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

1 Answer
May 25, 2018

Answer:

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#.