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

3 Answers
May 6, 2018

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

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