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

What is the product $\displaystyle \left ( 1-\frac{1}{2} \right )\left ( 1-\frac{1}{3} \right )\left ( 1-\frac{1}{4} \right )......\left ( 1-\frac{1}{n} \right )$ equal to  when simplified?

  1. $\displaystyle \frac{1}{n}$
  2. $1$
  3. $2$
  4. $0$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\displaystyle \left ( 1-\frac{1}{2} \right )\left ( 1-\frac{1}{3} \right )\left ( 1-\frac{1}{4} \right )......\left ( 1-\frac{1}{n} \right )=\frac{1}{2}\times \frac{2}{3}\times \frac{3}{4}\times ......\times \frac{n-2}{n-1}\times \frac{n-1}{n}=\frac{1}{n}$

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 $\displaystyle 3\frac{1}{2}$ is 

  1. $\displaystyle \frac{7}{2}$
  2. $\displaystyle \frac{2}{7}$
  3. $\displaystyle 1\frac{2}{3}$

  4. none
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The reciprocal of a number is just divide 1 by the number.
$\therefore$ Reciprocal of $3\cfrac 12$ i.e $\cfrac 72$ is $\cfrac 27$
Option B is correct.

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

Product of $\displaystyle \frac {12}{24}$ and $\displaystyle \frac {36}{72}$ is

  1. $\displaystyle \frac {16}{24}$
  2. $\displaystyle \frac {3}{5}$
  3. $4$
  4. $\displaystyle \frac {1}{4}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

We need to find product of $\displaystyle \frac {12}{24}, \frac {36}{72}$


$\therefore \displaystyle \frac{12}{24} \times \frac{36}{72} = \frac{1}{2} \times \frac{1}{2} $

$=\displaystyle  \frac{1}{4}$

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

Product of $\displaystyle \frac {10} {11} \times \frac {15} {3}\times \frac {0} {5}$ is

  1. $\displaystyle \frac {10} {33} $

  2. 0
  3. $\displaystyle \frac {150} {495} $

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

zero multiplied by any number is zero..

So $\dfrac{10}{11}\times \dfrac{15}{3}\times\dfrac{0}{5}=0 $

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  $ \displaystyle \left | x \right | =\left | \frac{-3}{5} \right |  $ and  $ \displaystyle \left | y \right | =\left | \frac{4}{-7} \right |  $ find  $ \displaystyle \left | x \right | \times\left | y \right |  $ 

  1. $ \displaystyle \frac{12}{35} $

  2. 1

  3. 0
  4. $ \displaystyle \frac{35}{12} $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$ \displaystyle \left | x \right | =\left | \frac{-3}{5} \right |  $ and  $ \displaystyle \left | y \right | =\left | \frac{4}{-7} \right |  $ 

Since $|x|=|-x|$, therefore $|x|\times |y|=\dfrac{3}{5}\times \dfrac{4}{7}=\dfrac{12}{35}$

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 $1\frac {1}{3}\times 3\frac {1}{4}\times \frac {7}{8}$

  1. $3\frac {18}{24}$
  2. $2\frac {19}{24}$
  3. $3\frac {19}{24}$
  4. $2\frac {18}{24}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To multiply mixed fractions we convert them into improper fractions.

In the question, 1 whole 1/3× 3 whole 1/4 ×7/8
(3×1+1)/3×(4×3+1)/4×7/8
=4/3×13/4×7/8
=2/3×13/4×7/4
=1/3×13/2×7/4
=91/24
=3 whole 19/24
So, option C is the correct answer.

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 $\displaystyle \frac{6}{3}$ is

  1. $\displaystyle -\frac{6}{3}$
  2. $\displaystyle -\frac{3}{6}$
  3. $\displaystyle \frac{3}{6}$

  4. 36
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
We find the reciprocal of a fraction we flip it.
The definition of "reciprocal" is simple. To find the reciprocal of any number, just calculate "1 ÷ (that number)." For a fraction, the reciprocal is just a different fraction, with the numbers "flipped" upside down (inverted).
In this case, the reciprocal of 6/3 is 3/6.
So option C is the correct answer.
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

The equivalent fraction of $ \displaystyle \frac{10}{11}  $ having the numerator 40 is _________

  1. $ \displaystyle \frac{40}{11} $
  2. $ \displaystyle \frac{44}{40} $
  3. $ \displaystyle \frac{40}{44} $
  4. $ \displaystyle \frac{10}{40} $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The equivalent to the given fraction 10/11 having the numerator 40 should have a denominator divisible by 11. The only option with a denominator divisible by 11 is option C. 44 is divisible by 11 and 40 is divisible by 10. So,

Option C is the correct answer.

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

The equivalent fraction of $ \displaystyle \frac{2}{3}  $ having the denominator 18 is

  1. $ \displaystyle \frac{2}{18} $
  2. $ \displaystyle \frac{18}{3} $
  3. $ \displaystyle \frac{12}{18} $
  4. $ \displaystyle \frac{18}{27} $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Only options A and C have denominators 18 in their options.

If we change anything in the denominator, we have to do a change of the same value in the numerator also. In option A this property is not fulfilled.
However in option C we find (2×6)/(3×6)
Option C is the equivalent fraction
2/3≈12/18
So option C is the correct answer.