To divide -2 1/8 ÷ 6 4/5, we can convert the mixed numbers to improper fractions.
First, let's convert -2 1/8 to an improper fraction. Multiply the whole number (-2) by the denominator of the fraction (8) and add the numerator (1). This gives us -17/8.
Next, let's convert 6 4/5 to an improper fraction. Multiply the whole number (6) by the denominator of the fraction (5) and add the numerator (4). This gives us 34/5.
Now, we can divide the two improper fractions. To do this, we multiply the first fraction (-17/8) by the reciprocal of the second fraction (5/34).
Multiplying the numerators (-17 * 5) gives us -85, and multiplying the denominators (8 * 34) gives us 272.
Therefore, the quotient of -2 1/8 ÷ 6 4/5 is -85/272.