Tag: part number

Questions Related to part number

Convert the following into fraction.
$22.5\%$

maths part number dividing fractions division of a fractions division of a fraction
    • $\dfrac{9}{40}$

  2. $\dfrac{225}{100}$

  3. $\dfrac{22}{100}$

  4. $\dfrac{5}{100}$

Show answer
Correct Option: A
Explanation:
     $22.5$%
$=\dfrac{22.5}{100}$
$=\dfrac{48}{2}\times \dfrac{1}{100}$
$=\dfrac{9}{40}$

Evaluate the following :

$\displaystyle  8 \times \dfrac {\dfrac{5}{24}}{\dfrac {7}{12}} $.

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

  1. $\displaystyle \frac {5 }{24}$

  2. $\displaystyle \frac {20}{7}$

  3. $\displaystyle \frac {2}{7}$

  4. $\displaystyle \frac {21}{5}$

Show answer
Correct Option: B
Explanation:

Given, $ 8 \times \displaystyle \frac {\frac {5}{24}}{\frac {7}{12}} $

$ \therefore 8 \times \displaystyle \frac {\frac {5 }{24}}{\frac {7}{12}} = 8 \times \frac {5\times 12}{7 \times 24}   $

$=\displaystyle \frac {5 \times 4}{7}$

$= \displaystyle \frac {20}{7} $

$I = \displaystyle \frac{3}{4}\div \frac{5}{6}$ 

$II = 3\displaystyle \div $[($4\displaystyle \div 5$)$\displaystyle \div 6$]
$III = [3\displaystyle \div (4\displaystyle \div 5)]\displaystyle \div 6$
$IV = 3\displaystyle \div 4(5\displaystyle \div 6)$
Select the correct option from the following.

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

  1. I and II are equal

  2. I and IV are equal

  3. I and III are equal

  4. All are equal

Show answer
Correct Option: B
Explanation:

$ I=\cfrac{3}{4}\times \cfrac{6}{5}=\cfrac{9}{10}$


$II=3\div \left [ \cfrac{4}{5}\times \cfrac{1}{6} \right ]=3\times \cfrac{15}{2}=\cfrac{45}{2}$
$III=\left [ 3\div \cfrac{4}{5} \right ]\div 6=3\times \cfrac{5}{4}\times \cfrac{1}{6}=\cfrac{5}{8}$
$ IV=3\div 4\times\cfrac{5}{6}=3\times \cfrac{3}{10}=\cfrac{9}{10}$

Hence, $I$ and $IV$ are equal.

The least fraction that must be added to $\displaystyle1\frac{1}{3}\div 1\frac{1}{2}\div 1\frac{1}{9}$  to make the result an integer is:

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

  1. $\displaystyle\frac{4}{5}$

  2. $\displaystyle\frac{3}{5}$

  3. $\displaystyle\frac{2}{5}$

  4. $\displaystyle\frac{1}{5}$

Show answer
Correct Option: D
Explanation:

$\displaystyle 1\frac{1}{3}\div 1\frac{1}{2}=\frac{4}{3}\div \frac{3}{2}\div \frac{10}{9}$
$\displaystyle =\frac{4}{3}\times \frac{2}{3}\div \frac{10}{9}=\frac{8}{9}\times \frac{9}{10}=\frac{4}{5}$
$\displaystyle \therefore \frac{1}{5}$ should be added to $\displaystyle \frac{4}{5}$ to make it an integer

The number of positive fractions m/n such that $1/3< m/n < 1$ and having the property that the fraction remains the same by adding some positive integer to the numerator and multiplying the denominator by the same positive integer is

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

  1. $1$

  2. $3$

  3. $6$

  4. infinite

Show answer
Correct Option: B
Explanation:

$m, n$ are integer
$1/3 < m/n < 1 $...(i)
$\displaystyle \frac{m + \alpha}{n \alpha} = \frac{m}{n}        n \neq 0$
$\alpha = \displaystyle \frac{m}{m - 1} = +$ve integer
$\therefore m = 2$
Using equation (i)
$n = 3, 4, 5$
$\therefore \displaystyle \frac{m}{n}= \frac{2}{3} , \frac{2}{4}, \frac{2}{5}$

$\dfrac{25 \% \, of  \ 50\% \ of \ 100 \%}{25 \,of \,100 \times 50 \%\, of \,100 }$ 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