Final answer:
The reciprocal of -2 5/6 is -6/17, which is obtained by converting the mixed number to an improper fraction and then inverting it while maintaining the negative sign.
Step-by-step explanation:
The reciprocal of a number is found by inverting the number, or flipping its numerator and denominator if it's a fraction. To find the reciprocal of -2 5/6, first convert the mixed number to an improper fraction. -2 5/6 is the same as -17/6 because 2 times 6 (the denominator) is 12, plus 5 equals 17, and you keep the negative sign. Therefore, the reciprocal of -17/6 will be -6/17 because we flip the numerator and the denominator. It's important not to remove the negative sign when finding the reciprocal. The sign of the reciprocal remains the same as the sign of the original number.