Tag: maths

Questions Related to maths

The value of $\dfrac { 0.1\times 0.1\times 0.1+0.02\times 0.02\times 0.02 }{ 0.2\times 0.2\times 0.2+0.04\times 0.04\times 0.04 } $ is:

maths calculations and mental strategies 4 mental additions and subtractions of decimals multiplication and division of decimals mental multiplication and division

  1. $0.0125$

  2. $0.125$

  3. $0.25$

  4. $0.5$

Show answer
Correct Option: B
Explanation:

Given expression $=\dfrac { { \left( 0.1 \right)  }^{ 3 }+{ \left( 0.02 \right)  }^{ 3 } }{ { 2 }^{ 3 }\left[ { \left( 0.1 \right)  }^{ 3 }+{ \left( 0.02 \right)  }^{ 3 } \right]  } =\dfrac { 1 }{ 8 } =0.125$

Evaluate : $\dfrac { { \left( 2.39 \right)  }^{ 2 }-{ \left( 1.61 \right)  }^{ 2 } }{ 2.39-1.61 } $

maths calculations and mental strategies 4 mental additions and subtractions of decimals multiplication and division of decimals mental multiplication and division

  1. $2$

  2. $4$

  3. $6$

  4. $8$

Show answer
Correct Option: B
Explanation:

Given Expression $=\dfrac { { a }^{ 2 }-{ b }^{ 2 } }{ a-b } =\dfrac { \left( a+b \right) \left( a-b \right)  }{ \left( a-b \right)  } =\left( a+b \right) =\left( 2.39+1.61 \right) =4$

$\dfrac { \left( 0.1667 \right) \left( 0.8333 \right) \left( 0.3333 \right)  }{ \left( 0.2222 \right) \left( 0.6667 \right) \left( 0.1250 \right)  } $ is approximately equal to:

maths calculations and mental strategies 4 mental additions and subtractions of decimals multiplication and division of decimals mental multiplication and division

  1. $2$

  2. $2.40$

  3. $2.43$

  4. $2.50$

Show answer
Correct Option: D
Explanation:

Given expression $=\dfrac { \left( 0.3333 \right)  }{ \left( 0.2222 \right)  } \times \dfrac { \left( 0.1667 \right) \left( 0.8333 \right)  }{ \left( 0.6667 \right) \left( 0.1250 \right)  } $


                             $=\dfrac { 3333 }{ 2222 } \times \dfrac { \dfrac { 1 }{ 6 } \times \dfrac { 5 }{ 6 }  }{ \dfrac { 2 }{ 3 } \times \dfrac { 125 }{ 1000 }  } $

                             $=\left( \dfrac { 3 }{ 2 } \times \dfrac { 1 }{ 6 } \times \dfrac { 5 }{ 6 } \times \dfrac { 3 }{ 2 } \times 8 \right) $

                             $=\dfrac { 5 }{ 2 } $
                             $= 2.50$

If $\dfrac { 144 }{ 0.144 } =\dfrac { 14.4 }{ x } $, then the value of $x$ is:

maths calculations and mental strategies 4 mental additions and subtractions of decimals multiplication and division of decimals mental multiplication and division

  1. $0.0144$

  2. $1.44$

  3. $14.4$

  4. $144$

Show answer
Correct Option: A
Explanation:

$\dfrac { 144 }{ 0.144 } =\dfrac { 14.4 }{ x } $

$\Rightarrow \dfrac { 144\times 1000 }{ 144 } =\dfrac { 14.4 }{ x } $

$\Rightarrow x=\dfrac { 14.4 }{ 1000 } =0.0144$

$0.75$ of a number is $1200$. What is $\displaystyle\frac{5}{8}$ of that number?

maths calculations and mental strategies 4 mental additions and subtractions of decimals multiplication and division of decimals mental multiplication and division

  1. $1000$

  2. $1060$

  3. $880$

  4. $8002$

Show answer
Correct Option: A
Explanation:

Let the required number be $x$
According to question, we have
$0.75$ of $x$ $=1200$
$\Rightarrow \displaystyle\frac{75}{100}\times x=1200$
$\Rightarrow \displaystyle x=1200\times \frac{100}{75}=1600$
Therefore, required number is $1600$.
Now, $\displaystyle\frac{5}{8}$ of the number $=\displaystyle\frac{5}{8}\times 1600=1000$.

Thus the required number is $1000$.

Solve for $x$:

$35.453 =\dfrac{34.968x+ 36.956(100- x)}{100}$

maths calculations and mental strategies 4 mental additions and subtractions of decimals multiplication and division of decimals mental multiplication and division

  1. $7.56$

  2. $756$

  3. $75.6$

  4. $0.756$

Show answer
Correct Option: C
Explanation:

$\\35.453\times 10=34.968x+36.956(100-x)\\ 3545.3=(34.968-36.956)x+3695.6\\\therefore x=(\frac{3545.3-3695.6}{34.968-36.956})\\ (\frac{-150.3}{-1.988})=75.6$

The terminating decimal expansion of the number $\dfrac{{337}}{{125}}$ is ........

maths calculations and mental strategies 4 mental additions and subtractions of decimals multiplication and division of decimals mental multiplication and division

  1. $2.666$

  2. $2.966$

  3. $2.696$

  4. $2.698$

Show answer
Correct Option: C
Explanation:

$\dfrac{337}{125}=2.696$

Find the value of $(1.01)^{5}$ correct upto $3$ decimal places

maths calculations and mental strategies 4 mental additions and subtractions of decimals multiplication and division of decimals mental multiplication and division

  1. $1.015$

  2. $2.625$

  3. $1.651$

  4. $1.051$

Show answer
Correct Option: D
Explanation:
${ \left( 1.01 \right)  }^{ 5 }$

$=1.01\times 1.01\times 1.01\times 1.01\times 1.01$

$=1.051$

The value of $\dfrac{8492 \times 3.72}{47.8 \times 52.24}$ is

maths calculations and mental strategies 4 mental additions and subtractions of decimals multiplication and division of decimals mental multiplication and division

  1. $1.265$

  2. $14.75$

  3. $1.475$

  4. $12.65$

Show answer
Correct Option: A

$\displaystyle \frac{24.23\times 1.423\times 34.21}{521.3\times 413.32\times 2.53}$ is same is 

maths calculations and mental strategies 4 mental additions and subtractions of decimals multiplication and division of decimals mental multiplication and division

  1. $\displaystyle \frac{2423\times 1423\times 3421}{5213\times 41332\times 253}$

  2. $\displaystyle \frac{2423\times 1423\times 3421}{5213\times 4133.2\times 2.53}$

  3. $\displaystyle \frac{2.423\times 14.23\times 342.1}{521.3\times 4133.2\times 2.53}$

  4. $\displaystyle \frac{24.23\times 14.23\times 3.421}{5.213\times 41332\times 0.253}$

Show answer
Correct Option: C
Explanation:

Option c is correct answer.

 
As in that expression total numbers after decimal is same as the given expression.


$\displaystyle \frac{24.23\times 1.423\times 34.21}{521.3\times 413.32\times 2.53}$  $=\displaystyle \frac{2.423\times 14.23\times 342.1}{521.3\times 4133.2\times 2.53}$