Free Practice Questions for Simplification in Maths

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

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

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

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

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

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

$=\frac{11}{24}$

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

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

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

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

$25+41 \times(28 \div 7)-13^{2}=?$

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

$[(61 / 13) \times 91] \div 7+9-25=?$

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

$(40+24) \div 8 \times 18-?=126$

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

$\left(15^{2}-114\right) \div 3-40+2^{3}=?$

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

$(15+24) \times 3 \div 13+18-5=?$

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

Given,

$78+85-(13 \times 8)+(81 \div 3)=?$

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

$48 \times 7 \div 12+3^{3}-7^{2}=\sqrt{?}$

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

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

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

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

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