To divide a mixed number by a fraction, we first convert the mixed number into an improper fraction. In this case, 12¾ can be written as 51/4. Then, we invert the divisor (⅖ becomes 5/2) and multiply it by the dividend. So, 51/4 ÷ 5/2 is the same as 51/4 * 2/5. Simplifying this gives us 255/20. Finally, we reduce the fraction to its simplest form, which is 255/8. Additionally, 255/8 can also be expressed as a mixed number, which is 31 7/8. Therefore, the correct answers are 255/8, 31.875, and 31 7/8.