Tag: division of a fractions

Questions Related to division of a fractions

$\dfrac{25 \% \, of  \ 50\% \ of \ 100 \%}{25 \,of \,100 \times 50 \%\, of \,100 }$ is equal to ______ .

maths part number dividing fractions division of a fractions division of a fraction

  1. $ 0.0001\%$

  2. $ 0.1\%$

  3. $ 0.01\%$

  4. $ 1\%$

Show answer
Correct Option: D
Explanation:

Given $\cfrac {25\%\quad of\quad 50\%\quad of\quad 100\%}{25\quad of\quad 100\times 50\%\quad of\quad 100}$

So, first solving solving numerator
$\cfrac {25}{100}$ of $\cfrac {50}{100}$ of $\cfrac {100}{100}$ 
$\implies \cfrac {25}{100}\left(\cfrac {50}{100}\left(\cfrac {100}{100}\right)\right)\quad equation (1)$  
Now taking denominator
$25$ of $100\times 50\%$ of $100$ 
So, $25$ of $100$ means $\cfrac {25}{100}$ which is $\cfrac {1}{4}$
$50\%$ of $100=\cfrac {50}{100}\times 100=50$
So, denominator becomes $\cfrac {1}{4}\times 50\quad equation (2)$
$\cfrac {Numerator}{Denominator}=\cfrac {equation (1)}{equation (2)}$
$=\cfrac {\cfrac {25}{100}\left(\cfrac{50}{100}\left(\cfrac{100}{100}\right)\right)}{\cfrac {1}{4}\times 50}$
$=\cfrac {\cfrac {1}{4}\times \cfrac {1}{2}}{\cfrac {1}{4}\times 50}$
$=\cfrac {1}{2}\times 50$
In terms of percent $=\cfrac {1}{100}\times 100=1\%$

The least number among $\displaystyle \frac{4}{9}, \, \sqrt{\frac{9}{49}},$ 0.45 and $(0.8)^2$ is

maths part number dividing fractions division of a fractions division of a fraction

  1. $\displaystyle \frac{4}{9}$

  2. $\displaystyle \sqrt{\frac{9}{49}}$

  3. 0.45

  4. $(0.8)^2$

Show answer
Correct Option: B
Explanation:
: Decimal equivalents of the given numbers.
$\displaystyle \frac{4}{9} \, = \, 0.44; \, \sqrt{\frac{9}{49}} \, = \, \frac{3}{7} \, = \, 0.43$
$\displaystyle 0.45 \, and \, (0.8)^2 \, = \, 0.64$
$\displaystyle \therefore$ Least number is 0.43
$\displaystyle = \, \sqrt{\frac{9}{49}}$

If $a=3567, b=10, c=100, d=1000$ & $e=10000$ then $\frac{a}{b}+\frac{a}{c}-\frac{a}{d}+\frac{a}{e}$ is less than

maths part number dividing fractions division of a fractions division of a fraction

  1. $3.962937$

  2. $3962.937$

  3. $39.62937$

  4. $39629.37$

Show answer
Correct Option: B,D
Explanation:

Given, a=3567, b=10, c=10, d=1000, e=10000
$\frac{a}{b}+\frac{a}{c}-\frac{a}{d}+\frac{a}{e}$put the values a, b, c, d , e
in the above expression, we get
$=356.7+35.67-3.567+0.3597$
$=389.1597$

For $a = 4$, it is known that the value of the fraction $\dfrac{(a+2)x + a^2-1}{ax-2a +18}$ is independent of $x$. The other values of a for which this is the case, belong to the interval 

maths part number dividing fractions division of a fractions division of a fraction

  1. $[-\infty, -2]$

  2. $[-2, 0]$

  3. $[0, 2]$

  4. $[2, 4]$

  5. $[4, +\infty]$

Show answer
Correct Option: A
Explanation:

$\cfrac { \left( a+2 \right) x+{ a }^{ 2 }-1 }{ ax-2a+18 } $ is independent of x.

$\cfrac { a+2 }{ a } =\cfrac { { a }^{ 2 }-1 }{ 18-2a } \ 18a+36-2{ a }^{ 2 }-4a={ a }^{ 3 }-a\ { a }^{ 3 }+2{ a }^{ 2 }-15a-36=0\ { a }^{ 3 }-4{ a }^{ 2 }+6{ a }^{ 2 }-24a+9a-36=0\ (a-4)({ a }^{ 2 }+6a+9)=0\ \therefore a=-3,-3$ 
Other values of a belongs to $(-\infty ,-2]$

If $a=1\frac{3}{4}$ and $b=1\frac{2}{3}$ then the false statement is

maths part number dividing fractions division of a fractions division of a fraction

  1. $\frac{a}{b}=\frac{b}{a}$

  2. $a\div b \neq b \div a$

  3. $a\times b=b\times a$

  4. $a\div b=ab$

Show answer
Correct Option: A,D
Explanation:

$\frac{a}{b}=\frac{\frac{7}{4}}{\frac{5}{3}}$
$=\frac{21}{20}$

$\frac{b}{a}=\frac{\frac{5}{3}}{\frac{7}{4}}$
$=\frac{20}{21}$

Now check all the options

If $\dfrac{p}{q}=\bigg( \dfrac{2}{3}\bigg)^3 \div \bigg( \dfrac{3}{2}\bigg)^{-3}$ then the value of $\bigg( \dfrac{p}{q}\bigg)^{-10}=.............$

maths part number dividing fractions division of a fractions division of a fraction

  1. $1$

  2. $0$

  3. $-1$

  4. none of these

Show answer
Correct Option: A
Explanation:
  $\dfrac{p}{q}=\left ( \dfrac{2}{3} \right )^{3}\times \left ( \dfrac{3}{2} \right )^{3}$

  $\Rightarrow \dfrac{p}{q}=1$ 

  $\Rightarrow (7)^{-10}$

  $\Rightarrow 1$