Quantitative Aptitude · Mathematics

Algebraic Simplification

146 Questions

Algebraic simplification involves reducing mathematical expressions to their simplest forms using exponent rules and identities. Test takers must manipulate equations to find rapid solutions. This skill is frequently assessed in SSC, banking, and railway quantitative aptitude sections.

Exponent rulesSurd operationsAlgebraic identitiesTrigonometric simplificationLogical expressions

Algebraic Simplification Questions

Multiple choice converting decimals to fractions and vice-versa decimal to fraction addition, subtraction and multiplication of fractions decimal fractions maths

Express the following as a fraction and simplify:

$2.45$

  1. $\cfrac {49}{20}$
  2. $\cfrac {20}{49}$
  3. $\cfrac {19}{20}$
  4. $\cfrac {20}{19}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To convert a decimal to a fraction, write it over the appropriate power of 10 and simplify:
$2.45 = 2\cfrac{45}{100} = 2\cfrac{9}{20}$    ...Mixed fraction

$=\cfrac{49}{20}$     ....Improper fraction

Multiple choice trigonometric equations trigonometric functions trigonometry maths

Simplify: $\tan5\tan { 30 } \times 4\tan { 85=\ _ \ _ \ _  } $

  1. $1$
  2. $4$
  3. $4/\surd 3$
  4. $4\surd 3$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
$\tan{{5}^{\circ}}\tan{{30}^{\circ}}\times 4\tan{{85}^{\circ}}$
$=4\tan{{5}^{\circ}}\times\dfrac{1}{\sqrt{3}}\tan{\left({90}^{\circ}-{5}^{\circ}\right)}$
$=4\tan{{5}^{\circ}}\times\dfrac{1}{\sqrt{3}}\cot{{5}^{\circ}}$
$=\dfrac{4}{\sqrt{3}}$ since $\tan{{5}^{\circ}}\cot{{5}^{\circ}}=1$
Multiple choice absolute value real numbers (rational and irrational numbers) real numbers basic algebra maths

The value of $|-5-6|\times |4 + 3|$ on simplification is

  1. $-7$
  2. $7$
  3. $77$
  4. $-77$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
$\left | x \right |  $   is a absolute valye function

Its value is always greater than $0$ or equal to $0$.

for example $\left | -1 \right |  =1$ 
and                 $\left | 1 \right | =1 $

given expression as per the question

$\left | -5-6 \right | \times \left | 4+3 \right |   $

$=\left | -11 \right | \times \left | 7 \right |   $

$=11 \times 7$

$=77$
Multiple choice maths algebraic formulae - expansion of squares introduction to factorization introduction to factorisation factorising algebraic expressions

Simplify: $\displaystyle \left( -80{ m }^{ 4 }npq \right) \div 10{ m }^{ 3 }{ pqn }^{ 2 }$

  1. $-8mn$
  2. $-8mnpq$
  3. $-8m$
  4. $\dfrac {-8m}{n}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\displaystyle \left( -80{ m }^{ 4 }npq \right) \div 10{ m }^{ 3 }{ pqn }^{ 2 }=\frac { -80{ m }^{ 4 }npq }{ 10{ m }^{ 3 }{ pqn }^{ 2 } } $

$\displaystyle =\quad -8\times \frac { { m }^{ 4 } }{ { m }^{ 3 } } \times \frac { n }{ { n }^{ 2 } } \times \frac { p }{ p } \times \frac { q }{ q } $
$\displaystyle =\quad -8{ m }^{ 4-3 }\times { n }^{ 1-2 }$
$\displaystyle =\quad -8m\times { n }^{ -1 }$
$\displaystyle =\quad \frac { -8m }{ n } \left( \because { n }^{ -1 }=\frac { 1 }{ n }  \right) $