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What is the value of $999 \frac{1}{7} + 999 \frac{2}{7} + 999 \frac{3}{7} + 999 \frac{4}{7} + 999 \frac{5}{7} + 999 \frac{6}{7}$ when simplified?
$1001$
$999$
$1000$
$5997$

A

1001

B

999

C

5997

D

1000

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Solution

Verified by Toppr

$999 \frac{1}{7} + 999 \frac{2}{7} + 999 \frac{3}{7} + 999 \frac{4}{7} + 999 \frac{5}{7} + 999 \frac{6}{7}$

$= 999 + \frac{1}{7} + 999 + \frac{2}{7} + 999 + \frac{3}{7} + 999 + \frac{4}{7} + 999 + \frac{5}{7} + 999 + \frac{6}{7}$

$= 999 \times 6 + (\frac{1}{7} + \frac{2}{7} + \frac{3}{7} + \frac{4}{7} + \frac{5}{7} + \frac{6}{7})$

$= 5994 + \frac{21}{7} = 5994 + 3 = 5997$

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