Discussion Forum

Simplify $\left(999\frac{1}{7}+999\frac{2}{7}+999\frac{3}{7}+999\frac{4}{7}+999\frac{5}{7}+999\frac{6}{7}\right)$

Answer:

Explanation:

Given exp.
$=\left(1000-\frac{6}{7}\right)+\left(1000-\frac{5}{7}\right)+\left(1000-\frac{4}{7}\right)$

$+\left(1000-\frac{3}{7}\right)+\left(1000-\frac{2}{7}\right)+\left(1000-\frac{1}{7}\right)$

$=6000-\left(\frac{6}{7}+\frac{5}{7}+\frac{4}{7}+\frac{3}{7}+\frac{2}{7}+\frac{1}{7}\right)$
$=6000-\frac{21}{7}$
$=6000-3=5997$