Tag: mental multiplication and division

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Questions Related to mental multiplication and division

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

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

  1. $1000$
  2. $1500$
  3. $2000$
  4. $2500$
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $2000$.

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

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

  1. 25%

  2. 100%

  3. 50%

  4. 120%
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $\dfrac{0.6}{1.2}\times 100= 50$%

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

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

  1. II only

  2. III only

  3. I and II

  4. I and III

  5. II and III
Reveal answer Fill a bubble to check yourself
E Correct answer
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

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

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

  1. $0.100$
  2. $0.01$
  3. $100$
  4. $1$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The expression is (0.44^2 + 0.06^2 + 0.024^2) / (0.044^2 + 0.006^2 + 0.0024^2). Since 0.44 = 10 * 0.044, 0.06 = 10 * 0.006, and 0.024 = 10 * 0.0024, the numerator is 10^2 times the denominator, which equals 100.

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

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

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

  3. 0

  4. -1
Reveal answer Fill a bubble to check yourself
C Correct answer
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) } } $
$=\frac{1}{27}-\frac{1}{27}$
$=0$

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

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

  1. $30$
  2. $60$
  3. $80$
  4. $100$
Reveal answer Fill a bubble to check yourself
D Correct answer
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 $a^2+2ab+b^2 = (a+b)^2]$
$=10^{2}$
$=100$