Final answer:
To divide -2 1/8 by 6 4/5, both mixed numbers are first converted to improper fractions, then the division is transformed into multiplication by taking the reciprocal of the divisor, resulting in -85/272 after multiplication and simplification.
Step-by-step explanation:
To divide -2 1/8÷6 4/5, first we need to convert the mixed numbers into improper fractions. For -2 1/8, this becomes -17/8 because 2×8 is 16 and adding the numerator 1 gives us 17. For 6 4/5, we have 5×6 which is 30, add the numerator 4 to get 34, so the fraction is 34/5.
Now we have the division of two fractions: (-17/8)÷(34/5). To divide by a fraction, we multiply by its reciprocal. The reciprocal of 34/5 is 5/34. Thus, the division becomes a multiplication: (-17/8)×(5/34).
When multiplying fractions, you multiply the numerators together and the denominators together. This gives us (-17×5)/(8×34), which is -85/272. To simplify, we look for any common factors between the numerator and denominator. In this case, there aren't any, so -85/272 is the simplest form of the quotient.
Thus, the answer to the division of -2 1/8 by 6 4/5 is -85/272.