Tag: mental additions and subtractions of decimals

Questions Related to mental additions and subtractions of decimals

Which of the following is equal to  $1?$

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

  1. $\dfrac { 0.304 \times 20 } { 304 \times 2 }$

  2. $\dfrac { 0.304 \times 20 } { 3 \cdot 04 \times 2 }$

  3. $\dfrac { 0.304 \times 2 } { 30 \cdot 4 \times 2 }$

  4. $\dfrac { 0.304 \times 2 } { 304 \times 0 \cdot 2 }$

Show answer
Correct Option: B
Explanation:

$\begin{array}{l} \dfrac { { 0.304\times 20 } }{ { 3.04\times 2 } }  \ =\dfrac { { 304\times 20\times 100 } }{ { 304\times 2\times 1000 } }  \ =1 \ Hence, \ B\, is\, the\, correct\, answer. \end{array}$

What decimal of an hour is a second ?

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

  1. 0.0025

  2. 0.00027

  3. 0.0256

  4. 0.000126

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Correct Option: B
Explanation:

Required decimal = $\dfrac{1}{60 \times 60}=\dfrac{1}{3600}=0.00027$

If $4.175 = \displaystyle\frac { 1 }{ 0.2395 } $, then what is $\displaystyle\frac { 1 }{ 0.0004175 } $ equal to ?

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

  1. 0.2395

  2. 2395

  3. 2.395

  4. 23.95

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Correct Option: B
Explanation:

$\displaystyle\frac { 1 }{ 0.0004175 } = \displaystyle\frac { 1 }{ \displaystyle\frac { 4.175 }{ 10000 }  } = \displaystyle\frac { 10000 }{ 4.175 } = \displaystyle\frac { 10000 }{ \displaystyle\frac { 1 }{ 0.2395 }  } $

$= 10000 \times 0.2395 = 2395$

Evaluate : $\left( 78.34+96.68-14.44 \right) \div 4$.

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

  1. $34.145$

  2. $16.58$

  3. $40.145$

  4. $45.346$

Show answer
Correct Option: C
Explanation:

$\left( 78.34+96.68-14.44 \right) \div 4=160.58\div 4=40.145$

$\displaystyle \frac{\left ( 0.35 \right )^{2}-\left ( 0.03 \right )^{2}}{0.19}=? $

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

  1. 0.32

  2. 0.48

  3. 0.76

  4. 0.64

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Correct Option: D
Explanation:

$\dfrac{(0.35)^{2}-(0.03)^{2}}{0.19}$=$\dfrac{(0.35+0.03)(0.35-0.03)}{0.19}$    $[a^2-b^2=(a+b)(a-b)]$


$=\dfrac{(0.38)(0.32)}{0.19}$


$=2\times{0.32}$

$=0.64$

So the correct answer will option D

What is $\displaystyle 0.\overline{09}\times7.\overline{3}$ equal to ?

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

  1. $\displaystyle 0.\overline{6}$

  2. $\displaystyle 0.\overline{7}$

  3. 0.6

  4. 0.7

Show answer
Correct Option: A
Explanation:

$\displaystyle 0.\overline{09}\times7.\overline{3}=\frac{9}{99}\times7\frac{3}{9}=\frac{9}{99}\times\frac{66}{9}=\frac{6}{9}=0.\overline{6}$

What is the value of $\displaystyle \left ( 4.7\times13.26+4.7\times9.43+4.7\times77.31 \right )?$

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

  1. $470$

  2. $235$

  3. $705$

  4. $940$

Show answer
Correct Option: A
Explanation:

given that 

we have find the the value of the expression .

$4.7\times 13.26 +4.7 \times 9.43 +4.7 \times 77.31$

Taking $4.7$ common 

$= 4.7 \times [13.26 + 9.43 +77.31]$

$= 4.7 \times [100]$

$ = 470$

So option $A $ is correct


$\displaystyle \frac{\left ( 2.3 \right )^{3}-0.027}{\left ( 2.3 \right )^{2}+0.69+0.09}=? $

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

  1. $2.6$

  2. $2$

  3. $2.33$

  4. $2.8$

Show answer
Correct Option: B
Explanation:
$\dfrac { { \left( 2.3 \right)  }^{ 3 }-0.027 }{ { \left( 2.3 \right)  }^{ 2 }+0.69+0.09 } \\ =\dfrac { 12.167-0.027 }{ 5.29+0.69+0.09 } \\ =\dfrac { 12.14 }{ 6.07 } \\ =2$
So, correct answer is option B.

$58+\cfrac{3}{100}+\cfrac{7}{1000}=..........$

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

  1. $58.0037$

  2. $58.37$

  3. $58.037$

  4. none of these

Show answer
Correct Option: C
Explanation:

$58+\cfrac{3}{100}+\cfrac{7}{1000}$
$=58+\cfrac{0}{10}+\cfrac{3}{100}+\cfrac{7}{1000}=58.037$

Which of the following is equal to $1$?

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

  1. $\displaystyle \frac{(0.11)^{2}}{(1.1)^{2}\times 0.1}$

  2. $\displaystyle \frac{(1.1)^{2}}{11^{2}\times (0.01)^{2}}$

  3. $\displaystyle \frac{(0.011)^{2}}{1.1^{2}\times 0.01^2}$

  4. $\displaystyle \frac{(0.11)^{2}}{1.1^{2}\times 0.01}$

Show answer
Correct Option: C
Explanation:
$\Rightarrow \cfrac{(0.11)^{2}}{(1.1)^{2}\times 0.1}=\cfrac{0.0121}{1.21\times 0.1}=\cfrac{0.0121}{0.121}=0.1$

$\Rightarrow \cfrac{(1.1)^{2}}{11^{2}\times (0.01)^{2}}=\cfrac{1.21}{121\times 0.0001}=\cfrac{0.01}{0.0001}=100$

$\Rightarrow \cfrac{(0.011)^{2}}{(1.1)^{2}\times (0.01)^{2}}=\cfrac{0.000121}{1.21\times 0.0001}=1$

$\Rightarrow \cfrac{(0.11)^{2}}{1.1^{2}\times 0.01}=\cfrac{0.0121}{1.21\times 0.01}=\cfrac{0.0121}{1.21}=1.21$