Question

How do you find the additive and multiplicative inverse of 4/3?

Answer 1

Additive inverse, `-4/3`
Multiplicative inverse, `3/4`

Explanation:

For a number `a`, it's multiplicative inverse `b` is such that `a*b = 1` which is the multiplicative identity.

For a number `a`, it's additive inverse `c` would be such that `a + c = 0` where `0` is additive identity.

Thus, for `a = 4/3`
It's additive inverse be `c`.

Then `4/3 + c = 0`

Now, adding `-4/3` to both sides,

`c = -4/3`.

Let the multiplicative inverse be `b`.

Then `a*b = 1`
`implies 4/3*b = 1`

Multiplying both sides with `3/4`

`b = 3/4`