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This is the second of our many quizzes on Integer operations. Click on this to access more such competitive quizzes on Number system.

Integer operations Quiz 2

mathematics

 Solve $\dfrac{{[\dfrac{{( - 18 - 9)}}{3}]}}{2} + [\dfrac{{( - 27)}}{9} + 9]$ and mark the correct answer.

 Use the properties $( - a) \times 1 =  - a$ and $\dfrac{a}{{ - 1}} =  - a$ to solve the question. 

  Applying the properties $( - a) \times 1 =  - a$ and $\dfrac{a}{{ - 1}} =  - a$. we get, $ \\  \dfrac{{[\dfrac{{( - 18 - 9)}}{3}]}}{2} + [\dfrac{{( - 27)}}{9} + 9] \\   \Rightarrow \dfrac{{\dfrac{{ - 27}}{3}}}{2} + [ - 3 + 9] \\   \Rightarrow  - \dfrac{9}{2} + 6 \\   \Rightarrow \dfrac{3}{2} \\  $

 In $5$ years the length of the island has changed by $ - 230$ cm. If the length is changed the same every year. Calculate the rate of change in length each year. 

 Use the property $\dfrac{a}{{ - 1}} =  - a$.

  Change in length of island in $5$ years $= - 230cm$ $ \\ $ Rate of change in length of island per year $= \dfrac{{ - 230}}{5} =  - 46$

 Some number which is added to $ - 12$ gives $42$. Divide that number by $2$ and then add $3$ to it. Which is the correct answer?

 Use the property $( - a) \times 1 =  - a$ to solve the problem.

Let the number added be $x$. According to the question we can write, $ \\   x + ( - 12) = 42 \\   \Rightarrow x = 54 \\  $ Then the number is divided by  $2$ and $3$ is added to it. we get, $ \\ \dfrac{{54}}{2} + 3 = 27 + 3 = 30$

 Solve $\dfrac{{[16 - 12( - 3)]}}{2} + [ - 11 - 9] = \dfrac{{[21 - 9]x}}{3}$ for $x$.

 Use the properties $( - a) \times 1 =  - a$ and $\dfrac{a}{{ - 1}} =  - a$. 

 Applying the properties $( - a) \times 1 =  - a$ and $\dfrac{a}{{ - 1}} =  - a$. we get, $  \dfrac{{[16 - 12( - 3)]}}{2} + [ - 11 - 9] = \dfrac{{[21 - 9]x}}{3} \\   \Rightarrow \dfrac{{[16 + 36]}}{2} + [ - 20] = \dfrac{{12x}}{3} \\   \Rightarrow 26 - 20 = 4x \\   \Rightarrow 6 = 4x \\   \Rightarrow x = \dfrac{3}{2} \\  $

 If the age of Firoz $5$ years ago was $24$ then what will be his age after $5$ years.

 First find the present age of Firoz then find his age after 5 year.

 Let the present age of Firoz be $x$ $ \\ $ Now since the age of Firoz 5 years ago was 24, hence we can write this as  $ \\ x - 5 = 24 \\ $ By solving we get $ \\  x - 5 = 24 \\   \Rightarrow x = 24 + 5 \\   \Rightarrow x = 29 \\  $ Hence we can write the present age of Firoz is $29$ year. $ \\ $ Therefore the age of Firoz after $5$ years will be $ \\  y = 29 + 5 \\   \Rightarrow y = 34 \\  $