Final answer:
The additive inverse of 32 is -32, which is obtained by subtracting 32 from itself. The multiplicative inverse of 32 is ¼ or 0.03125, which is the number that when multiplied by 32 results in 1.
Step-by-step explanation:
To find the additive inverse of 32, we subtract 32 from itself, which will always result in 0. Therefore, the additive inverse of 32 is -32.
Now, to find the multiplicative inverse (or reciprocal) of 32, we must find a number which, when multiplied by 32, results in the multiplicative identity, which is 1. The multiplicative inverse of 32 is ¼ or 0.03125.
The additive inverse of a number is the value that, when added to the original number, yields zero. For 32, its additive inverse is -32 since 32 + (-32) equals zero. On the other hand, the multiplicative inverse, or reciprocal, of 32 is a number that, when multiplied by 32, equals the multiplicative identity, which is 1. In this case, the multiplicative inverse of 32 is 1/32 or 0.03125. These concepts are fundamental in algebra and provide a basis for understanding the properties of addition and multiplication in the number system.