Question

What is the opposite and reciprocal of 5/9?

Answer 1

The opposite (additive inverse) of `5/9` is `-5/9`

The reciprocal (multiplicative inverse) of `5/9` is `9/5`

Explanation:

Addition

The additive identity is `0`. This has the property that for any number `a`:

`a + 0 = 0 + a = a`

If `a` is any number, then `-a` is called the opposite or additive inverse of `a`. It has the property that:

`a + (-a) = (-a) + a = 0`

The additive inverse of `5/9` is `-5/9`

Multiplication

The multiplicative identity is `1`. This has the property that for any number `a`:

`a * 1 = 1 * a = a`

If `a` is any non-zero number, then `1/a` is called the reciprocal or multiplicative inverse of `a`. It has the property that:

`a * (1/a) = (1/a) * a = 1`

The multiplicative inverse of `5/9` is `1/(5/9) = 9/5`