Final answer:
To divide 4 1/3 by -5/6, we convert the division into multiplication by taking the reciprocal of the divisor. We then multiply the mixed numbers by converting them into improper fractions and multiply the numerators and denominators separately. The resulting expression is -78/15.
Step-by-step explanation:
To find the division expression equivalent to 4 1/3 divided by -5/6, we can change the division into multiplication by taking the reciprocal of the divisor. The reciprocal of -5/6 is -6/5. So, the division expression becomes 4 1/3 multiplied by -6/5.
To multiply mixed numbers, we first convert them into improper fractions. 4 1/3 is equal to (3*4 + 1) / 3 = 13/3. Multiplying 13/3 by -6/5, we multiply the numerators and denominators separately: (13 * -6) / (3 * 5).
The result of multiplying the numerators is -78 and the result of multiplying the denominators is 15. So, the final answer is -78/15.