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#.
