Multiplicative Inverse Calculator
Result
About Multiplicative Inverse
The multiplicative inverse (or reciprocal) of a number is the number that, when multiplied by the original number, gives a product of 1.
Formula:
For a number a, its multiplicative inverse is 1/a, where a ≠ 0
Properties:
- Every non-zero number has a unique multiplicative inverse
- The product of a number and its inverse is always 1
- Zero has no multiplicative inverse
- The inverse of a fraction a/b is b/a
Examples:
| Number | Multiplicative Inverse | Verification |
|---|---|---|
| 5 | 1/5 = 0.2 | 5 × 0.2 = 1 |
| 2/3 | 3/2 = 1.5 | 2/3 × 3/2 = 1 |
| -4 | -1/4 = -0.25 | -4 × -0.25 = 1 |
Applications:
- Division operations (dividing by a number is the same as multiplying by its inverse)
- Solving equations
- Matrix operations
- Cryptography
- Signal processing
Tips:
- Remember that zero has no multiplicative inverse
- For fractions, simply flip the numerator and denominator
- The inverse of a negative number is also negative
- Multiplying a number by its inverse always gives 1
- For decimal numbers, use 1 divided by the number
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