How this calculator works
A multiplicative inverse is the value that multiplies the original number to give 1. Reverse a fraction's numerator and denominator, then reduce it. Convert mixed numbers to improper fractions first. For decimal inputs, the exact fraction uses the numeric decimal spelling. Taking a reciprocal twice recovers the original number.
Formula
x × x^(-1) = 1; reciprocal(x) = 1/x for x != 0. The reciprocal of n/d is d/n.
Worked example
The reciprocal of 3/4 is 4/3. For -2 1/2 = -5/2, the reciprocal is -2/5 = -0.4. A known reciprocal of 0.25 gives original number 4.
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Frequently asked questions
Why does zero have no inverse?
Every finite number multiplied by zero gives zero, so no product can equal 1.
Can the reciprocal be negative?
Yes. It has the same sign as the original non-zero number.
What if the decimal answer is too large?
The calculator rejects a non-finite decimal result. Use smaller magnitudes when the reciprocal exceeds numeric display range.