Exercise 1

Calculate:

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

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

Convert the following numbers to a fraction:

0.0051,       0.\overline{051}          0.0\overline{51}

Exercise 3

Convert the following numbers to a fraction:

0.037,       0.0\overline{37},        0.03\overline{7},    1.\overline{0001},   1.0001,     1.0\overline{001}

Exercise 4

Convert to fraction form:

1 5. \overline{6} + 0.1

0.1 + 0. \overline{1} - 0.0 \overline{1}

3. 2. \overline{3} : 1.5

Exercise 5

Solve:

1 \frac{\frac{3}{2} + \frac{1}{4}}{\frac{5}{6} - \frac{1}{3}}

2 \frac{ - 1 + \frac{3}{4} - \frac{1}{3}}{2 - \frac{1}{4}}

 

Exercise 6

Solve:

1 - \frac{1}{1 - \frac{1}{1 - \frac{1}{2}}}

 

Exercise 7

Simplify the following:

(\frac{2}{3})^2 \cdot (\frac{2}{3})^3

(\frac{2}{3})^{-2} \cdot (\frac{2}{3})^3

(\frac{2}{3})^2 \cdot (\frac{2}{3})^{-3}

(\frac{2}{3})^{-2} \cdot (\frac{2}{3})^{-3}

(\frac{2}{3})^{-2} \cdot (\frac{3}{2})^{-3}

(\frac{2}{3})^2 : (\frac{2}{3})^3

(\frac{2}{3})^{-2} : (\frac{2}{3})^{-3}

(\frac{2}{3})^2 : (\frac{2}{3})^{-3}

(\frac{2}{3})^{-2} : (\frac{2}{3})^{-3}

10  (\frac{3}{2})^{-3} \cdot (\frac{2}{3})^{-3}

11  [(\frac{2}{3})^2]^{-3}

12  (\frac{4}{9})^{-2} : (\frac{27}{8})^{-3}

Exercise 8

Solve:

\frac {(\frac{2}{3})^ 5 (\frac{2}{3})^ 0 (\frac{2}{3})^ {-3} (\frac{81}{16})^ {-2}} { (\frac{3}{2})^ {-5} (\frac{2}{3}) [ (\frac{2}{3})^ 5 ] ^{-2} (\frac{8}{27})^ 3}

Exercise 9

Solve:

(\frac{2 - \frac{1}{5})^2}{(3 - \frac{2}{9})^{-1}} :  \frac{(\frac{6}{7} \cdot \frac{5}{4} - \frac{2}{7} : \frac{1}{2})^3}{(\frac {1}{2} - \frac {1}{3} \cdot \frac{1}{4} : \frac{1}{5})} - 5 \frac{1}{7}

Exercise 10

Solve:

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

Exercise 11

Solve:

[{\frac{2}{3} - \frac{1}{9}) + 13 (\frac{2}{3} - 1)^2] : [ (\frac{1}{2} - 1) : 2 \frac{1}{2}]

Exercise 12

Solve

[(2 - 1 \frac{3}{5})^2 + (\frac{5}{8} - \frac{3}{4}) - (\frac{6}{5} \cdot \frac{1}{3})^4 \cdot (7\frac{1}{2})^3] : (5 - \frac{6}{5})

 

 

Solution of exercise 1

Calculate:

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 2

Convert the following numbers to a fraction:

0.0051,       0.\overline{051},         0.05\overline{1}

0.0051 = \frac{51}{10000}

0.\overlone{051} = \frac{51}{1000}

0.05\overline{1} = \frac{51 - 5} {900} = \frac{46}{900} = \frac{23}{450}

 

Solution of exercise 3

Convert the following numbers to a fraction:

0.037,    0.\overline{037},         0.03\overline{7},        1.\overline{0001},      1.00011.0\overline{001}

0.037 = \frac{37}{1000}

0.\overline{037} = \frac{37}{999}

0.03\overline{7} = \frac{37 - 3}{900} = \frac{34} {900} = \frac{17}{450}

1.\overline{0001} = \frac{10001 - 1}{9999} = \frac{1000}{9999}

1.0001 = \frac{10001}{10000}

1.0\overline{001} = \frac{10001 - 10}{9990} = \frac{9991}{9990}

 

Solution of exercise 4

Convert to fraction form:

1. 5.\overline{6} + 0.1 = \frac{56 - 5}{9} + \frac{1}{10} = \frac{51}{9} + \frac{1}{10} = \frac{510 + 9}{90} = \frac{519}{90}

 

2. 0.1 + 0. \overline{1} - 0.0 \overline{1} = \frac{1}{10} + \frac{1}{9} - \frac{1}{90} = \frac{9 + 10 - 1}{90} = \frac{18}{90} = \frac{2}{10} = \frac{1}{5}

3.  2.\overline{3} : 1.5 = \frac{23 - 2}{9} : \frac{15}{10} = \frac{21}{9} : \frac{3}{2} = \frac{42}{27} = \frac{14}{9}

 

Solution of exercise 5

Solve:

1. \frac{\frac{3}{2} + \frac{1}{4}} {\frac{5}{6} - \frac{1}{3}}

= \frac{\frac{6 + 1}{4}}{\frac{5 - 2}{6}} = \frac{\frac{7}{4}}{\frac{3}{6}} = \frac{7}{4} : \frac{3}{6} = \frac{7}{4} : \frac{1}{2} = \frac{14}{4} = \frac{7}{2}

2. \frac{-1 + \frac{3}{4} - \frac{1}{3}} {2 - \frac{1}{4}}

= \frac{\frac{-12 + 9 - 4}{12}} {\frac{8 - 1} {4}}

= \frac{\frac{-7}{12}} {\frac{7}{4}}

= \frac{-7}{12} : \frac{7}{4}

= -\frac{28}{84}

= -\frac{7}{21}

= - \frac{1}{3}

 

Solution of exercise 6

Solve:

1 - \frac{1}{1 - \frac{1}{1 - \frac{1}{2}}}

= 1 - \frac{1} {1 - \frac{1}{\frac{2 - 1} {2}}}

= 1 - \frac{1}{1 - \frac{1}{\frac{1}{2}}}

= 1 - \frac{1}{1- 2}

= 1 - \frac{1}{-1}

= 1 + 1 = 2

 

Solution of exercise 7

Simplify the following:

1.  (\frac{2}{3})^2 \cdot (\frac{2}{3})^3 = (\frac{2}{3})^5

2. (\frac{2}{3})^{-2} \cdot (\frac{2}{3})^3 = \frac{2}{3}

3. (\frac{2}{3})^2 \cdot (\frac{2}{3})^{-3} = (\frac{2}{3})^{-1} = \frac{3}{2}

4. (\frac{2}{3})^{-2} \cdot (\frac{2}{3})^{-3} = (\frac{2}{3})^{-5} = (\frac{3}{2})^5
5.  (\frac{2}{3})^{-2} \cdot (\frac{3}{2})^{-3} = (\frac{2}{3})^ {-2} \cdot (\frac{2}{3})^3 = \frac{2}{3}
6. (\frac{2}{3})^2 : (\frac{2}{3})^3 = (\frac{2}{3})^{-1} = \frac{3}{2}
7.  (\frac{2}{3})^{-2} : (\frac{2}{3})^3 = (\frac{2}{3})^{-5} = (\frac{3}{2})^5
8. (\frac{2}{3})^2 : (\frac{2}{3})^{-3} = (\frac{2}{3})^5
9.  (\frac{2}{3})^{-2} : (\frac{2}{3})^{-3} = \frac{2}{3}
10. (\frac{3}{2})^{-2} : (\frac{2}{3})^{-3} = (\frac{2}{3})^2 : (\frac{2}{3})^{-3} = (\frac{2}{3})^5
11.  [(\frac{2}{3})^2]^3 = (\frac{2}{3})^6
12. (\frac{4}{9})^{-2} : (\frac{27}{8})^{-3} = [(\frac{2}{3})^2]^{-2} : [(\frac{3}{2})^3]^{-3} = (\frac{2}{3})^{-4} : (\frac{3}{2})^{-9}

= (\frac{2}{3})^{-4} : (\frac{2}{3})^9 = (\frac{2}{3})^{-13} = (\frac{3}{2})^{13}

Solution of exercise 8

Solve:

\frac{(\frac{2}{3})^5(\frac{2}{3})^0 (\frac{2}{3})^{-3} (\frac{81}{16})^{-2}} { (\frac{3}{2})^{-5} (\frac{2}{3}) [(\frac{2}{3})^5]^{-2} (\frac{8}{27})^3}

 

= \frac{(\frac{2}{3})^5(\frac{2}{3})^0 (\frac{2}{3})^{-3} [(\frac{3}{2})^4]^{-2}} { (\frac{3}{2})^{-5} (\frac{2}{3}) [(\frac{2}{3})^5]^{-2} [(\frac{2}{3})^3]^3}

 

= \frac{(\frac{2}{3})^5(\frac{2}{3})^0 (\frac{2}{3})^{-3} (\frac{3}{2})^{-8}} { (\frac{3}{2})^{-5} (\frac{2}{3}) (\frac{2}{3})^{10} (\frac{2}{3}^9)}

 

= \frac{(\frac{2}{3})^5 (\frac{2}{3})^0 (\frac{2}{3})^{-3} (\frac{2}{3})^8} {(\frac{2}{3})^5(\frac{2}{3})(\frac{2}{3})^{10}(\frac{2}{3})^9}

 

= \frac{(\frac{2}{3})^ {10}} {\frac{2}{3}^{25}} = (\frac{2}{3})^{-15} = (\frac{3}{2})^15

 

Solution of exercise 9

Solve:

\frac{(2 - \frac{1}{5})^2} {(3 - \frac{2}{9})^{-1}} : \frac{(\frac{6}{7} \cdot \frac{5}{4} - \frac{2}{7} : \frac{1}{2})^3} {(\frac{1}{2} - \frac{1}{3} \cdot \frac{1}{4} : \frac{1}{5})} - 5 \frac{1}{7}

 

= \frac{(\frac{10 - 1}{5})^2} {(\frac{27 - 2}{9})^{-1}} : \frac{(\frac{30}{28} - \frac{4}{7})^3}{(\frac{1}{2} - \frac{1}{12} : \frac{1}{5})} - \frac{35 + 1}{7}

 

= \frac{(\frac{9}{5})^2} {(\frac{25}{9})^{-1}} : \frac{(\frac{15}{14} - \frac{4}{7})^3} {(\frac{1}{2} - \frac{5}{12})} - \frac{36}{7}

 

= \frac{(\frac{9}{5})^2}{(\frac{25}{9})^{-1}} : \frac{(\frac{15 - 8}{14})^3} {(\frac{6 - 5}{12})}} - \frac{36}{7}

 

= \frac{(\frac{9}{5})^2} {(\frac{25}{9})^{-1}} : \frac{(\frac{1}{2})^3} { \frac{1}{12}} - \frac{36}{7}

 

= \frac{\frac{81}{25}} {\frac{9}{25}} :\frac{\frac{1}{8}}{\frac{1}{12}} - \frac{36}{7} = \frac{81}{9} : \frac{12}{8} - \frac{36}{7}

 

= 9 : \frac{3}{2} - \frac{36}{7} = \frac{18}{3} - \frac{36}{7} = 6 - \frac{36}{7} = \frac{42 - 36}{7} = \frac{6}{7}

 

Solution of exercise 10

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 - 9}{12}) = \frac{2}{3} : \frac{31}{12} = \frac{24}{93} = \frac{8}{31}

 

Solution of exercise 11

Solve:

[(\frac{2}{3} - \frac{1}{9}) + 13 (\frac{2}{3} - 1)^2] : [ (\frac{1}{2} - 1) : 2\frac{1}{2}]

= [(\frac{6 - 1}{9} + 13 (\frac{2 - 3}{3})^2]:[(\frac{1-2}{2}): \frac{2\cdot 2 + 1}{2}]

=[\frac{5}{9} + 13 (\frac{-1}{3})^2]:(-\frac{1}{2}:\frac{5}{2})

=(\frac{5}{9} + 13 \cdot \frac{1}{9}):(-\frac{1}{2}:\frac{5}{2})

=(\frac{5}{9} + \frac{13}{9}) : (-\frac{2}{10})

=\frac{18}{9} :(-\frac{1}{5}) = 2 :(-\frac{1}{5}) = -10

 

Solution of exercise 12

Solve:

[(2 - 1\frac{3}{5})^2 + (\frac{5}{8} - \frac{3}{4}) - (\frac{6}{5} \cdot \frac{1}{3})^4 \cdot (7\frac{1}{2})^3] : (5 - \frac{6}{5})

=[(2 - \frac{8}{5})^2 + (\frac{5}{8} - \frac{3}{4}) - (\frac{6}{15})^4 \cdot (\frac{15}{2})^3]: (5 - \frac{6}{5})

= [(\frac{2}{5})^2 + \frac{5}{8} - \frac{3}{4} - (\frac{2}{5})^4 \cdot (\frac{15}{2})^3] : \frac{19}{5}

= (\frac{4}{25} + \frac{5}{8} - \frac{3}{4} - \frac{54000}{5000}) : \frac{19}{5} = (\frac{4}{25} + \frac{5}{8} - \frac{3}{4} - \frac{54}{5}) : \frac{19}{5}

= \frac{32 + 125 - 150 - 2160}{200} : \frac{19}{5}

= \frac{-2153}{200} : \frac{19}{5} = \frac{10765}{3800} = -\frac{2153}{760}

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.