Additive inverse: change all signs. Multiplicative inverse: flip it over.
It is -a/3
The multiplicative inverse of -3 is -(1/3) or negative one-third. The multiplicative inverse of a number is the number that you multiply it by to get a result of 1 (the multiplicative identity). So, since -3 times -(1/3) is 1, -(1/3) is the multiplicative inverse of -3. Similarly, +3 is the ADDITIVE inverse of -3. The additive inverse of a number is the number you add to it to get a result of 0 (the additive identity). So, since -3 + (+3) = 0, +3 is the additive inverse of -3. The original answer given here was that the multiplicative inverse of -3 is +3, which is flat incorrect.
-5
-1/4
-1/2
4/7
Oh, dude, the additive inverse of 3 over 4 is -3 over 4. It's like flipping the sign of the fraction, you know? So, if you owed someone 3/4 of a pizza, the additive inverse would mean you now have 3/4 of a pizza. Cool, right?
+7/9, positive seven over nine.
If the multiplicative inverse of a number is the number that you could multiply with the original number in order to obtain one, then the mulitplicative inverse of -15 and 2/3 is -3/47 negative three fourtysevenths, or negative three over fourtyseven.
the inverse of any number is the fraction of ONE over that number. so, inverse of ten is ONE/TEN or one tenth. the inverse of 3 is ONE/THREE or one third the inverse of one fourth is a bit trickier, but not if you go slowly, ONE over ONE FOURTH, which mathematically changes to 4. the inverse of cat is ONE over CAT (which is senseless, but might help you remember how to do inverses).
It depends on the context. The additive inverse of a number, X, is the number -X such that their sum is 0. The multiplicative inverse of a (non-zero) number, Y, is the number -Y such that their product is 1. The inverse of a function f, is the function g (over appropriate domains and ranges) such that if f(X) = Y then g(Y) = X. So, for example, if f(X) = 2X then g(X) = X/2 or if f(X) = exp(X) then g(X) = ln(X), and so on.