Let's start by converting the mixed numbers into improper fractions.
First, remember that "negative three and one fourth" is the same as "-3 1/4". To convert this mixed number into an improper fraction, you multiply the whole number (3) by the denominator of the fraction (4), then you add the result to the numerator of the fraction. This is so because there are 4 quarters in 1, thus there would be 3*4 quarters in 3. To this, we add the remaining quarter which is the fraction part.
3*4 = 12, adding 1 gives 13. Since the original number was negative, we have -13. The denominator remains the same. So, -3 1/4 = -13/4.
"Two and one third", or "2 1/3", is handled similarly. Multiply the whole number (2) by the denominator of the fraction (3), then add the numerator of the fraction (1).
2*3 = 6, adding 1 gives 7. So, 2 1/3 = 7/3.
Now, we should remember that dividing by a fraction is the same as multiplying by its reciprocal. So, -13/4 ÷ 7/3 is the same as -13/4 * 3/7.
Let's calculate that:
-13/4 * 3/7 = (-13 * 3) / (4 * 7) = -39/28.
So, if we simplify the fraction, we would get: -39/28 = -1 11/28.
Therefore, the result of negative three and one fourth divided by two and one third equals to negative one and eleven twenty-eighths.