Quantitative Aptitude

Number System and Simplification

585 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 equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

If the fractions $\cfrac{3}{5}$,$\cfrac{2}{11}$, $\cfrac{4}{7}$, $\cfrac{1}{3}$, $\cfrac{5}{6},$ and $\cfrac{3}{8}$are arranged in the ascending order which fraction will be at the 3rd place ?

  1. $\cfrac{1}{3}$
  2. $\cfrac{3}{5}$
  3. $\cfrac{2}{11}$
  4. $\cfrac{3}{8}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

LCM of the denominators of given rational numbers i.e. 5, 11, 7, 3, 6, and 8 = 9240

Now by equating the denominators we get, 
$\dfrac { 3 }{ 5 } =\dfrac { 5652 }{ 9240 }$

$\dfrac { 2 }{ 11 } =\dfrac { 1680 }{ 9240 }$

$\dfrac { 4 }{ 7 } =\dfrac { 5280 }{ 9240 }$

$\dfrac { 1 }{ 3 } =\dfrac { 3080 }{ 9240 }$

$\dfrac { 5 }{ 6 } =\dfrac { 7700 }{ 9240 }$

$\dfrac { 3 }{ 8 } =\dfrac { 3465 }{ 9240 }$
 On seeing the rational numbers it is clear that the rational number at third position in ascending order is $\dfrac { 3465 }{ 9240 } \  i.e.\dfrac { 3 }{ 8 }$
So, correct answer is option D. 

Multiple choice maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

The fraction equivalent to $\displaystyle \frac{1}{2}$ is

  1. $\displaystyle \frac{2}{4}$
  2. $\displaystyle \frac{3}{6}$
  3. $\displaystyle \frac{8}{16}$

  4. all the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\displaystyle \frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}$
$\displaystyle \frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}$
$\displaystyle \frac{1}{2} = \frac{1 \times 8}{2 \times 8} = \frac{8}{16}$
So, $\displaystyle \frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{8}{16}$

Multiple choice maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

Which of the following fractions is less than $\displaystyle \frac{7}{8}$ and greater than $\displaystyle \frac{1}{3}$?

  1. $\displaystyle \frac{1}{4}$
  2. $\displaystyle \frac{23}{24}$
  3. $\displaystyle \frac{11}{12}$
  4. $\displaystyle \frac{17}{24}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\displaystyle \frac{1}{3} = 0.333000,$ $\displaystyle \frac{7}{8} = 0.875$
$\displaystyle \frac{1}{4} = 0.25,$ $\displaystyle \frac{23}{24} = 0.9583000,$ $\displaystyle \frac{11}{12} = 0.9166000$
$\displaystyle \frac{17}{24} = 0.7083000$
Since $0.7083000 \displaystyle \left ( =\frac{17}{24} \right )$ is greater than 
$0.333000 \displaystyle \left ( =\frac{1}{3} \right )$ and less than $0.875 \displaystyle \left ( =\frac{17}{24} \right )$$\displaystyle \left ( =\frac{7}{8} \right )$
Therefore $\displaystyle \frac{17}{24}$ lies between $\displaystyle \frac{1}{3}$ and $\displaystyle \frac{7}{8}$

Multiple choice maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

Which of the following fractions is the largest ?

  1. $\displaystyle \frac{13}{16}$
  2. $\displaystyle \frac{7}{8}$
  3. $\displaystyle \frac{31}{40}$
  4. $\displaystyle \frac{63}{80}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\displaystyle \frac{13}{16}=\frac{13\times 5}{16\times 5}=\frac{65}{80}, \frac{7\times 10}{8\times 10}=\frac{70}{80},\frac{31}{40}=\frac{31\times 2}{40\times 2}$
$\displaystyle =\frac{62}{80}$ and last fraction is $\displaystyle =\frac{63}{80}$
Out of these the largest fraction is $\displaystyle \frac{70}{80}$ $\displaystyle =\frac{7}{8}$

Multiple choice maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

$\displaystyle \frac{4}{15}$of $\displaystyle \frac{5}{7}$ of a number is greater than $\displaystyle \frac{4}{9}$ of $\displaystyle \frac{2}{5}$ of the same number by $8$. What is half of that number?

  1. $630$
  2. $315$
  3. $210$
  4. $105$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the number be $x$

So from the question, we have
$\dfrac{4}{15}.\dfrac{5}{7}.x-\dfrac{4}{9}.\dfrac{2}{5}.x=8$
$\Rightarrow \dfrac {4x}{21}-\dfrac {8x}{45}=8$
$\Rightarrow x=\dfrac {24\times 7\times 15}{4}$
$\Rightarrow x=6\times 7\times 15$
$\Rightarrow x=630$
Half of that number is equal to $315$.

Multiple choice maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

Compare $\displaystyle \frac {9}{16}$ .......... $\displaystyle \frac {13}{5}$

  1. $=$
  2. $>$
  3. $<$

  4. None
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given fractions are

$\displaystyle \frac{9}{16} = 0.5625$

$\displaystyle \frac{13}{5}=2.6$

Hence$ \displaystyle \frac{9}{16}<\frac{13}{5}$

OR
$9\times 5<13\times16$
 $ \displaystyle \frac{9}{16}<\frac{13}{5}$

Multiple choice maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

By how much is $\displaystyle \frac {19}{20}$ greater than $\displaystyle \frac {2}{20}$ ?

  1. $\displaystyle \frac {21}{10}$
  2. $\displaystyle \frac {21}{40}$
  3. $\displaystyle \frac {17}{20}$
  4. $\displaystyle \frac {17}{40}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\displaystyle \frac {19}{20}\, -\, \displaystyle \frac {2}{20}\, =\, \displaystyle \frac {19-2}{20}\, =\, \displaystyle \frac {17}{20}$

Multiple choice maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

Which fractions are in order from the least to the greatest ? 

  1. $\displaystyle{\frac{1}{2}, \frac{2}{3}, \frac{2}{6}}$
  2. $\displaystyle{\frac{1}{2}, \frac{2}{6}, \frac{2}{3}}$
  3. $\displaystyle{\frac{2}{6}, \frac{2}{3}, \frac{1}{2}}$
  4. $\displaystyle{\frac{2}{6}, \frac{1}{2}, \frac{2}{3}}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
We are going to convert fraction into decimal.
$\Rightarrow$  $\dfrac{1}{2}=0.5$

$\Rightarrow$  $\dfrac{2}{3}=0.67$

$\Rightarrow$  $\dfrac{2}{6}=0.33$

Arranging above decimals in ascending order $=0.33,\,0.5,\,0.67$
Which can be written as $\dfrac{2}{6},\dfrac{1}{2},\dfrac{2}{3}$
$\therefore$   The fractions are in order from least to greatest are $\dfrac{2}{6},\dfrac{1}{2},\dfrac{2}{3}.$
Multiple choice maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

The fraction equivalent to $\displaystyle \frac{1}{2}$ is

  1. $\displaystyle \frac{2}{4}$
  2. $\displaystyle \frac{3}{6}$
  3. $\displaystyle \frac{8}{16}$

  4. all the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\displaystyle \frac{1}{2}=\frac{1\times 2}{2\times 2}=\frac{2}{4}$


$\displaystyle \frac{1}{2}=\frac{1\times 3}{2\times 3}=\frac{3}{6}$

$\displaystyle \frac{1}{2}=\frac{1\times 8}{2\times 8}=\frac{8}{16}$

So, $\displaystyle \frac{1}{2}=\frac{2}{4}=\frac{3}{6}=\frac{8}{16}$

Multiple choice maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

The fraction equivalent to $\displaystyle \frac{1}{2}$ is ____

  1. $\displaystyle \frac{3}{6}$
  2. $\displaystyle \frac{5}{10}$
  3. $\displaystyle \frac{9}{18}$

  4. all the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Doing the simplest form of all these options..

$\dfrac{3}{6} = \dfrac{1}{2}$
$\dfrac{5}{10}= \dfrac{1}{2}$ 
$\dfrac{9}{18} = \dfrac{1}{2}$
hence option D is correct..

Multiple choice maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

$\displaystyle\frac{15}{\square}$ is a fraction that lies between $\displaystyle\frac{1}{7}$ and $\displaystyle\frac{1}{8}$. What is the missing whole number in the box?

  1. $112$
  2. $56$
  3. $32$
  4. $65$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the missing number be $x$

$\dfrac{1}{7}<\dfrac{15}{x}<\dfrac{1}{8}$
Multiplying  numerator and denominator by 15
$\therefore$ $\dfrac{15}{105}<\dfrac{15}{x}<\dfrac{15}{120}$
So any number between $105$ and $120$ will be the value of $x$.
Hence the correct answer is option A

Multiple choice maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

Which of the following statements is true?

  1. $\displaystyle\frac{5}{7} <\frac{7}{9} <\frac{9}{11} <\frac
    {11}{13}$
  2. $\displaystyle\frac{11}{13} < \frac{9}{11} < \frac{7}{9} < \frac{5}{7}$
  3. $\displaystyle\frac{5}{7} < \frac{11}{13} < \frac{7}{9} < \frac{9}{11}$
  4. $\displaystyle\frac{5}{7} < \frac{9}{11} <\frac{11}{13} < \frac{7}{9}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\dfrac{5}{7} , \dfrac{7}{9} , \dfrac{9}{11}, \dfrac{11}{13}$

making same deomenator,
$\dfrac{5}{7}= \dfrac{5\times 9 \times 11 \times 13}{7\times 9\times 11\times 13}$
$=\dfrac{6435}{9009}$ ...........................(1)


$\dfrac{7}{9}= \dfrac{7\times 7\times 11\times 13}{9\times 7\times 11\times 13}$

$=\dfrac{7007}{9009}$ ............................(2)

$\dfrac{9}{11}=\dfrac{9\times 7\times 9\times 13}{7\times 9\times 11\times 13}$

$=\dfrac{7371}{9009}$................................(3)

$\dfrac{11}{13}=\dfrac{11\times 7 \times 9 \times 11}{7 \times 9 \times 11 \times 13}$

$=\dfrac{7623}{9009}$.................................(4)

From equations (1), (2), (3) and (4);
$\dfrac{5}{7}$  <  $\dfrac{7}{9} $< $\dfrac{9}{11}$ < $\dfrac{11}{13}$

Multiple choice maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

Which of the following fractions has the highest value $3/5$, $4/3$, $2/5$, $1/2$.

  1. $3/5$
  2. $4/3$
  3. $2/5$
  4. $1/2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Given fractions, $\dfrac{3}{5},  \dfrac{4}{3},  \dfrac{2}{5},  \dfrac{1}{2}$

LCM of $2, 3$ and $5$ is $30 $

So, 
$\dfrac{3}{5} \times \dfrac{6}{6} = \dfrac{18}{30}$

$\dfrac{4}{3} \times \dfrac{10}{10} = \dfrac{40}{30}$

$\dfrac{2}{5} \times \dfrac{6}{6} = \dfrac{12}{30}$

$\dfrac{1}{2} \times \dfrac{15}{15} = \dfrac{15}{30}$

As in above fraction all denominators are same and $40$ is the biggest numerator. 

So, $\dfrac{4}{3}$ is the biggest fraction.
Multiple choice maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

A student was asked to solve the fraction $\cfrac { \cfrac { 7 }{ 3 } +\left( 1\cfrac { 1 }{ 2 }  \times\cfrac { 5 }{ 3 } \right) }{ 2+1\cfrac { 2 }{ 3 }  } $ and his answer was $\cfrac{1}{4}$. By how much was his answer wrong?

  1. $1$
  2. $\cfrac{1}{55}$
  3. $\cfrac{1}{220}$

  4. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
$ \dfrac{\dfrac{7}{3}+(1\dfrac{1}{2}\times \dfrac{5}{3})}{2+1\dfrac{2}{3}}$

$ = \dfrac{\dfrac{7}{3}+(\dfrac{3}{2}\times \dfrac{5}{3})}{(2+\dfrac{5}{3})}$

$  = \dfrac{\dfrac{7}{3}+\dfrac{5}{2}}{\dfrac{11}{3}} = \dfrac{14+15}{6}\times \dfrac{3}{11} = \dfrac{29}{22}$

$ \Rightarrow $ His answer was wrong by

$ \dfrac{29}{22}-\dfrac{1}{4} = \dfrac{116-22}{88} = \dfrac{94}{88} = \dfrac{47}{44}$