Free Practice Questions for Simplification in Maths

$=\frac{\frac{1}{5} \div \frac{1}{25}}{\frac{1}{25} \div \frac{1}{5}}=\frac{\frac{25}{5}}{\frac{5}{25}}=\frac{25}{5} \times \frac{25}{5}$
$=25$

$\frac{(0.623)^{3}+(0.377)^{3}}{(0.623)^{2}-(0.623 \times 0.377)+(0.377)^{2}}$
$=\frac{(0.623+0.377)\left(0.623^{3}-0.623 \times 0.377+0.377^{2}\right)}{(0.623)^{2}-0.623 \times 0.377+(0.377)^{2}}$
${\left[\because a^{3}+b^{3}=(a+b)\left(a^{2}-a b+b^{2}\right)\right] }$
$=0.623+0.377=1.000=1$

$4 \frac{2}{3} \times \frac{9}{14}+5 \frac{1}{6} \times 2 \frac{2}{5}$

On solving the given question,

$\frac{14}{3} \times\frac{9}{14}+\frac{31}{6}\times\frac{12}{5}$

$\Rightarrow$3+$\frac{62}{5}$

$\Rightarrow$$\frac{62+15}{5}$

$\Rightarrow$$15 \frac{2}{5}$

$\begin{aligned} 243 \times 124 &-25340 \\=& 30132-25340=4792 \end{aligned}$

$5-\left[\frac{3}{4}+\left\{2 \frac{1}{2}-\left(0.5+\frac{\overline{1}}{6}-\frac{1}{7}\right)\right\}\right]$
$=5-\left[\frac{3}{4}+\left\{\frac{5}{2}-\left(\frac{1}{2}+\frac{7-6}{42}\right)\right\}\right]$
$\left.=5-\left[\frac{3}{4}+\left\{\frac{5}{2}-\left(\frac{1}{2}+\frac{1}{42}\right)\right\}\right]\right]$
$\left.=5-[\frac{3}{4}+\left\{\frac{5}{2}-\frac{22}{42}\right\}\right]$
$=5-\left[\frac{3}{4}+\frac{105-22}{42}\right]=5-\left[\frac{3}{4}+\frac{83}{42}\right]$
$=5-\left[\frac{63+166}{84}\right]=5-\frac{229}{84}$
$=\frac{420-229}{84}=\frac{191}{84}$

$45-[28-\{37-(15-?)\}]=58$
$\begin{array}{lrl}\Rightarrow & -[28-\{37-(15-?)\}] & =58-45 \\ \Rightarrow & -[28-\{37-(15-?)\}] & =13 \\ \Rightarrow & 28-\{37-(15-?)\} & =-13 \\ \Rightarrow & 28+13 & =37-(15-?) \\ \Rightarrow & 41 & =37-(15-?) \\ \Rightarrow & (15-?) & =37-41 \\ \Rightarrow & (15-?) & =-4 \\ \Rightarrow & (15+4) & =? \\ \Rightarrow & ? & =19\end{array}$

$\frac{(598+178)^{2}-(598-178)^{2}}{598 \times 178}$
$=\frac{4 \times 598 \times 178}{598 \times 178} \quad\left[\because(a+b)^{2}-(a-b)^{2}=4 a b\right]$
$=4$

$19587 \times 637+19587 \times 363$
$=19587(637+363)$
$=19587 \times 1000$ $[a b+a c=a(b+c)]$
$=19587000$

$?+3699+1985-2047=31111$

$\Rightarrow$$?+3637=31111$

$\Rightarrow$$?=31111-3637$

$\Rightarrow$$?=27474$

Let $856=a$ and $167=b$

Then, by placing the value in the given expression,

$\frac{(a+b)^{2}+(a-b)^{2}}{a \times a+b \times b} $

$\frac{a^{2}+b^{2}+2 a b+a^{2}+b^{2}-2 a b}{a^{2}+b^{2}} $

$=\frac{2\left(a^{2}+b^{2}\right)}{\left(a^{2}+b^{2}\right)} =2$