Question

How do you find the additive and multiplicative inverse of -1 1/5?

Answer 1

Additive inverse: `11/5`
Multiplicative inverse: `-5/11`

Explanation:

The identity element `o` for a set and a binary operation is the element such that `o@a=a@o=o` for all `a` in the set, where `@` is the binary operator.

The inverse `b` of a number `a` under a binary operator `@` is the number such that `a@b=b@a=o`, where `o` is the identity element.

The additive inverse for a number `a` is a number `b` such that `a+b=b+a=0` (since `0` is the identity element for addition under the reals).

The multiplicative inverse for a number `a` is a number `b` such that `a*b=b*a=1` (since `1` is the identity element for addition under the reals).

The additive inverse of the number `-11/5` is the number `b` such that `b+(-11/5)=0`. Add `11/5` to both sides to get `b=11/5`.

The multiplicative inverse of the number `-11/5` is the number `b` such that `b*(-11/5)=1`. Multiply `-5/11` to both sides to get `b=-5/11`.