Definition
Reciprocal
A reciprocal is a nonzero number’s partner that multiplies with it to make 1.
What it means
A number and its reciprocal form a make-one pair. For a nonzero fraction, swap the numerator and denominator: 3/5 pairs with 5/3. A whole number such as 4 can be written 4/1, so its reciprocal is 1/4. Zero has no reciprocal.
Remember it
A number and its reciprocal are a make-one pair.
Example
The reciprocal of 3/5 is 5/3 because (3/5) × (5/3) = 15/15 = 1.
Watch for
Zero has no reciprocal because zero multiplied by any number is still zero, never 1.
Common mix-up
A reciprocal is not an opposite: the reciprocal of 3 is 1/3, while the opposite of 3 is −3.
Exact meaning
For any nonzero number x, its reciprocal is 1/x, the number whose product with x is 1. For a nonzero fraction a/b, the reciprocal is b/a.