Tag: calculations and mental strategies 4

Questions Related to calculations and mental strategies 4

Evaluate the square root of $\displaystyle \frac{0.342\times 0.684}{0.000342\times 0.000171}$.

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

  1. $1000$

  2. $1500$

  3. $2000$

  4. $2500$

Show answer
Correct Option: C
Explanation:

Consider the given fraction $\dfrac { 0.342\times 0.684 }{ 0.000342\times 0.000171 }$ and find the square root as follows:

 
$\sqrt { \dfrac { 0.342\times 0.684 }{ 0.000342\times 0.000171 }  } \ =\sqrt { \dfrac { 342\times 684 }{ 342\times 171 } \times \dfrac { 1000000\times 1000000 }{ 1000\times 1000 }  } \quad \quad \quad \quad \quad \quad \quad \left{ \because \quad 0.1=\dfrac { 1 }{ 10 }  \right} \ =\sqrt { 4\times 1000000 } \ =\sqrt { 4000000 } \ =\sqrt { { \left( 2000 \right)  }^{ 2 } } \ =2000$

Hence, the square root of $\dfrac { 0.342\times 0.684 }{ 0.000342\times 0.000171 }$ is $2000$.

The value of $\displaystyle \frac{3.157\times 4126\times 3.198}{63.972\times 2835.121}$ is closest to

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

  1. $0.002$

  2. $0.02$

  3. $0.2$

  4. $2$

Show answer
Correct Option: C
Explanation:

The expression approximately =$\displaystyle \frac{3.2\times 4126\times 3.2}{64\times 2835}=0.232=0.2 (approx)$

A student was asked to simplify $\displaystyle \frac{0.6\times 0.6\times 0.6+0.5\times 0.5\times 0.5+0.1\times 0.1-0.09}{0.6\times 0.6+0.5\times 0.5+0.1\times 0.1-0.41}$ and his answer was 0.6 By what per cent was his answer wrong

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

  1. 25%

  2. 100%

  3. 50%

  4. 120%

Show answer
Correct Option: C
Explanation:

$\displaystyle \frac{0.6\times 0.6\times 0.6+0.5\times 0.5\times

0.5+0.1\times 0.1-0.09}{0.6\times 0.6+0.5\times 0.5+0.1\times

0.1-0.41}$


$\dfrac{0.216+0.125+0.01-0.09}{0.36+0.25+0.01-0.41}= \dfrac{0.261}{0.21} = 1.2$

Student got answer as $0.6$

Hence His Answer was wrong with $\dfrac{0.6}{1.2}\times 100= 50$%

The square root of $\frac {(0.75)^3}{1-(0.75)}+(0.75+(0.75)^2+1)$ is

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

  1. 1

  2. 2

  3. 3

  4. 4

Show answer
Correct Option: B
Explanation:

$\frac {(.75)^3+(1)^3-(.75)^3}{1-(0.75)}=\frac {1}{.25}=4$
square root $=2$

If x and y are positive numbers such that x + y = 1, which of the following could be the value of 100x + 200y?
I. 80
II. 140
III. 199

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

  1. II only

  2. III only

  3. I and II

  4. I and III

  5. II and III

Show answer
Correct Option: E
Explanation:

Given x+y=1  So 100x+100y=100 and 200x+200y =200

So       100 < 100x + 200y <200
II and III satisfies this situation So correct answer will be Option E

Evaluate:


$\displaystyle \frac{(6.4)^{2}-(5.4)^{2}}{(8.9)^{2}+(8.9\times 2.2)+(1.1)^{2}}$

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

  1. $0.118$

  2. $0.112$

  3. $0.110$

  4. $0.104$

Show answer
Correct Option: A
Explanation:

Given exp =$\displaystyle \frac{(6.4+5.4)(6.4-5.4)}{(8.9+1.1)^{2}}=\frac{11.8\times1 }{100}=0.118$

Simplify: $12.28 \times 1.5 - 36 \div 2.4$

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

  1. $3.24$

  2. $3.42$

  3. $4.32$

  4. $4.23$

Show answer
Correct Option: B
Explanation:

$\displaystyle 12.28\times 1.5-\frac{36}{2.4}=18.42-15=3.42$

The value of the following is $\displaystyle \frac{(0.44)^{2}+(0.06)^{2}+(0.024)^{2}}{(0.044)^{2}+(0.006)^{2}+(0.0024)^{2}}$

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

  1. $0.100$

  2. $0.01$

  3. $100$

  4. $1$

Show answer
Correct Option: C

$\displaystyle \frac{(0.22)^{3}+(0.11)^{3}+(0.32)^{3}}{(0.66)^{3}+(0.96)^{3}+(0.33)^{3}}-\frac{(0.32)^{3}+(0.45)^{3}-(0.77)^{3}}{81(0.32)(0.45)(0.77)}$ equals

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

  1. 1

  2. $\displaystyle \frac{1}{11}$

  3. 0

  4. -1

Show answer
Correct Option: C
Explanation:

$\frac{(0.22)^{3}+(0.11)^{3}+(0.32)^{3}}{(0.66)^{3}+(0.96)^{3}-(0.33)^{3}}+\frac{(0.32)^{3}+(0.45)^{3}-(0.77)^{3}}{81(0.32)(0.45)(0.77)}$
$=\frac { 8(0.11)^{ 3 }+(0.11)^{ 3 }+(0.32)^{ 3 } }{ 216(0.11)^{ 3 }+27(0.32)^{ 3 }+27(0.11)^{ 3 } } -\frac { (0.32)^{ 3 }+(0.45)^{ 3 }-(0.32+0.45)^{ 3 } }{ 81(0.32)(0.45)(0.77) } $
$=\frac { 9(0.11)^{ 3 }+(0.32)^{ 3 } }{ 243(0.11)^{ 3 }+27(0.32)^{ 3 } } -\frac { (0.32)^{ 3 }+(0.45)^{ 3 }-(0.32+0.45)^{ 3 } }{ 81(0.32)(0.45)(0.77) } $
$=\frac { 9(0.11)^{ 3 }+(0.32)^{ 3 } }{ 27{ 9(0.11)^{ 3 }+(0.32)^{ 3 }}  } -\frac { (0.32)^{ 3 }+(0.45)^{ 3 }-[(0.32)^{ 3 }+(0.45)^{ 3 }+3(0.32)(0.45)(0.32)+(0.45) }{ { 81(0.32)(0.45)(0.77) } } $
$=\frac{1}{27}-\frac{1}{27}$
$=0$

What is the value of $(7.5 \times 7.5 + 37.5 + 2.5 \times 2.5) ?$

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

  1. $30$

  2. $60$

  3. $80$

  4. $100$

Show answer
Correct Option: D
Explanation:

$(7.5 \times 7.5 + 37.5 + 2.5 \times 2.5) $

$=(7.5)^{2}+2\times 7.5\times 2.5+(2.5)^{2}$
$ =(7.5+2.5)^{2}$         ....[Using $a^2+2ab+b^2 = (a+b)^2]$
$=10^{2}$
$=100$