Final answer:
To divide 4 and one-third by -5/6, convert the mixed number to an improper fraction and multiply by the reciprocal of -5/6.
Step-by-step explanation:
To divide 4 and one-third by -5/6, we can convert the mixed number into an improper fraction. 4 and one-third is equivalent to (4x3+1)/3 = 13/3. Dividing by -5/6 is the same as multiplying by its reciprocal, which is -6/5. Therefore, (13/3) ÷ (-5/6) becomes (13/3) x (-6/5). Multiply the numerators together to get -78 and multiply the denominators to get 15. So, the answer is -78/15.