Tag: mental multiplication

$\left(2^2 + 4^2 + 6^2 + ... + 20^2\right) = \left(1 \times 2\right)^2 + \left(2\times 2\right)^2 + \left(2 \times 3\right)^2 + ... + \left(2 \times 10\right)^2$

$= \left(2^2 \times 1^2\right) + \left(2^2 \times 2^2\right) + \left(2^2 \times 3^2\right) + ... + \left(2^2 \times 10^2\right)$

$= 2^2 \times \left [1^2 + 2^2 + 3^2 + ... + 10^2\right]$

$\left(1^2+2^2+3^2+....+n^2\right) = \frac{1}{6}n\left(n+1\right)\left(2n+1\right)$

$=\left(4\times\frac{1}{6}\times 10\times 11\times 21\right)$

$=\left(4\times 5\times 77\right)$

$= 1540$

In every 15 min there was a break of 5 min
If total 60 min break in all movie then number of commercial break =$\frac{60}{5}=12$
If 12 breaks are in movie then the duration of movie=$12\times 15+15=195    minutes$

Let, $\frac {2x}{3}=96$
$x=\frac {96\times 3}{2}=144$
$\therefore \frac {3}{4}\times 144=3\times 36=108$

$\displaystyle \left ( \left ( 3^2 \right )^{4/3} \div \left ( 3^3 \right )^{2/3} \right ) \times 3^{3/2}$
$= 3^{8/3} \div 3^2 \times 3^{3/2}$
$= \displaystyle 3^{8/3 - 2 + 3/2} $
$= \displaystyle  3^{ \displaystyle \frac{16 - 12 + 9}{6}}$
$= 3^{13/ 6}$

$1+9\times 10 = 91$

$\displaystyle\frac{0.24\times0.35}{0.02\times0.14\times0.15}= \frac{0.084}{0.00042}=200$

Let the smaller number is x 

Let the divisor number is x

Let the number is x

$46)57804(1256$
$\underline {46}$
$118$
$\underline {92}$
$260$
$\underline {230}$
$304$
$\underline {276}$
$\underline {28}$