Free Practice Questions for Simplification in Maths

$3 \times 7+5-6 \div 3-9+45 \div 5 \times 4-45$
$\Rightarrow 3 \times 7+5-2-9+9 \times 4-45$
$\Rightarrow 21+5-2-9+36-45$
$\Rightarrow 62-56=6$

$\Rightarrow 45-3 \times(4$ of $6+12 \div 3 \times 6-4 \times 5)+6$
$=45-3 \times(24+4 \times 6-20)+6$
$=45-3 \times(24+24-20)+6$
$=45-3 \times 28+6$
$=45-84+6$
$=51-84=-33$

$\Rightarrow 12-[3+\{4$ of $2 \div 8-(8-6 \div 3)\}]$
$=12-[3+\{4$ of $2 \div 8-(8-2)\}]$
$=12-[3+\{4$ of $2 \div 8-6\}]$
$=12-\left[3+\left\{\frac{8}{8}-6\right\}\right]$
$=12-[3-5]$
$=12+2$
$=14$

$\Rightarrow\left(\frac{1}{4} \times \frac{3}{4} \div 1 \frac{1}{4}\right.$ of $\left.\frac{2}{5}\right) \div\left(\frac{3}{4} \div 1 \frac{2}{3}\right.$ of $\left.\frac{4}{5}\right)-\left(\frac{1}{2}-\frac{1}{2} \times \frac{1}{4}\right)$
$=\left(\frac{1}{4} \times \frac{3}{4} \div \frac{5}{4}\right.$ of $\left.\frac{2}{5}\right) \div\left(\frac{3}{4} \div \frac{5}{3}\right.$ of $\left.\frac{4}{5}\right)-\left(\frac{1}{2}-\frac{1}{8}\right)$
$=\left(\frac{1}{4} \times \frac{3}{4} \div \frac{1}{2}\right) \div\left(\frac{3}{4} \div \frac{4}{3}\right)-\left(\frac{4-1}{8}\right)$
$=\left(\frac{1}{4} \times \frac{3}{4} \times 2\right) \div\left(\frac{3}{4} \times \frac{3}{4}\right)-\frac{3}{8}$
$=\frac{3}{8} \div \frac{9}{16}-\frac{3}{8}$
$=\frac{3}{8} \times \frac{16}{9}-\frac{3}{8}$
$=\frac{2}{3}-\frac{3}{8}$
$=\frac{16-9}{24}$
$=\frac{7}{24}$

Using BODMAS
$
\begin{aligned}
&=\left(\frac{7}{16} \div 10 \frac{1}{2} \text { of } 7 \frac{1}{5}\right) \times 3 \frac{3}{5}-1 \frac{1}{3} \times 1 \frac{1}{8} \div \frac{1}{2}+\frac{3}{4} \\
&=\left(\frac{7}{16} \div \frac{21}{2} \text { of } \frac{36}{5}\right) \times \frac{18}{5}-\frac{4}{3} \times \frac{9}{8} \div \frac{1}{2}+\frac{3}{4} \\
&=\left(\frac{7}{16} \div \frac{378}{5}\right) \times \frac{18}{5}-\frac{4}{3} \times \frac{9}{8} \div \frac{1}{2}+\frac{3}{4} \\
&=\frac{7}{16} \times \frac{5}{378} \times \frac{18}{5}-\frac{4}{3} \times \frac{9}{8} \times 2+\frac{3}{4} \\
&=\frac{1}{48}-3+\frac{3}{4} \\
&=\frac{1-144+36}{48}=-\frac{107}{48}
\end{aligned}
$

Using BODMAS identity
$
\begin{aligned}
&=8-[88 \div 2 \text { of } 11-(22-72 \div 4)] \\
&=8-[88 \div 2 \text { of } 11-4] \\
&=8-[88 \div 22-4] \\
&=8-[4-4] \\
&=8
\end{aligned}
$

$\Rightarrow\{5-5 \div(10-12) \times 8+9\} \times 3+5+5 \times 5 \div 5$ of 5
$=\left\{5-\frac{5}{-2} \times 8+9\right\} \times 3+5+5 \times 5 \div 25$
$=\{5+20+9\} \times 3+5+5 \times \frac{5}{25}$
$=34 \times 3+5+1$
$=102+6$
$=108$

\begin{aligned}
&\Rightarrow 2 \text { of } 5-\frac{1}{2}-\left[4 \div 2-\frac{1}{3}-\left\{\frac{3}{4}-\left(5-\frac{1}{2}-\frac{3}{4}\right)\right\}\right] \\
&=10-\frac{1}{2}-\left[2-\frac{1}{3}-\left\{\frac{3}{4}-\left(5-\frac{\frac{2-3}{4}}{}\right)\right\}\right] \\
&=10-\frac{1}{2}-\left[\frac{6-1}{3}-\left\{\frac{3}{4}-\left(5-\frac{-1}{4}\right)\right\}\right] \\
&=10-\frac{1}{2}-\left[\frac{5}{3}-\left\{\frac{3}{4}-\left(5+\frac{1}{4}\right)\right\}\right] \\
&=10-\frac{1}{2}-\left[\frac{5}{3}-\left\{\frac{3}{4}-\frac{21}{4}\right\}\right] \\
&=10-\frac{1}{2}-\left[\frac{5}{3}-\left\{\frac{-18}{4}\right\}\right] \\
&=10-\frac{1}{2}-\left[\frac{5}{3}+\frac{18}{4}\right] \\
&=10-\frac{1}{2}-\left[\frac{20+54}{12}\right] \\
&=10-\frac{1}{2}-\frac{74}{12} \\
&=\frac{120-6-74}{12} \\
&=\frac{40}{12} \\
&=\frac{10}{3}
\end{aligned}

$
\begin{aligned}
&\Rightarrow \text { Using BODMAS concept } \\
&=523+523 \times 523 \div 523 \\
&=523+523 \times 1 \\
&=1046
\end{aligned}
$

$\Rightarrow$ Using BODMAS concept
$=42 \div 9$ of $6-[64 \div 48 \times 3-15 \div 8 \times(11-17) \div 9] \div 14$
$=42 \div 54-[64 \div 48 \times 3-15 \div 8 \times(-6) \div 9] \div 14$
$=42 \div 54-\left[\frac{4}{3} \times 3-\frac{15}{8} \times \frac{-2}{3}\right] \div 14$
$=\frac{7}{9}-\left[4+\frac{5}{4}\right] \div 14$
$=\frac{7}{9}-\frac{21}{4} \div 14$
$=\frac{7}{9}-\frac{21}{4} \times \frac{1}{14}$
$=\frac{7}{9}-\frac{3}{8}$
$=\frac{56-27}{72}=\frac{29}{72}$

$\Rightarrow \frac{5 \frac{5}{8}}{6 \frac{3}{7}}$ of $\frac{6 \frac{7}{11}}{9 \frac{1}{8}} \div \frac{8}{9}\left(2 \frac{3}{11}+\frac{13}{22}\right)$ of $\frac{9}{5}$
$=\frac{\frac{45}{8}}{\frac{45}{7}}$ of $\frac{\frac{73}{11}}{\frac{73}{8}} \div \frac{8}{9}\left(\frac{25}{11}+\frac{13}{22}\right)$ of $\frac{9}{5}$
$=\frac{7}{8}$ of $\frac{8}{11} \div \frac{8}{9}\left(\frac{50+13}{22}\right)$ of $\frac{9}{5}$
$=\frac{7}{11} \div \frac{8}{9}\left(\frac{63}{22}\right)$ of $\frac{9}{5}$
$=\frac{7}{11} \div \frac{28}{11}$ of $\frac{9}{5}$
$=\frac{7}{11} \div \frac{252}{55}$
$=\frac{7}{11} \times \frac{55}{252}$
$=\frac{5}{36}$

$\Rightarrow 5 \times[6 \times 2\{3 \times 7 \div(5 \times 3)\}]$
$=5 \times[6 \times 2\{3 \times 7 \div 15\}]$
$=5 \times\left[6 \times 2\left\{3 \times \frac{7}{15}\right\}\right]$
$=5 \times\left[6 \times 2 \times \frac{7}{5}\right]$
$=5 \times \frac{84}{5}$
$=84$

$\Rightarrow$ Using BODMAS concept
$=25-4$ of $(14.4 \div 9)+16 \times 0.4$
$=25-4$ of $1.6+16 \times 0.4$
$=25-6.4+6.4$
$=25$

 $\Rightarrow$ Using BODMAS concept
$
\begin{aligned}
&=\frac{5}{6} \div \frac{5}{6} \text { of } \frac{5}{6} \times 1 \frac{2}{3}+\frac{3}{4} \div \frac{4}{3} \text { of } 1 \frac{1}{2}-1 \frac{1}{2}-\frac{5}{6} \div \frac{3}{4} \\
&=\frac{5}{6} \div \frac{25}{36} \times \frac{5}{3}+\frac{3}{4} \div 2-\frac{3}{2}-\frac{5}{6} \div \frac{3}{4}
\end{aligned}
$
$
\begin{aligned}
&=\frac{6}{5} \times \frac{5}{3}+\frac{3}{8}-\frac{3}{2}-\frac{10}{9} \\
&=2+\frac{3}{8}-\frac{3}{2}-\frac{10}{9} \\
&=\frac{144+27-108-80}{72} \\
&=-\frac{17}{72}
\end{aligned}
$

$\Rightarrow$ Using BODMAS concept
$
\begin{aligned}
&=(-5) \text { of }(-45) \div(-15)-(-3)+5 \times \frac{1}{15} \\
&=225 \div(-15)+3+\frac{1}{3} \\
&=-15+3+\frac{1}{3} \\
&=-11 \frac{2}{3}
\end{aligned}
$

$\frac{1}{4} \div 4 \frac{2}{9}$ of $\frac{9}{19}+\left(\frac{5}{4}-\frac{3}{8}\right)$
$= \frac{1}{4} \div \frac{38}{9}$ of $\frac{9}{19}+\left(\frac{10-3}{8}\right)$
$= \frac{1}{4} \div 2+\left(\frac{7}{8}\right)$
$= \frac{1}{4} \times \frac{1}{2}+\left(\frac{7}{8}\right)$
$= \frac{1}{8}+\frac{7}{8}=1$

$(5 \div 8)$ of $(4 \div 5)$ of $25\left(15^2-13^2\right)$
$\Rightarrow \frac{5}{8}$ of $\frac{4}{5}$ of $25 \times 56$
$\Rightarrow \frac{1}{2} \times 25 \times 56$
$\Rightarrow 700$

$\Rightarrow 25-[20-(10-(7-2))]$
$\Rightarrow 25-[20-(10-5)]$
$\Rightarrow 25-[20-(5)]$
$\Rightarrow 25-15$
$\Rightarrow 10$

$\Rightarrow \frac{18 \times 4 \div 2 \text { of } 3-4}{2 \times(9-7)+1-2 \times 3 \div 4 \text { of } \frac{1}{2}}$
$\Rightarrow \frac{18 \times 4 \div 6-4}{2 \times 2+1-2 \times 3 \div 2}$
$\Rightarrow \frac{12-4}{4+1-3}$
$\Rightarrow \frac{8}{2}=4$

$2-\left[2 \frac{1}{2} \times\left(\frac{-2}{3}\right)-5\left\{\frac{1}{5}-\left(\frac{3}{5}-\frac{7}{10}\right)\right\}\right]$

$\Rightarrow 2-\left[\frac{5}{2} \times\left(\frac{-2}{3}\right)-5\left\{\frac{1}{5}-\left(-\frac{1}{10}\right)\right\}\right]$

$\Rightarrow 2-\left[-\frac{5}{3}-5\left\{\frac{1}{5}+\frac{1}{10}\right\}\right]$

$\Rightarrow 2-\left[-\frac{5}{3}-5\left\{\frac{3}{10}\right\}\right]$

$\Rightarrow 2-\left[-\frac{5}{3}-\left\{\frac{3}{2}\right\}\right]$

$\Rightarrow 2-\left[-\frac{5}{3}-\left\{\frac{3}{2}\right\}\right]$

$\Rightarrow 2-\left[\frac{-10-9}{6}\right]$

$\Rightarrow 2-\left(\frac{-19}{6}\right)=\frac{31}{6}=5 \frac{1}{6}$