Question

What is the opposite and reciprocal of -11/9?

Answer 1

The opposite and reciprocal of `-11/9` is `9/11`.

Explanation:

The opposite of `-11/9` is its additive inverse `11/9`. The sum of a number and its additive inverse equal `0`.

Additive inverse property:

`color(red)a+color(blue)(-a)=color(purple)0=color(blue)(-a)+color(red)a`

The reciprocal of a fraction is its multiplicative inverse. The product of a number and its multiplicative inverse equals `1`.

Multiplicative inverse property:

`color(magenta)axxcolor(teal)(1/a)=color(purple)1=color(teal)(1/a)xxcolor(magenta)a`

The multiplicative inverse of `11/9` is `9/11`.