Free Practice Questions for Simplification in Maths

$\Rightarrow$ Using BODMAS concept
$\begin{array}{rl}& =60÷[50+7-\{14+(24\text{ of }2÷3)-12÷4\times 2+18÷4\times 2\}]\\ & =60÷[50+7-\{14+16-12÷4\times 2+18÷4\times 2\}]\\ & =60÷[50+7-\{14+16-3\times 2+\frac{9}{2}\times 2\}]\\ & =60÷[50+7-\{14+16-6+9\}]\\ & =60÷[50+7-33]\\ & =60÷24=\frac{5}{2}\end{array}$

$\Rightarrow \frac{5}{7}÷5\frac{1}{3}$ of $\frac{5}{14}-\frac{5}{14}\times 6\frac{3}{10}+(0.\overline{57}÷0.6\bar{3}\times 5\frac{1}{2})\times \frac{7}{15}$

$=\frac{5}{7}÷\frac{16}{3}$ of $\frac{5}{14}-\frac{5}{14}\times \frac{63}{10}+(\frac{57}{99}÷\frac{(63-6)}{90}\times \frac{11}{2})\times \frac{7}{15}$

$=\frac{5}{7}\times \frac{42}{80}-\frac{9}{4}+(\frac{57}{99}\times \frac{90}{57}\times \frac{11}{2})\times \frac{7}{15}$

$=\frac{3}{8}-\frac{9}{4}+\frac{7}{3}$

$=\frac{(9-54+56)}{24}$

$=\frac{11}{24}$

$45-[36-\{29-(25-\overline{7+4})\}]$
By using BODMASS rule
$\begin{array}{rl}& =45-[36-(29-(25-11)\}]\\ & =45-[36-\{29-14)]\\ & =45-[36-15]\\ & =45-21\\ & =24\end{array}$

$\frac{[\frac{1}{9}÷\frac{1}{9}\text{ of }\frac{1}{9}]\times \frac{1}{9}}{\frac{1}{9}+\frac{1}{9}\text{ of }\frac{1}{9}}$
By using BODMAS rule
$=\frac{[\frac{1}{9}÷\frac{1}{9}\times \frac{1}{9}]\times \frac{1}{9}}{\frac{1}{9}+\frac{1}{9}\times \frac{1}{9}}$
$=\frac{[\frac{1}{9}\times 81]\times \frac{1}{9}}{\frac{9+1}{81}}$
$=\frac{9\times \frac{1}{9}}{\frac{10}{81}}$
$=\frac{81}{10}$
$=8\frac{1}{10}$

$40\mathrm{\%}$ of $60+16.66\mathrm{\%}\times 54-20+13=?$

$\Rightarrow \frac{40}{100}\times 60+\frac{1}{6}\times 54-20+13=?(16.66\mathrm{\%}=\frac{1}{6})$
$\Rightarrow 24+9-20+13=?$
$\Rightarrow ?=46-20$
$\Rightarrow ?=26$

$25+41\times (28÷7)-{13}^2=?$

$\Rightarrow 25+41\times (4)-{13}^2=?$
$\Rightarrow ?=25+164-169$
$\Rightarrow ?=20$

$[(61/13)\times 91]÷7+9-25=?$

$\Rightarrow [\frac{61}{13}\times 91]÷7+9-25=?$
$\Rightarrow \frac{61\times 7}{7}+9-25=?$
$\Rightarrow ?=70-25$
$\Rightarrow ?=45$

$(40+24)÷8\times 18-?=126$

$\Rightarrow (64)÷8\times 18-?=126$
$\Rightarrow 8\times 18-?=126$
$\Rightarrow ?=144-126=18$

$({15}^2-114)÷3-40+2^3=?$

$\Rightarrow (225-114)÷3-40+8=?$
$\Rightarrow 37-40+8=?$
$\Rightarrow ?=5$

$(15+24)\times 3÷13+18-5=?$

$\Rightarrow (39)\times 3÷13+18-5=?$
$\Rightarrow ?=9+18-5$
$\Rightarrow ?=22$

Given,

$78+85-(13\times 8)+(81÷3)=?$

$\Rightarrow 163-(104)+(27)=?$
$\Rightarrow ?=59+27$
$\Rightarrow ?=86$

$48\times 7÷12+3^3-7^2=\sqrt{?}$

$\Rightarrow \frac{48\times 7}{12}+27-49=\sqrt{?}$
$\Rightarrow 28+27-49=\sqrt{?}$
$\Rightarrow 6=\sqrt{?}$
$\Rightarrow ?=36$

$\frac{734\times 734\times 734-127\times 127\times 127}{734\times 734+734\times 127+127\times 127}$
$=\frac{(734-127)(734\times 734+734\times 127+127\times 127)}{(734\times 734+734\times 127+127\times 127)}$
$=(734-127)=607$
$a^3-b^3=(a-b)(a^2+ab+b^2)$

$11\frac{2}{3}÷9\frac{3}{8}\times 5\frac{3}{5}=\frac{35}{3}÷\frac{75}{8}\times \frac{28}{5}$
$=\frac{35}{3}\times \frac{8}{75}\times \frac{28}{5}=\frac{7}{3}\times \frac{8}{15}\times \frac{28}{5}=\frac{1568}{225}$

$\begin{array}{rl}1+\frac{2}{1+\frac{3}{2-\frac{1}{1+\frac{1}{2}}}}& =1+\frac{2}{1+\frac{3}{2-\frac{2}{3}}}\\ & =1+\frac{2}{1+\frac{3}{4/3}}=1+\frac{2}{1+\frac{9}{4}}\\ & =1+\frac{8}{13}=\frac{13+8}{13}=\frac{21}{13}\end{array}$

$\frac{(589+187{)}^2-(589-187{)}^2}{589\times 187}$
$=\frac{4\times 589\times 187}{589\times 187}$
$=4(a+b{)}^2-(a-b{)}^2=4ab$