Tag: mental multiplication and division

Questions Related to mental multiplication and division

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. $144$

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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. $8002$

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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. $12.65$

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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.


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

Simplify : $\displaystyle \frac{3.6\times 0.48\times 2.50}{0.12\times 0.09\times 0.5}$

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

  1. 80

  2. 800

  3. 8000

  4. 80,000

Show answer
Correct Option: B
Explanation:

$\displaystyle \frac{3.6\times 0.48\times 2.50}{0.12\times 0.09\times 0.5}=\frac{36\times 48\times 250}{12\times 9\times 5}=800 $


No of decimal places in num and den being equal

Which number is equal to
$\left ( \displaystyle \frac {0.1}{0.01}\, +\, \displaystyle \frac {0.01}{0.1} \right )\, ?$

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

  1. $10.1$

  2. $1.10$

  3. $1.01$

  4. $10.01$

Show answer
Correct Option: A
Explanation:

Let us first write the decimals as fractions as follows:


$0.1=\dfrac { 1 }{ 10 } \ 0.01=\dfrac { 1 }{ 100 }$ 

Now, the given expression $\dfrac { 0.1 }{ 0.01 } +\dfrac { 0.01 }{ 0.1 }$ can be solved as follows:
 
$\dfrac { 0.1 }{ 0.01 } +\dfrac { 0.01 }{ 0.1 } =\dfrac { \dfrac { 1 }{ 10 }  }{ \dfrac { 1 }{ 100 }  } +\dfrac { \dfrac { 1 }{ 100 }  }{ \dfrac { 1 }{ 10 }  } =\dfrac { \dfrac { 1 }{ 1 }  }{ \dfrac { 1 }{ 10 }  } +\dfrac { \dfrac { 1 }{ 10 }  }{ \dfrac { 1 }{ 1 }  } =10+\dfrac { 1 }{ 10 } =\dfrac { (10\times 10)+1 }{ 10 } =\dfrac { 100+1 }{ 10 } =\dfrac { 101 }{ 10 } =10.1$

Hence, $\dfrac { 0.1 }{ 0.01 } +\dfrac { 0.01 }{ 0.1 }=10.1$

Simplify : $\displaystyle \frac{0.2\times0.2+0.2\times0.02}{0.044}$

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

  1. $0.4$

  2. $0.2$

  3. $0.1$

  4. $1$

Show answer
Correct Option: D
Explanation:

We will first convert the decimals into fraction in the given fraction and then solve it as follows:


$\dfrac { 0.2\times 0.2+0.2\times 0.02 }{ 0.044 } =\dfrac { \left( \dfrac { 2 }{ 10 } \times \dfrac { 2 }{ 10 }  \right) +\left( \dfrac { 2 }{ 10 } \times \dfrac { 2 }{ 100 }  \right)  }{ \dfrac { 44 }{ 1000 }  } =\dfrac { \dfrac { 4 }{ 100 } +\dfrac { 4 }{ 1000 }  }{ \dfrac { 44 }{ 1000 }  } =\dfrac { \dfrac { 40+4 }{ 1000 }  }{ \dfrac { 44 }{ 1000 }  } =\dfrac { \dfrac { 44 }{ 1000 }  }{ \dfrac { 44 }{ 1000 }  } =1$

Hence, $\dfrac { 0.2\times 0.2+0.2\times 0.02 }{ 0.044 } =1$