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 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}$


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

Which of the following fraction is the smallest? $\dfrac{7}{6}, \dfrac{7}{9}, \dfrac{4}{5}, \dfrac{5}{7}$

  1. $\dfrac{7}{6}$
  2. $\dfrac{7}{9}$
  3. $\dfrac{4}{5}$
  4. $\dfrac{5}{7}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
let the fractions be a, b, c, d
$ \dfrac{a}{b} = \dfrac{7}{6}\times \dfrac{9}{7} = \dfrac{9}{6}> 1\Rightarrow a> b$
a is not smallest
$ \dfrac{b}{c} = \dfrac{7}{9}\times \dfrac{4}{5} = \dfrac{28}{45}< 1\Rightarrow c> b$
 c is not smallest
$ \dfrac{b}{d} = \dfrac{7}{9}\times \dfrac{7}{5} = \dfrac{49}{45}> 1\Rightarrow b> d$
$ \Rightarrow $ d  is smallest $\Rightarrow (D)$
Multiple choice maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

The fraction $\displaystyle \frac{3}{5}$ is found between which pair of fractions on a number line?

  1. $\displaystyle \frac{7}{10}$ and $\displaystyle \frac{3}{4}$
  2. $\displaystyle \frac{2}{5}$ and $\displaystyle \frac{1}{2}$
  3. $\displaystyle \frac{1}{3}$ and $\displaystyle \frac{5}{13}$
  4. $\displaystyle \frac{2}{7}$ and $\displaystyle \frac{8}{11}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

(a) Let us consider the first set of fraction $\dfrac { 7 }{ 10 } ,\dfrac { 3 }{ 4 }$ and another given fraction $\dfrac { 3 }{ 5 }$ 


Taking the LCM to make the denominators same of the above fractions, we have

$\dfrac { 7\times 2 }{ 10\times 2 } ,\dfrac { 3\times 4 }{ 5\times 4 } ,\dfrac { 3\times 5 }{ 4\times 5 } \\ =\dfrac { 14 }{ 20 } ,\dfrac { 12 }{ 20 } ,\dfrac { 15 }{ 20 } \\ \Rightarrow \dfrac { 12 }{ 20 } <\dfrac { 14 }{ 20 } <\dfrac { 15 }{ 20 } \\ \Rightarrow \dfrac { 3 }{ 5 } <\dfrac { 7 }{ 10 } <\dfrac { 3 }{ 4 }$   

Therefore, $\dfrac { 3 }{ 5 }$ does not lie between the first set of fraction $\dfrac { 7 }{ 10 } ,\dfrac { 3 }{ 4 }$.

(b) Now, consider the set of fraction $\dfrac { 2 }{ 5 } ,\dfrac { 1 }{ 2 }$ and another given fraction $\dfrac { 3 }{ 5 }$

Taking the LCM to make the denominators same of the above fractions, we have

$\dfrac { 2\times 2 }{ 5\times 2 } ,\dfrac { 3\times 2 }{ 5\times 2 } ,\dfrac { 1\times 5 }{ 2\times 5 } \\ =\dfrac { 4 }{ 10 } ,\dfrac { 6 }{ 10 } ,\dfrac { 5 }{ 10 } \\ \Rightarrow \dfrac { 4 }{ 10 } <\dfrac { 5 }{ 10 } <\dfrac { 6 }{ 10 } \\ \Rightarrow \dfrac { 2 }{ 5 } <\dfrac { 1 }{ 2 } <\dfrac { 3 }{ 5 }$     

Therefore, $\dfrac { 3 }{ 5 }$ does not lie between the set of fraction $\dfrac { 2 }{ 5 } ,\dfrac { 1 }{ 2 }$.

(c) Now, consider the set of fraction $\dfrac { 1 }{ 3 } ,\dfrac { 5 }{ 13 }$ and another given fraction $\dfrac { 3 }{ 5 }$


Taking the LCM to make the denominators same of the above fractions, we have

$\dfrac { 1\times 65 }{ 3\times 2 } ,\dfrac { 3\times 39 }{ 5\times 39 } ,\dfrac { 5\times 15 }{ 13\times 15 } \\ =\dfrac { 65 }{ 195 } ,\dfrac { 108 }{ 195 } ,\dfrac { 75 }{ 195 } \\ \Rightarrow \dfrac { 65 }{ 195 } <\dfrac { 75 }{ 195 } <\dfrac { 108 }{ 195 } \\ \Rightarrow \dfrac { 1 }{ 3 } <\dfrac { 5 }{ 13 } <\dfrac { 3 }{ 5 }$     

Therefore, $\dfrac { 3 }{ 5 }$ does not lie between the set of fraction $\dfrac { 1 }{ 3 } ,\dfrac { 5 }{ 13 }$.

(d) Now, consider the set of fraction $\dfrac { 2 }{ 7 } ,\dfrac { 8 }{ 11 }$ and another given fraction $\dfrac { 3 }{ 5 }$

Taking the LCM to make the denominators same of the above fractions, we have

$\dfrac { 2\times 55 }{ 7\times 55 } ,\dfrac { 3\times 77 }{ 5\times 77 } ,\dfrac { 8\times 35 }{ 11\times 35 } \\ =\dfrac { 110 }{ 385 } ,\dfrac { 221 }{ 385 } ,\dfrac { 280 }{ 385 } \\ \Rightarrow \dfrac { 110 }{ 385 } <\dfrac { 221 }{ 385 } <\dfrac { 280 }{ 385 } \\ \Rightarrow \dfrac { 2 }{ 7 } <\dfrac { 3 }{ 5 } <\dfrac { 8 }{ 11 }$     

Therefore, $\dfrac { 3 }{ 5 }$ lies between the set of fraction $\dfrac { 2 }{ 7 } ,\dfrac { 8 }{ 11 }$.

Hence, the fraction $\dfrac { 3 }{ 5 }$ is found between $\dfrac { 2 }{ 7 }$ and $\dfrac { 8 }{ 11 }$ on a number line.

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

Which one of the following sets of fractions is in the correct sequence of ascending order of their values ?

  1. $\displaystyle -\frac{1}{2},\frac{5}{6},\frac{-4}{9}$
  2. $\displaystyle -\frac{3}{7},\frac{-5}{6},\frac{3}{5}$
  3. $\displaystyle -\frac{1}{2},-\frac{4}{9},\frac{5}{6}$
  4. $\displaystyle -\frac{4}{9},\frac{5}{6},\frac{1}{6}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

(a) Let us consider the first set of fraction $-\dfrac { 1 }{ 2 } ,\dfrac { 5 }{ 6 } ,-\dfrac { 4 }{ 9 }$ 


Taking the LCM to make the denominators same of the above fractions, we have

$-\dfrac { 1\times 9 }{ 2\times 9 } ,\dfrac { 5\times 3 }{ 6\times 3 } ,-\dfrac { 4\times 2 }{ 9\times 2 } \\ =-\dfrac { 9 }{ 18 } ,\dfrac { 15 }{ 18 } ,-\dfrac { 8 }{ 18 } \\ \Rightarrow -\dfrac { 9 }{ 18 } <-\dfrac { 8 }{ 18 } <\dfrac { 15 }{ 18 } \\ \Rightarrow -\dfrac { 1 }{ 2 } <-\dfrac { 4 }{ 9 } <\dfrac { 5 }{ 6 }$   

Therefore, the first set of fraction $-\dfrac { 1 }{ 2 } ,\dfrac { 5 }{ 6 } ,-\dfrac { 4 }{ 9 }$ is not in ascending order.

(b) Now, consider the set of fraction $-\dfrac { 3 }{ 7 } ,-\dfrac { 5 }{ 6 } ,\dfrac { 3 }{ 5 }$ 

Taking the LCM to make the denominators same of the above fractions, we have

$-\dfrac { 3\times 30 }{ 7\times 30 } ,-\dfrac { 5\times 15 }{ 6\times 15 } ,\dfrac { 3\times 42 }{ 5\times 42 } \\ =-\dfrac { 90 }{ 210 } ,-\dfrac { 175 }{ 210 } ,\dfrac { 126 }{ 210 } \\ \Rightarrow -\dfrac { 175 }{ 210 } <-\dfrac { 90 }{ 210 } <\dfrac { 126 }{ 210 } \\ \Rightarrow -\dfrac { 5 }{ 6 } <-\dfrac { 3 }{ 7 } <\dfrac { 3 }{ 5 }$    

Therefore, the set of fraction $-\dfrac { 3 }{ 7 } ,-\dfrac { 5 }{ 6 } ,\dfrac { 3 }{ 5 }$ is not in ascending order.


(c) Now, consider the set of fraction $-\dfrac { 1 }{ 2 } ,-\dfrac { 4 }{ 9 } ,\dfrac { 5 }{ 6 }$ 


Taking the LCM to make the denominators same of the above fractions, we have

$-\dfrac { 1\times 9 }{ 2\times 9 } ,-\dfrac { 4\times 2 }{ 9\times 2 } ,\dfrac { 5\times 3 }{ 6\times 3 } \\ =-\dfrac { 9 }{ 18 } ,-\dfrac { 8 }{ 18 } ,\dfrac { 5 }{ 18 } \\ \Rightarrow -\dfrac { 9 }{ 18 } <-\dfrac { 8 }{ 18 } <\dfrac { 5 }{ 18 } \\ \Rightarrow -\dfrac { 1 }{ 2 } <-\dfrac { 4 }{ 9 } <\dfrac { 5 }{ 6 }$    

Therefore, the set of fraction $-\dfrac { 1 }{ 2 } ,-\dfrac { 4 }{ 9 } ,\dfrac { 5 }{ 6 }$ is in ascending order.

(d) Now, consider the set of fraction $-\dfrac { 4 }{ 9 } ,\dfrac { 5 }{ 6 } ,\dfrac { 1 }{ 6 }$ 

Taking the LCM to make the denominators same of the above fractions, we have

$-\dfrac { 4\times 2 }{ 9\times 2 } ,\dfrac { 5\times 3 }{ 6\times 3 } ,\dfrac { 1\times 3 }{ 6\times 3 } \\ =-\dfrac { 8 }{ 18 } ,\dfrac { 15 }{ 18 } ,\dfrac { 3 }{ 18 } \\ \Rightarrow -\dfrac { 8 }{ 18 } <\dfrac { 3 }{ 18 } <\dfrac { 15 }{ 18 } \\ \Rightarrow -\dfrac { 4 }{ 9 } <\dfrac { 1 }{ 6 } <\dfrac { 5 }{ 6 }$    

Therefore, the set of fraction $-\dfrac { 4 }{ 9 } ,\dfrac { 5 }{ 6 } ,\dfrac { 1 }{ 6 }$ is not in ascending order.

Hence, the only set of fraction in ascending order is $-\dfrac { 1 }{ 2 } ,-\dfrac { 4 }{ 9 } ,\dfrac { 5 }{ 6 }$

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
Here we have four factors $\dfrac{5}{7},  \dfrac{7}{9},   \dfrac{9}{11},   \dfrac{11}{13}$
LCM of 7, 9, 11 and 13 is 9009
So, 
$\dfrac{5}{7} \times\dfrac{1287}{1287}$ = $\dfrac{6435}{9009}$

$\dfrac{7}{9} \times\dfrac{1001}{1001}$ = $\dfrac{7007}{9009}$

$\dfrac{9}{11} \times\dfrac{819}{819}$ = $\dfrac{7371}{9009}$

$\dfrac{11}{13} \times\dfrac{693}{693}$ = $\dfrac{7623}{9009}$
As, 
6435 < 7007 < 7371 < 7623
So, $\dfrac{5}{7} < \dfrac{7}{9} <  \dfrac{9}{11} <  \dfrac{11}{13}$

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

Arrange the following numbers in descending order.
$-2,\, \displaystyle {\frac{4}{-5},\, \frac{-11}{20},\, \frac{3}{4}}$

  1. $\displaystyle {\frac{3}{4}\, >\, -2\, >\, \frac{-11}{20}\, >\, \frac{4}{-5}}$
  2. $\displaystyle {\frac{3}{4}\, >\, \frac{-11}{20}\, >\, \frac{4}{-5}\, >\, -2}$
  3. $\displaystyle {\frac{3}{4}\, >\, \frac{4}{-5}\, >\, -2\, >\, \frac{-11}{20}}$
  4. $\displaystyle {\frac{3}{4}\, >\, \frac{4}{-5}\, >\, \frac{-11}{20}\, >\, -2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The rational number $\dfrac {4}{-5}$ is same as $\dfrac {-4}{5}$.


Now consider the given rational numbers $-2,\dfrac {-11}{20},\dfrac {-4}{5}$ and $\dfrac {3}{4}$ and make their denominator same by taking the LCM of the denominators as follows:

LCM$(5,20,4)=20$

The given fractions now with denominator $20$ can be written as:

$\dfrac { -2\times 20 }{ 1\times 20 } =\dfrac { -40 }{ 20 } \ \dfrac { -4\times 4 }{ 5\times 4 } =\dfrac { -16 }{ 20 } \ \dfrac { -11\times 1 }{ 20\times 1 } =\dfrac { -11 }{ 20 } \ \dfrac { 3\times 5 }{ 4\times 5 } =\dfrac { 15 }{ 20 }$ 

The descending order of the rational numbers is:

$\dfrac { 15 }{ 20 } >\dfrac { -11 }{ 20 } >\dfrac { -16 }{ 20 } >\dfrac { -40 }{ 20 } \ \Rightarrow \dfrac { 3 }{ 4 } >\dfrac { -11 }{ 20 } >\dfrac { 4 }{ -5 } >-2$ 

Hence, the descending order is $\dfrac { 3 }{ 4 } >\dfrac { -11 }{ 20 } >\dfrac { 4 }{ -5 } >-2$.

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

Which of the following statements is true ?

  1. $\displaystyle\frac{-2}{3}\, <\, \frac{4}{-9}\,<\,\frac{-5}{12}\, <\, \frac{7}{-18}$
  2. $\displaystyle\frac{7}{-18}\, <\, \frac{-5}{12}\,<\,\frac{4}{9}\, <\, \frac{-2}{3}$
  3. $\displaystyle\frac{4}{-9}\, <\, \frac{7}{-18}\,<\,\frac{-5}{12}\, <\, \frac{2}{-3}$
  4. $\displaystyle\frac{-5}{12}\, <\, \frac{-2}{3}\,<\,\frac{4}{-9}\, <\, \frac{7}{-18}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

This question is very easy if we solve it by verification
process.

Take (A) i.e. $\displaystyle\frac{-2}{3}\,<\,\frac{4}{-9}\, \frac{-5}{12}\, <\,\frac{7}{-18}$

First take \displaystyle\frac{-2}{3},\,\frac{-4}{9}$

$-2\,\times\,9,\, 4\,\times\,3$

-18, -12

$\because\, -12\,>\,-18$

So, $\displaystyle\frac{-4}{9}, \frac{-5}{12}$

$- 4\,\times\, 12, \, - 5\,\times\, 9$

- 48, - 45

$\because\, -45\, >\, -48$

So, $\displaystyle\frac{-5}{12}\,>\, \frac{-4}{9},\,i.e.,\frac{-4}{9}\, <\, \frac{-5}{12}$

Finally, $\displaystyle\frac{-5}{12}, \frac{-7}{18}$

$5\,\times\, 18, \, -7\,\times\, 12$

- 90, - 84

$\because\, -84\, >\, -90$

So, $\displaystyle\frac{-7}{18}\, >\, \frac{-5}{12}, i.e., \frac{-5}{12}\, <\, \frac{-7}{18}$

$\therefore\, \displaystyle\frac{-2}{3}\, <\, \frac{-4}{9}\,<\,  \frac{-5}{12}\,<\, \frac{-7}{18}$

You can identify the answer by observing the question by practicing this method.