The problem is to evaluate the expression $\frac{6}{7} \div 2\frac{1}{7}$.

1. Problem Description

The problem is to evaluate the expression $\frac{6}{7} \div 2\frac{1}{7}$.

2. Solution Steps

First, we convert the mixed number $2\frac{1}{7}$ to an improper fraction.

$2\frac{1}{7} = \frac{2 \times 7 + 1}{7} = \frac{14 + 1}{7} = \frac{15}{7}$

So, the expression becomes $\frac{6}{7} \div \frac{15}{7}$.

To divide fractions, we multiply by the reciprocal of the divisor.

$\frac{6}{7} \div \frac{15}{7} = \frac{6}{7} \times \frac{7}{15}$

We can simplify this by canceling the 7s.

$\frac{6}{7} \times \frac{7}{15} = \frac{6}{1} \times \frac{1}{15} = \frac{6}{15}$

Now, we simplify the fraction $\frac{6}{15}$ by dividing both the numerator and denominator by their greatest common divisor, which is

3. $\frac{6}{15} = \frac{6 \div 3}{15 \div 3} = \frac{2}{5}$

3. Final Answer

$\frac{2}{5}$