Reciprocal
It is just: 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":
| Number |
|
Reciprocal |
| 5 |
= 5/1 |
|
1/5 |
| 8 |
= 8/1 |
|
1/8 |
| 1,000 |
= 1,000/1 |
|
1/1,000 |
For Fractions, Flip the Whole Fractiom Over
Example: the reciprocal of 3/4 is 4/3
Read more at Reciprocal of a Fraction.
Flipping a Flip
If 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)
If 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:
2 × (1/2) = 2 x 0.5 = 1
And let us try another:
10 × (1/10) = 10 x 0.1 = 1
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".
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