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

Reduce fraction to lowest form:
$\dfrac{144}{36}$

  1. $\dfrac{4}{1}$
  2. $\dfrac{12}{2}$
  3. $\dfrac{1}{36}$
  4. $\dfrac{4}{9}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\dfrac{144}{36}$


Dividing numerator and denominator by $12$, we get
$\dfrac{144}{36} = \dfrac{12}{3}$

Dividing both numerator and denominator again by $3$, we get

$\dfrac{12}{3} = \dfrac{4}{1}$

This is the lowest form

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

Reduce fraction to lowest form:
$\dfrac{125}{625}$

  1. $\dfrac{1}{5}$
  2. $\dfrac{12}{625}$
  3. $\dfrac{5}{625}$
  4. $\dfrac{15}{25}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\dfrac{125}{625}$


Dividing numerator and denominator by $25$, we get
$\dfrac{125}{625} = \dfrac{5}{25}$

Dividing again both numerator and denominator by $5$, we get

$\dfrac{5}{25} = \dfrac{1}{5}$

This is the lowest form

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

Which of these statements is CORRECT?

  1. $\dfrac {3}{6}$ and $\dfrac {1}{2}$ are equivalent fractions
  2. $\dfrac {1}{2}$ of an hour is equal to $20$ minutes
  3. $\dfrac {5}{6}$ is equal to $\dfrac {6}{5}$
  4. $1\ mm$ is $\dfrac {1}{100}$ of $1\ cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

(A) $\dfrac {3}{6} = \dfrac {3\div 3}{6\div 3} = \dfrac {1}{2}$
(B) $\dfrac {1}{2}$ of an hour $= \dfrac {1}{2}\times 60$ minutes = $30$ minutes
(C) $\dfrac {5}{6} = 0.8333, \dfrac {6}{5} = 1.2$
$\therefore \dfrac {5}{6}\neq \dfrac {6}{5}$
(D) $\dfrac {1}{100}$ of $1$ cm = $\dfrac {1}{100}\times 10$ mm = $\dfrac {1}{10}$ mm.

Hence the correct answer is option A.

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

A fraction $\displaystyle\frac{x}{y}$ can be expressed as a terminating decimal if y has no prime factors other than _________.

  1. $2, 3$
  2. $3, 5$
  3. $2, 5$
  4. $2, 3, 5$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If the denominator has a prime factor $2$ or $5$ then it is a terminating decimal

Hence the correct answer is option C

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

The value of $\left(\displaystyle 1-\frac{1}{3}\right)\left(\displaystyle 1-\frac{1}{4}\right)\left(\displaystyle 1-\frac{1}{5}\right)\left(\displaystyle 1-\frac{1}{6}\right).....\left(\displaystyle 1-\frac{1}{n}\right)$ is _________.

  1. $\displaystyle\frac{1}{n}$
  2. $\displaystyle\frac{2}{n}$
  3. $\displaystyle\frac{2(n-1)}{4}$
  4. $\displaystyle\frac{2}{n(n+1)}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
We need to find value of $\left(1-\dfrac {1}{3}\right)\left (1-\dfrac {1}{4}\right)\left (1-\dfrac {1}{5}\right)\left(1-\dfrac {1}{6}\right).....\left (1-\dfrac {1}{n}\right)$
Solving each bracket, we get 
$\dfrac{2}{3} \times \dfrac{3}{4} \times \dfrac{4}{5} . . . . ...\dfrac{n-3}{n-2}\times \dfrac{n-2}{n-1} \times \dfrac{n-1}{n}$
Starting from $1^{st}$ term each denominator is cancelled out by next numerator.
Finally, we get $\dfrac{2}{n}$
Multiple choice maths fraction lowest form of a fraction simplest ratio lowest form of fractions

The product of the $9$ fractions $\left(\displaystyle 1-\frac{1}{2}\right)\left(\displaystyle 1-\frac{1}{3}\right)\left(\displaystyle 1-\frac{1}{4}\right)..........\left(\displaystyle 1-\frac{1}{10}\right)=$____________.

  1. $\displaystyle\frac{10}{11}$
  2. $\displaystyle\frac{1}{9}$
  3. $\displaystyle\frac{1}{10}$
  4. $\displaystyle\frac{1}{2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
We need to simplify $\left (1-\dfrac {1}{2}\right)\left (1-\dfrac {1}{3}\right)\left (1-\dfrac {1}{4}\right).....\left (1-\dfrac {1}{10}\right)$
Simplifying each bracket, we get
$\dfrac{1}{2} \times \dfrac{2}{3} \times \dfrac{3}{4} . . . . ...\dfrac{7}{8}\times \dfrac{8}{9} \times \dfrac{9}{10}$
As we can see 
Starting from $1^{st}$ term, each denominator is cancelled out by next numerator.
Finally we get $\dfrac{1}{10}$

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

The standard form of $\displaystyle\frac{192}{-168}$ is _________.

  1. $\displaystyle\frac{-2}{3}$
  2. $\displaystyle\frac{-8}{7}$
  3. $\displaystyle\frac{-1}{7}$
  4. $\displaystyle\frac{-6}{7}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

the standard form of $ - \dfrac{192}{168}$

$=-\dfrac{2 \times 3\times 4\times 8}{2\times 3\times 4\times 7}$
$-\dfrac{8}{7}$

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

Which of the following sum is in the simplest form?

  1. $\dfrac{4}{9}+\dfrac{-5}{9}$
  2. $\dfrac{-2}{5}+\dfrac{13}{20}$
  3. $\dfrac{-5}{12}+\dfrac{11}{-12}$
  4. $\dfrac{-7}{8}+\dfrac{1}{12}+\dfrac{2}{3}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
A. $\dfrac{4}{9} + \dfrac{-5}{9} = \dfrac{-1}{9}$ Simplest Form

B. $\dfrac{-2}{5} + \dfrac{13}{20} = \dfrac{-8+13}{20} = \dfrac{5}{20}$ Not the simplest form

C. $\dfrac{-5}{12} + \dfrac{11}{-12} = \dfrac{-5-11}{12} = \dfrac{-16}{12}$ Not the simplest form

D. $\dfrac{-7}{8} + \dfrac{1}{12} + \dfrac{2}{3} = \dfrac{-21+2+16}{24} = \dfrac{-3}{24}$ Not the simplest form

$\Rightarrow$ Only A gives answer in simplest form
Multiple choice maths fraction lowest form of a fraction simplest ratio lowest form of fractions

Which of the following is not equivalent to $\dfrac{4}{8}$ ?

  1. $\cfrac { 1 }{ 2 } $
  2. $\cfrac { 16 }{ 32 } $
  3. $1$
  4. $\cfrac { 12 }{ 24 } $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

we have, $\dfrac{4}{8}=$ $\dfrac{1}{2}=$$\dfrac{16}{32}=$$\dfrac{12}{24}$

Among the given values, the one which is not equivalent to $\dfrac{4}{8}$ is 1.

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

Reduce the following fractions to their lowest forms.
a. $\dfrac{36}{144}$


b. $\dfrac{65}{117}$

c. $\dfrac{180}{120}$

  1. $a=\dfrac{1}{4}, b=\dfrac{65}{117}, c=\dfrac{2}{3}$
  2. $a=\dfrac{1}{4}, b=\dfrac{5}{9}, c=\dfrac{3}{2}$
  3. $a=\dfrac{1}{4}, b=\dfrac{65}{117}, c=\dfrac{3}{2}$
  4. $a=\dfrac{3}{4}, b=\dfrac{65}{117}, c=\dfrac{2}{3}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\\(a.)(\frac{36}{144})=(\frac{3}{12})=(\frac{1}{4})\\(b.)(\frac{65}{117})=(\frac{13\cdot 5}{13\cdot 9})=(\frac{5}{9})\\(c.)(\frac{180}{120})=(\frac{60\cdot 3}{60\cdot 2})=(\frac{3}{2})$

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

If $\displaystyle\,5\,\dfrac{7}{x}\,\times\,y\,\dfrac{1}{13}\,=\,12$, where fractions are in their lowest terms, then $x - y$ is equal to 

  1. $2$
  2. $4$
  3. $7$
  4. $9$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\displaystyle 5\,\frac{7}{x}\,\times\,y\,\frac{1}{13}\,=\,12$
By Hit and Trial method. 
Let $x = 9, y = 2$
Where the fractions are in their lowest terms, then x should be maximum possible single digit and $y$ is minimum possible single digit.
Putting this value in equ. (1)
$\displaystyle \,5\,\times\,\frac{7}{9}\,\times\,2\,\times\,\frac{1}{13}\,=\,\frac{52}{9}\,\times\,\frac{27}{13}\,=\,12
$
$\therefore \,x\,-\,y\,=7$
Hence, option 'C' is correct.