Reciprocal
It is simply: 1/number
Very simple! To get the reciprocal of a number, just divide 1 by the number.
Example: the reciprocal of 2 is ½ (a half)
More Examples:
Number  Reciprocal  As a Decimal 

5  ^{1}/_{5}  = 0.2 
8  ^{1}/_{8}  = 0.125 
1,000  ^{1}/_{1,000}  = 0.001 
Like Turning the Number Upside Down
In fact, if you think that a whole number could be written as "number/1", then the reciprocal is just like "flipping it over":

For Fractions, Flip the Whole Fraction Over
Example: the reciprocal of ^{3}/_{4} is ^{4}/_{3}
Read more at Reciprocal of a Fraction.
Flipping a FlipIf you take the reciprocal of a reciprocal you end up back where you started! 
Example:
The reciprocal of 4 is ^{1}/_{4}
The reciprocal of ^{1}/_{4} is 4 (back to 4 again)
It may help you to remember that "Reciprocal" comes from the Latin reciprocus meaning returning. Like going to the shops and then returning home again.
But Not Zero
Every number has a reciprocal except 0 (1/0 is undefined)
Multiply a Number by Its Reciprocal and You Get 1
Let us try multiplying a number by its reciprocal:
And let us try another:
Yes! You always get 1
In fact that is a way to define Reciprocal:
Reciprocal: what to multiply a value by to get 1
In terms of multiplying it is the Inverse, so it is also called the "Multiplicative Inverse".