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

Question

Jace Anderson · Accepted Answer

undefined The reciprocal of a number is obtained by taking the multiplicative inverse of the number, which means finding another number that, when multiplied by the original number, equals 1. For example, the reciprocal of 2 is $ \frac{1}{2} $ because $ 2 \times \frac{1}{2} = 1 $.

The opposite of a number is obtained by changing the sign of the number while keeping its magnitude unchanged. For example, the opposite of 3 is -3, and the opposite of -5 is 5.

Nathan Axel · 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.

#4*¼=1# ¼ is the reciprocal of 4 #7+(-7)=0# -7 is the opposite of 7

Eva Abramson · Answer

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

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#.

Savannah Anderson · Answer

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#