does 0/4 have an additive or multiplicative inverse?
It does have an additive inverse: itself. 0/4 0 is the additive identity, and the identity for any operation is always its own inverse, because 0 + 0 0. However, it has no multiplicative inverse. If it did, there would be a number x such that 0x 1, which is impossible.
One could argue that it does not have an additive inverse because you are looking for its opposite and since 0/4 0 and 0 is neither positive nor negative how can you find its opposite? It definitely does not have a multiplicative inverse because that refers to its reciprocal and if you flip 0/4 over you get 4/0 and you cannot divide by 0! Plus when you take a number times its multiplicative inverse you should get 1!!!
One could argue that it does not have an additive inverse because you are looking for its opposite and since 0/4 0 and 0 is neither positive nor negative how can you find its opposite? It definitely does not have a multiplicative inverse because that refers to its reciprocal and if you flip 0/4 over you get 4/0 and you cannot divide by 0! Plus when you take a number times its multiplicative inverse you should get 1!!!
