Write the sign > or <, to create a correct statement.

\frac{2}{3} \square \frac{3}{5},      \frac{2}{5} \square \frac{3}{7}\frac{5}{7} \square \frac{6}{8},      \frac{4}{3} \square \frac{5}{4}

\frac{2}{3}> \frac{3}{5},      \frac{2}{5}< \frac{3}{7}\frac{5}{7} <\frac{6}{8},      \frac{4}{3} >\frac{5}{4}

Solution of exercise 6

Order the following fractions from smallest to largest:

\frac{5}{12}\frac{2}{15}\frac{5}{4}\frac{7}{5}

We will make the denominators same by multiplying every fraction by a constant.

\frac{25}{60}\frac{8}{60}\frac{75}{60}\frac{84}{60}

\frac{2}{12} < \frac{5}{12} < \frac{5}{4} < \frac{7}{5}

 

Solution of exercise 7

Classify the following fractions as either proper or improper:

\frac{2}{3}\frac{5}{6}\frac{8}{5}\frac{7}{9}\frac{5}{2}\frac{5}{12}\frac{3}{4}\frac{7}{5}

 

Proper: \frac{2}{3},      \frac{5}{6},      \frac{7}{9},       \frac{5}{12},       \frac{3}{4}

Improper:      \frac{8}{5},        \frac{5}{2},        \frac{7}{5}

 

Solution of exercise 8

Solve:

5 \frac{1}{4} + 1 \frac{1}{6}

= \frac{5 \cdot 4 + 1}{4} + \frac{1 \cdot 6 + 1}{6} = \frac{21}{4} + \frac{7}{6} = \frac{63 + 14}{12} = \frac{77}{12}

 

Solution of exercise 9

Solve using two different methods:

\frac{1}{2} \cdot (\frac{3}{4} + \frac{1}{8})

= \frac{1}{2} \cdot (\frac{3}{4} + \frac{1}{8}) = \frac{1}{2} \cdot (\frac{6 + 1} {8}) = \frac{1}{2} \cdot \frac{7}{8} = \frac{7}{16}

 

Solution of exercise 10

Solve:

(3 + \frac{1}{4}) - (2 + \frac{1}{6}) = 3 + \frac{1}{4} - 2 - \frac{1}{6} = 1 + \frac{1}{4} - \frac{1}{6} = \frac{12 + 3 - 2}{12} = \frac{13}{12}

= \frac{1}{2}: (\frac{1}{4} + \frac{1}{3})

\frac{1}{2} : (\frac{1}{4} + \frac{1}{3}) = \frac{1}{2} : (\frac{3 + 4}{12}) = \frac{1}{2} : \frac{7}{12} = \frac{12}{14} = \frac{6}{7}

(\frac{5}{3} - 1) \cdot (\frac{7}{2} - 2) = (\frac{5 - 3}{2}) \cdot (\frac{7 - 4}{2}) = \frac{2}{3} \cdot \frac{3}{2} = \frac{6}{6} = 1

=(\frac{3}{4} + \frac{1}{2}) : (\frac{5}{3} + \frac{1}{6})

=(\frac{3}{4} + \frac{1}{2}) : (\frac{5}{3} + \frac{1}{6}) = (\frac{3 + 2}{4}) : (\frac{10 + 1}{6}) = \frac{5}{4} : \frac{11}{6} = \frac{30}{44} = \frac{15}{22}

 

Solution of exercise 11

Solve:

\frac{2}{3} : [ 5 : (\frac{2}{4} + 1) - 3 (\frac{1}{2} - \frac{1}{4})]

= \frac{2}{3}: [ 5 : (\frac{2 + 4} {4}) - 3 ( \frac{2 - 1}{4})]

= \frac{2}{3} : (5 : \frac{6}{4} - 3 \cdot \frac{1}{4})

= \frac{2}{3} : (\frac{10}{3} - \frac{3}{4})

\frac{2}{3} : (\frac{40 - 19}{12}) = \frac{2}{3} : \frac{31}{12} = \frac{24}{93} = \frac{8}{31}

Solution of exercise 12

Perform the divisions:

\frac{1}{2} : 3 = \frac{1}{6}

2   3 : \frac{1}{2} = 6

3   \frac{3}{5} : \frac{1}{2} = \frac{6}{5}

Need a Maths teacher?

Did you like the article?

1 Star2 Stars3 Stars4 Stars5 Stars 5.00/5 - 1 vote(s)
Loading...

Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.