Final answer:
The additive inverse of 5/9 is -5/9, and the multiplicative inverse, or reciprocal, is 9/5, because these are the respective values that when added or multiplied by 5/9 yield zero and one.
Step-by-step explanation:
The student has asked to identify the additive and multiplicative inverses of the fraction 5/9. The additive inverse of a number is what you add to the original number to get zero. For 5/9, the additive inverse is -5/9 because (5/9) + (-5/9) = 0. Therefore, the additive inverse is -5/9.
The multiplicative inverse, or reciprocal, of a number is what you multiply the original number by to get one. For 5/9, the multiplicative inverse is 9/5 because (5/9) * (9/5) = 45/45 = 1. Therefore, the multiplicative inverse is 9/5.
A correct answer to the question is: Additive inverse: -5/9, Multiplicative inverse: 9/5, which corresponds to option d.
The additive inverse of a number is the value that, when added to the original number, equals zero. The multiplicative inverse, also known as the reciprocal, of a number is the value that, when multiplied by the original number, equals one.
In the case of 5/9, the additive inverse is -5/9 because 5/9 + (-5/9) = 0. The multiplicative inverse is 9/5 because (5/9) * (9/5) = 1.