Question

How do you find the additive and multiplicative inverse of 5/9?

Answer 1

Additive inverse of `5/9` is `-5/9` and multiplicative inverse of `5/9` is `9/5`

Explanation:

Additive inverse of a number is the number which when added to it makes the sum zero `0` - the additive identity element . Observe that `0` is known as additive identity element as when this is added to any number, it results in the same number.

Obviously additive inverse of `x` is `-x` and hence additive inverse of `5/9` is `-5/9`.

Multiplicative inverse of a number is the number which when multiplied to it makes the product one `1` - the multiplicative identity element . Observe that `1` is known as multiplicative identity element as when this when multiplied to any number, results in the same number.

Obviously multiplicative inverse of `x` is `1/x` and hence additive inverse of `5/9` is `1/(5/9)=9/5`.