Add the fractions -1/2 and 6/7.

1. Identify the operation and numbers: The problem asks to add two fractions: $-\frac{1}{2}$ and $\frac{6}{7}$.
2. Find a common denominator: To add fractions, they must have the same denominator. The least common multiple (LCM) of 2 and 7 is 14. This will be our common denominator.
3. Convert the fractions to have the common denominator:
- For the first fraction, $-\frac{1}{2}$, multiply the numerator and denominator by 7: $$-\frac{1 \times 7}{2 \times 7} = -\frac{7}{14}$$
- For the second fraction, $\frac{6}{7}$, multiply the numerator and denominator by 2: $$ \frac{6 \times 2}{7 \times 2} = \frac{12}{14}$$
4. Add the fractions with the common denominator: Now that both fractions have the same denominator, add their numerators: $$-\frac{7}{14} + \frac{12}{14} = \frac{-7 + 12}{14}$$
5. Calculate the sum of the numerators: $$-7 + 12 = 5$$
So the sum is: $$\frac{5}{14}$$
6. Simplify the result: The fraction $\frac{5}{14}$ is already in its simplest form because 5 and 14 have no common factors other than 1.