Quantitative Aptitude

Number System and Simplification

548 Questions

Number system and simplification questions assess mathematical proficiency in handling fractions, decimals, and complex algebraic expressions. Test takers must simplify surds, calculate reciprocals, and solve intricate number pattern equations. This foundational quantitative aptitude topic is critical for achieving high scores in SSC and banking exams.

Fraction simplificationDecimal operationsSurds and indicesPercentage calculationsComplex number algebra

Number System and Simplification Questions

Multiple choice maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

If we multiply a fraction by itself, the fraction thus obtained is $\displaystyle\frac{16}{81}$. The original fraction is?

  1. $\displaystyle\frac{8}{27}$
  2. $\displaystyle 2\frac{2}{3}$
  3. $\displaystyle 2\frac{1}{3}$
  4. $\displaystyle\frac{4}{9}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the original fraction be $\dfrac{x}{y}$.

$\Rightarrow$  According to the given question,
$\Rightarrow$  $\dfrac{x}{y}\times \dfrac{x}{y}=\dfrac{16}{81}$

$\Rightarrow$  $\left(\dfrac{x}{y}\right)^2=\dfrac{16}{81}$
$\rightarrow$  Taking square root on both sides we get,
$\Rightarrow$  $\dfrac{x}{y}=\dfrac{4}{9}$

Multiple choice maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

If $\dfrac{m}{n} = \dfrac{4}{3}$ and $\dfrac{r}{t} = \dfrac{9}{14}$, the value of $\dfrac{3mr - nt}{4nt - 7mr}$ is:

  1. $-5\dfrac{1}{2}$
  2. -$ \dfrac{11}{14}$
  3. -$1 \dfrac{1}{4}$
  4. $\dfrac{11}{14}$

  5. none of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\cfrac { m }{ n } =\cfrac { 4 }{ 3 } ,\cfrac { r }{ t } =\cfrac { 9 }{ 14 } \ m=\cfrac { 4n }{ 3 } ,r=\cfrac { 9t }{ 14 } \ mr=\cfrac { 6nt }{ 7 } \ 3mr-nt=\cfrac { 18nt }{ 7 } -nt=\cfrac { 11nt }{ 7 } \ 4nt-7mr=4nt-6nt=-2nt\ \cfrac { 3mr-nt }{ 4nt-7mr } =-\cfrac { 11 }{ 14 } $

Multiple choice maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

If $\large{1\frac{2}{7}}$ of $\large{\frac{56}{63}}$ is simplified. Then the answer is

  1. $\large{\frac{8}{7}}$
  2. $\large{1\frac{1}{7}}$
  3. $\large{\frac{8}{5}}$
  4. $\large{1\frac{3}{5}}$
Reveal answer Fill a bubble to check yourself
A,B Correct answer
Explanation

$\large{1\frac{2}{7}}$ of $\large{\frac{56}{63}}$
$=\large{\frac{9}{7}} \times \large{\frac{56}{63}}$
$=\large{\frac{8}{7}}$ or $\large{1\frac{1}{7}}$.

Multiple choice maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

If $\dfrac {3}{4}$ of $\dfrac {1}{2}$ of a number is $60$ then the number is:

  1. $160$
  2. $400$
  3. $500$
  4. $700$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
let the number be $x$

now $\dfrac 34$ of $\dfrac 12$ of x is $60$

$\Rightarrow \dfrac { 3 }{ 4 } (\dfrac { 1 }{ 2 } (x))=60\\ \Rightarrow \dfrac { 3x }{ 8 } =60\\ \Rightarrow x=\dfrac { 60\times 8 }{ 3 } =160$ 
Multiple choice maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

$\dfrac{\dfrac { 540 }{ 11 } \times 7}{343\dfrac { 7 }{ 11 }}$ 

  1. 1

  2. 2

  3. 3

  4. 4
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\begin{array}{l} In\, \, L.H.S \ No.=\frac { { 540\times 7 } }{ { 11 } } \times \frac { { 11 } }{ { \left( { 343\times 11+7 } \right)  } }  \ \frac { { 540\times 7 } }{ { 7\left( { { 7^{ 2 } }\times 11+1 } \right)  } }  \ No.=\frac { { 540 } }{ { 539+1 } } =1 \end{array}$

Whole number is 1.

Multiple choice maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

Multiply $\dfrac{6}{13}$ by the reciprocal of $\dfrac{-7}{16}$

  1. $\dfrac{-95}{91}$
  2. $\dfrac{-96}{91}$
  3. $\dfrac{96}{91}$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Reciprocal of $\dfrac{-7}{16}$ is $\dfrac{-16}{7}$

Now $\dfrac{6}{13}\times$ Reciprocal of $\dfrac{-7}{16}$

$=\dfrac{6}{13}\times\dfrac{-16}{7}$

$=\dfrac{6\times -16}{13\times 7}=\dfrac{-96}{91}$
Multiple choice maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

Two-Third of a number and $\displaystyle \frac{25}{216}$ of its reciprocal are equal. What is the number?

  1. $\displaystyle \frac{25}{144}$
  2. $\displaystyle \frac{5}{12}$
  3. $\displaystyle \frac{144}{25}$
  4. $\displaystyle \frac{12}{5}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the number be x Given $\displaystyle \frac{2}{3}x=\frac{25}{216}\times\frac{1}{x}$
$\displaystyle\Rightarrow x^{2}=\frac{25}{216 _{72}}\times\frac{3^{1}}{2}=\frac{25}{144}$
$\displaystyle\Rightarrow x=\sqrt{\frac{25}{144}}=\frac{5}{12}$

Multiple choice maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

$\displaystyle \left ( 999\frac{999}{1000}\times 7 \right )$ is equal to 

  1. $\displaystyle 6993\frac{7}{1000}$
  2. $\displaystyle 7000\frac{7}{1000}$
  3. $\displaystyle 6633\frac{7}{1000}$
  4. $\displaystyle 6999\frac{993}{1000}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given expression $\displaystyle =\left ( 999+\frac{999}{1000} \right )\times7$
$\displaystyle=1000-1+1-\frac{1}{1000}\times7$
$\displaystyle=\left ( 1000-\frac{1}{1000} \right )\times7=7000-\frac{7}{1000}$
$\displaystyle=6999+1-\frac{7}{1000}=6999+\frac{993}{1000}$
$\displaystyle=6999\frac{993}{1000}$

Multiple choice maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

Reciprocal of $\displaystyle \frac {7}{5}$ is

  1. $1\displaystyle \frac {2}{5}$
  2. $\displaystyle \frac {5}{7}$
  3. $5\displaystyle \frac {2}{3}$
  4. $\displaystyle \frac {12}{5}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

We know that the reciprocal of any number $n$ is $\dfrac {1}{n}$. When we multiply a number by its reciprocal, we get $1$ as the answer. For example: $n\times \dfrac { 1 }{ n } =1$ 


Therefore, the reciprocal of  the given fraction $\dfrac {7}{5}$ is as follows:

$\dfrac { 1 }{ \dfrac { 7 }{ 5 }  } =\dfrac { 5 }{ 7 } \quad \quad \quad \quad \quad \quad \quad \left{ \because \quad \dfrac { 1 }{ \dfrac { 1 }{ x }  } =\dfrac { x }{ 1 }  \right}$ 

Hence, the reciprocal of $\dfrac {7}{5}$ is $\dfrac {5}{7}$.