Question 1

The value of $$999\frac{1}{7}+999\frac{2}{7}+999\frac{3}{7}+999\frac{4}{7}+999\frac{5}{7}+999\frac{6}{7}$$ is equal to:

Solution

We can write $$999\frac{1}{7}+999\frac{2}{7}+999\frac{3}{7}+999\frac{4}{7}+999\frac{5}{7}+999\frac{6}{7}$$ as,

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

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

=$$5994+3$$

=$$5997$$

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