What is a multiplicative inverse?
It is the number that multiplies with the original to give 1—also called the reciprocal.
Multiplicative Inverse Calculator
Flip a fraction or take 1 divided by a decimal to find the multiplicative inverse.
Choose input type and value
Select fraction or decimal mode, then enter the value to invert.
About this calculator
How to use Multiplicative Inverse Calculator, plus the formulas and logic behind the results.
Tool description
The multiplicative inverse of x is 1/x. For a fraction a/b, the reciprocal is b/a (when a ≠ 0).
How to use
- Choose fraction or decimal input.
- Enter the fraction parts or the decimal value.
- Select Calculate to view the reciprocal.
- Confirm that original × inverse equals 1.
Formulas & reference
Inverse of a/b = b/a (a ≠ 0)Inverse of x = 1/x (x ≠ 0)x × (1/x) = 1
Examples
- Inverse of 2/5 is 5/2
- Inverse of 4 is 1/4
- Inverse of 0.25 is 4
- Inverse of −3/4 is −4/3
Calculation logic
Fraction mode swaps numerator and denominator and simplifies. Decimal mode computes 1/x and optionally expresses it as a fraction.
Zero has no multiplicative inverse. Both modes block division by zero.
Multiplicative Inverse Calculator FAQ
Common questions about this calculator and how to use the results.
What is the reciprocal of a fraction?
Swap numerator and denominator: the reciprocal of a/b is b/a.
Does zero have an inverse?
No. Division by zero is undefined, so 0 has no multiplicative inverse.
Can decimals be inverted?
Yes. The inverse of a non-zero decimal x is 1/x.
What about negative numbers?
The inverse keeps the negative sign: the inverse of −2 is −1/2.
How can I check the answer?
Multiply the original by the inverse; the product should be 1.