Question

What is the opposite and reciprocal of 6/5?

Answer 1

The opposite of `6/5` is `-6/5`

The reciprocal of `6/5` is `5/6`

Explanation:

The opposite of a number is its additive inverse.

In our example:

`6/5 + -6/5 = 0`

In general, the opposite of `x` is `-x`.

If you think of these two numbers sitting on the real line, then they are on opposite sides of the origin, `0`, at the same distance.

The reciprocal of a number is its multiplicative inverse.

In our example:

`6/5 * 5/6 = 1`

In general, the reciprocal of `x` is `1/x`.

Notice that the reciprocal of `0` is undefined - `0` has no multiplicative inverse.