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 fraction lowest form of a fraction simplest ratio lowest form of fractions

Which of the following are true?

(a) $\displaystyle \frac{35}{16}=2.1875$
(b) $\displaystyle \frac{17}{8}=2.125$
(c) $\displaystyle \frac{327}{500}=0.654$
(d) $\displaystyle \frac{14588}{625}=23.3408$

  1. $a,b,c,d$
  2. $a,c,d$
  3. $a,b,c$
  4. $a,b,d$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

(i) $\displaystyle \frac{35}{16} = \frac{35 \times 5^4}{2 \times 5^4}= \frac{35 \times 625}{(10)^4}= \frac{21875}{10000}=2.1875$
(ii) $\displaystyle \frac{17}{8} = \frac{17 \times 5^3}{2^3 \times 5^3} = \frac{17 \times 125}{(10)^3}=\frac{2125}{1000}=2.125$
(iii) $\displaystyle \frac{327}{500} = \frac{327}{5\times 5 \times 5 \times 2 \times 2}$
$=\displaystyle \frac{327}{5^3 \times 2^2} = \frac{327}{5^3 \times 2^3}= \frac{654}{(10)^3} = 0.654$
(iv) $\displaystyle \frac{14588}{625} = \frac{2^2 \times 7 \times 521}{5^4} = \frac{2^6 \times 7 \times 521}{2^4 \times 5^4}$
$\displaystyle =\frac{233408}{10^4}=23.3408$

Multiple choice maths fraction lowest form of a fraction simplest ratio lowest form of fractions

If $2a-5b = 0$ then find the value of $\displaystyle \frac{a+b}{a-b}$.

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

Given, $ 2a-5b = 0 $

$=>2a = 5b $

$ => \dfrac {a}{b} = \dfrac {5}{2} $

Applying componendo and dividendo,

Now, $ \dfrac {a+b}{a-b} = \dfrac{5+2}{5-2} =

\dfrac {7}{3} $

Multiple choice maths fraction lowest form of a fraction simplest ratio lowest form of fractions

If $2a-5b = 0$ then find the value of  $\displaystyle \frac{a-b}{b}$

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

Given, $ 2a-5b = 0 $
$=> 2a = 5b $
$ => \dfrac {a}{b} = \dfrac {5}{2} $
 
Now, $ \dfrac {a-b}{b} = \dfrac {a}{b} - 1 = \dfrac {5}{2} - 1 = \dfrac{5-2}{2} = \dfrac {3}{2} $

Multiple choice maths fraction lowest form of a fraction simplest ratio lowest form of fractions

If $2a-5b = 0$ then find the value of  $\displaystyle \frac{a+b}{b}$

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

Given, $ 2a-5b = 0 $
$=>. 2a = 5b $
$ => \frac {a}{b} = \frac {5}{2} $
 
Now, $ \frac {a+b}{b} = \frac {a}{b} + 1 = \frac {5}{2} + 1 = \frac{5+2}{2} = \frac {7}{2} $

Multiple choice maths fraction lowest form of a fraction simplest ratio lowest form of fractions

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

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


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

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

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

Multiple choice maths fraction lowest form of a fraction simplest ratio lowest form of fractions

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

  1. $\displaystyle \frac {3}{6}$
  2. $\displaystyle \frac {5}{10}$
  3. $\displaystyle \frac {9}{8}$

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

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

Multiple choice maths fraction lowest form of a fraction simplest ratio lowest form of fractions

$1.\bar{3}$ is equal to

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

$1.\bar{3}$
Let $1.3333...$ be $x$
$1.3333...=x$  {i}
$13.333...=10x$ {ii} [Multiplied by $10$]
                               
$        12  =9x$
$=>x=\frac{12}{9}$
$=>x=\frac{4}{3}$

Multiple choice maths fraction lowest form of a fraction simplest ratio lowest form of fractions

The fraction equivalent to $\displaystyle \frac {1} {3} $ is ................

  1. $\displaystyle \frac {3} {9} $
  2. $\displaystyle \frac {5} {15} $
  3. $\displaystyle \frac {6} {18} $

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

3×3=9 so 3/9=1/3

5×3=15 so 5/15=1/3
6×3=18 so 6/18=1/3
So all the given options are equivalent to 1/3
Option D is the correct answer.

Multiple choice maths fraction lowest form of a fraction simplest ratio lowest form of fractions

Which number should come in place of $\displaystyle \ \Box, \dfrac { 1 }{ 4 } +\dfrac { 2 }{ 4 } +\dfrac { \Box  }{ 4 } =1\dfrac { 1 }{ 2 } $

  1. $1$
  2. $2$
  3. $3$
  4. $4$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$=\displaystyle \frac { 3 }{ 2 } -\frac { 1 }{ 4 } -\frac { 2 }{ 4 }=  \frac { 6-1-2 }{ 4 }= \frac{3} {4} $ 

Multiple choice maths fraction lowest form of a fraction simplest ratio lowest form of fractions

What is the value of $\dfrac {1}{1 + \sqrt {2} + \sqrt {3}} + \dfrac {1}{1 - \sqrt {2} + \sqrt {3}}$?

  1. $1$
  2. $\sqrt {2}$
  3. $\sqrt {3}$
  4. $2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The value of $\dfrac {1}{(1 + \sqrt {3})+\sqrt {2}} + \dfrac {1}{(1 + \sqrt {3}) - \sqrt {2}}$ is
$=\dfrac {(1 + \sqrt {3} - \sqrt {2}) + (1 + \sqrt {3} + \sqrt {2})}{(1 + \sqrt {3})^{2} - (\sqrt {2})^{2}}$
$= \dfrac {2(1 + \sqrt {3})}{1 + 3 + 2\sqrt {3} - 2}$
$= \dfrac {2(1 + \sqrt {3})}{2(1 + \sqrt {3})} = 1$