What is the opposite and reciprocal of 2 3/4?

1 Answer
Jul 9, 2015

Answer:

The opposite (additive inverse) of #2 3/4 = 11/4# is #-2 3/4 = -11/4#

The reciprocal (multiplicative inverse) of #2 3/4 = 11/4# is #4/11#.

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 #2 3/4 = 11/4# is #-2 3/4 = -11/4#

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 #2 3/4 = 11/4# is #1/(11/4) = 4/11#.