What is the difference between a reciprocal of a number and a opposite of the number?

3 Answers
May 6, 2018

Answer:

When you multiply a reciprocal with its original number, the result is 1.
When you add the opposite to its original number, the result is 0.

Explanation:

#4*¼=1#

¼ is the reciprocal of 4

#7+(-7)=0#

-7 is the opposite of 7

May 6, 2018

Answer:

The reciprocal of a number is its inverse under multiplication.
The opposite of a number is its inverse under addition.

Explanation:

The number #1# is the identity for multiplication, since for any number #x#, we have:

#1 * x = x * 1 = x#

If #x != 0# then it has a reciprocal #1/x# which is its (right and left) inverse under multiplication:

#x * 1/x = 1/x * x = 1#

The number #0# is the identity for addition, since for any number #x#, we have:

#0 + x = x + 0 = x#

For any #x#, there is an additive inverse #-x# called the opposite of #x# such that:

#x + (-x) = (-x)+x = 0#

So for example the reciprocal of #2# would be #1/2# and its opposite would be #-2#.

May 6, 2018

A reciprocal is one over the number

Reciprocal of 2#=> 1/2#

#3/4 =>. 4/3#

0.45#=>1/0.45=100/45=20/9#

The opposite of a number is more about the operation:

The opposite of +4 is -4

#xx4# is #-:4#

#sqrt 4# is #4^2#