Exercise 1

Calculate:

1.  27 + 3 · 5 – 16 =

2. 27 + 3 – 45 : 5 + 16 =

3. (2 · 4 + 12) (6 − 4) =

4. 3 · 9 + (6 + 5 – 3) – 12 : 4 =

5.  2 + 5 · (2 · 3)³ =

6.  440 − [30 + 6 (19 − 12)] =

7.  2{4 [7 + 4 (5 · 3 − 9)] − 3 (40 − 8)} =

8. 7 · 3 + [6 + 2 · (2³ : 4 + 3 · 2) – 7 · \sqrt{4}] + 9 : 3 =

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Exercise 2

Calculate:

1. (7 − 2 + 4) − (2 − 5) =

2. 1 − (5 − 3 + 2) − [5 − (6 − 3 + 1) − 2]=

3. −12 · 3 + 18 : (−12 : 6 + 8) =

4. 2 · [( −12 + 36) : 6 + (8 − 5) : (−3)] − 6 =

5. [(−2)5 · (−3)²] : (−2)² =

6. 6 + {4 − (17 − (4 · 4)] + 3} − 5 =

Exercise 3

Calculate:

1. (3 − 8) + [5 − (−2)] =

2. 5 − [6 − 2 − (1 − 8) − 3 + 6] + 5 =

3. 9 : [6 : (− 2)] =

4. [(−2)5 − (−3)³]² =

5. (5 + 3 · 2 : 6 − 4 ) · (4 : 2 − 3 + 6) : (7 − 8 : 2 − 2)² =

6. [(17 − 15)³ + (7 − 12)²] : [(6 − 7) · (12 − 23)] =

Exercise 4

Calculate:

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 5

Calculate:

\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 6

Calculate:

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

Exercise 7

Calculate:

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

Exercise 8

Calculate:

[(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:

1. 27 + 3 · 5 – 16 =

= 27 + 15 − 16 = 26

 

2. 27 + 3 – 45 : 5 + 16=

27 + 3 – 9 + 16 = 37

 

3. (2 · 4 + 12) (6 − 4) =

= (8 + 12) (2) = 20 · 2 = 40

 

4. 3 · 9 + (6 + 5 – 3) – 12 : 4 =

= 27 + 8 – 3 = 32

 

5. 2 + 5 · (2 ·3)³ =

= 2 + 5 · (6)³ = 2 + 5 · 216 = 2 + 1080 = 1082

 

6. 440 − [30 + 6 (19 − 12)] =

= 440 − (30 + 6 · 7)] = 440 − (30 + 42) =

= 440 − (72) = 368

 

7. 2{4[7 + 4 (5 · 3 − 9)] − 3 (40 − 8)} =

= 2[4 (7 + 4 · 6) − 3 (32)] = 2[4 (7 + 24) − 3 (32)]=

2[4 (31) − 3 (32)]= 2 (124 − 96)= 2 (28)= 56

 

8.  7 · 3 + [6 + 2 · (2³ : 4 + 3 · 2) – 7 · \sqrt{4}] + 9 : 3 =

= 21 + [ 6 + 2 · (2+ 6) – 14] +3 =

= 21 + ( 6 + 2 · 8 – 14) +3 =

= 21 + ( 6 + 16 – 14) + 3 =

= 21 + 8 + 3 = 32

 

Solution of exercise 2

Calculate:

1. (7 − 2 + 4) − (2 − 5) = 9 − (−3) = 9 + 3 =12

 

2. 1 − (5 − 3 + 2) − [5 − (6 − 3 + 1) − 2] =

= 1 − (4) − [5 − (4) − 2] =

= 1 − (4) − (5 − 4 − 2)=

= 1 − (4) − (−1) =

= 1 − 4 + 1 = −2

 

3. −12 · 3 + 18 : (−12 : 6 + 8) =

= −12 · 3 + 18 : (−12 : 6 + 8) =

− 12 · 3 + 18 : (−2 + 8) =

= −12 · 3 + 18 : 6 =

= −36 + 3 = −33

 

4.  2 · [( −12 + 36) : 6 + (8 − 5) : (−3)] − 6 =

= 2 · [24 : 6 +3 : (−3)] − 6 =

= 2 · [ 4 + (−1)] − 6 =

2 · 3 − 6 = 6 − 6 = 0

 

5. [(−2)5 · (−3)²] : (−2)² =

(−32 · 9) : 4 = −288 : 4 = −72

 

6. 6 + {4 − (17 − (4 · 4)] + 3} − 5 =

= 6 + {4 − [(17 − (4 · 4)] + 3} − 5 =

6 + [4 − (17 − 16) + 3] − 5 =

= 6 + (4 − 1 + 3) − 5 =

6 + 6 − 5 = 7

 

Solution of exercise 3

Calculate:

1. (3 − 8) + [5 − (−2)] = −5 + (5 + 2) = −5 + 7= 2

 

2. 5 − [6 − 2 − (1 − 8) − 3 + 6] + 5 =

= 5 − [6 − 2 − (−7) − 3 + 6] + 5 =

= 5 − [6 − 2 + 7 − 3 + 6] + 5 =

= 5 − 14 + 5 = −4

 

3.  9 : [6 : (−2)] = 9 : (−3) = −3

 

4. [(−2)5 − (−3)³]² =

= [− 32 − (−27)] = (−32 + 27)² =

= (−5)² = 25

 

5. (5 + 3 · 2 : 6 − 4 ) · (4 : 2 − 3 + 6) : (7 − 8 : 2 − 2)² =

= (5 + 6 : 6 − 4 ) · (4 : 2 − 3 + 6) : (7 − 8 : 2 − 2)² =

= (5 + 1 − 4 ) · (2 − 3 + 6) : (7 − 4 − 2)² =

= 2 · 5 : 1² =

= 2 · 5 : 1 = 10 : 1 = 10

 

6. [(17 − 15)³ + (7 − 12)²] : [(6 − 7) · (12 − 23)] =

= [(2)³ + (−5)²] : [(−1) · (−11)] =

= (8 + 25) : [(−1) · (−11)] =

= (8 + 25) : 11 =

= 33: 11 = 3

 

Solution of exercise 4

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{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 5

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 6

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 7

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 \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}) = - \frac{10}{1} = -10

 

Solution of exercise 8

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}

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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.