Question

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?

• A. $5997$
• B. $999$
• C. $1000$
• D. $1001$

Answer 1

Answer: (A)

$5997$

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

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

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

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