# Simplification questions

Simplifications are mathematical problems that require simplifying complex expressions or equations to their simplest form. The simplification questions and answers are accessible here to allow learners to practice for competitive exams. The questions are prepared using the concept of simplification and the latest exam pattern. The questions in this section are based on competitive exam papers, the CBSE syllabus (2022-2023), and the NCERT curriculum. Find the topics linked to Simplification and practice questions typically asked in exams.

1. $[-2 (\frac{2}{ 8} )]+ [-6(\frac{7}{ 8} )] + [9(\frac{5 }{ 8} )]$ = ?

$[-2 (\frac{2}{ 8} )]+ [-6(\frac{7}{ 8} )] + [9(\frac{5 }{ 8} )]$
= $[ (\frac{-4}{ 8} )]+ [(\frac{-42}{ 8} )] + [(\frac{45}{ 8} )]$
= $\frac{-4 -42 +45}{8}$
=$\frac{-1}{8}$

1. $8192 \div 32\div 16 \div 8\div 4\div 2 \div 1$ =?

$8192 \div 32\div 16 \div 8\div 4\div 2 \div 1$
= $8192 \times \frac{1}{32}\times \frac{1}{16}\times \frac{1}{8}\times \frac{1}{2}\times \frac{1}{1}$
=$\frac{8192}{32\times16 \times8\times4\times2}$
=$\frac{1}{4}$
=0.25

1. Simplify the expression $441 \div\left[270 \div \frac{3}{7}+\left(17 \div \frac{1}{3}\right)-\left(8 \frac{1}{2}-\frac{5}{2}\right)\right]$

$441 \div\left[270 \div \frac{3}{7}+\left(17 \div \frac{1}{3}\right)-\left(8 \frac{1}{2}-\frac{5}{2}\right)\right]$

Using BODMAS

$\Rightarrow 441 \div\left[270 \div \frac{3}{7}+\left(17 \div \frac{1}{3}\right)-\left(\frac{17}{2}-\frac{5}{2}\right)\right]$

$\Rightarrow 441 \div\left[270 \div \frac{3}{7}+(51)-(6)\right]$

$\Rightarrow 441 \div[630+(51)-(6)]$

$\Rightarrow 441 \div[675]=\frac{49}{75}$

1. Simplify the following expression: $\frac{7}{12} \div \frac{1}{10} \text { of } \frac{2}{3}-\frac{5}{3} \times \frac{9}{10}+\frac{5}{8} \div \frac{3}{4} \text { of } \frac{2}{3}$

The value of $\frac{7}{12} \div \frac{1}{10}$ of $\frac{2}{3}-\frac{5}{3} \times \frac{9}{10}+\frac{5}{8} \div \frac{3}{4}$ of $\frac{2}{3}$

By using BODMAS rules - $=\frac{7}{12} \times \frac{30}{2}-\frac{5}{3} \times \frac{9}{10}+\frac{5}{8} \times \frac{12}{6}$ $=\frac{35}{4}-\frac{3}{2}+\frac{5}{4}$ $=\frac{35-6+5}{4}$ $=\frac{34}{4}$ $=8 \frac{1}{2}$

Hence, option D is correct.

1. $\left(\frac{1}{2} \div \frac{1}{2} \times \frac{1}{2}+\frac{1}{2}-\frac{1}{2}+\frac{1}{2} \times \frac{1}{2} \div \frac{1}{2}\right)$ of $\left(\frac{1}{2}+\frac{1}{2}\right) ?$

$\left(\frac{1}{2} \div \frac{1}{2} \times \frac{1}{2}+\frac{1}{2}-\frac{1}{2}+\frac{1}{2} \times \frac{1}{2} \div \frac{1}{2}\right)$ of $\left(\frac{1}{2}+\frac{1}{2}\right) ?$
$\Rightarrow ?=1 \times \frac{1}{2}+\frac{1}{2}-\frac{1}{2}+\frac{1}{2} \times 1$ of 1 $\Rightarrow ?=\frac{1}{2}+0+\frac{1}{2}$
$\therefore ?=1$