What is the opposite and reciprocal of 5/9?

1 Answer
Jul 9, 2015

Answer:

The opposite (additive inverse) of #5/9# is #-5/9#

The reciprocal (multiplicative inverse) of #5/9# is #9/5#

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 #5/9# is #-5/9#

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 #5/9# is #1/(5/9) = 9/5#