Final answer:
The additive inverse of a number is the value that makes the sum equal to zero. For the fractions (-6/7) and (101/213), their additive inverses are (6/7) and (-101/213), respectively, which is Option A.
Step-by-step explanation:
The additive inverse of a number is the value that, when added to the original number, will result in zero. To find the additive inverse of a fraction, we change the sign of the numerator while keeping the denominator the same.
Considering the fractions given in the question:
- The additive inverse of (-6/7) is (6/7).
- The additive inverse of (101/213) is (-101/213).
Therefore, the answer to the question is Option A: the additive inverses are (6/7) and (-101/213), resulting in a sum of zero for both cases when added to the original numbers.