Question

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

Answer 1

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

Answer 2

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`.

Answer 3

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`