Use this calculator to find the multiplicative inverse (or reciprocal) of any number. Works with integers, decimals, simple fractions and mixed numbers. The result includes the complete step-by-step solution.
Multiplicative Inverse Calculator
Input data
How to use the calculator
- Select the number type from the drop-down menu: integer/decimal, simple fraction, or mixed number.
- Fill in the fields with the number values.
- Click Calculate to see the multiplicative inverse.
- The calculator shows the decimal result, the inverted fraction, and the verification n × (1/n) = 1.
Multiplicative Inverse Formulas
| Number type | Inverse formula | Example |
|---|---|---|
| Integer n | 1/n | Inverse of 5 = 1/5 = 0.2 |
| Decimal | 1/x | Inverse of 2.5 = 1/2.5 = 0.4 |
| Fraction p/q | q/p | Inverse of 3/4 = 4/3 ≈ 1.333 |
| Mixed number a b/c | c/(ac+b) | Inverse of 2 1/3 = 3/7 ≈ 0.429 |
Frequently asked questions
What is the multiplicative inverse?
The multiplicative inverse (or reciprocal) of a number n is the value 1/n, such that n × (1/n) = 1. For a fraction p/q, simply swap the numerator and denominator: the inverse is q/p.
Example: The inverse of 4 is 1/4 = 0.25, because 4 × 0.25 = 1.
What is the multiplicative inverse of a fraction?
To find the inverse of a fraction p/q, swap the numerator and denominator: the inverse is q/p. Example: the inverse of 3/4 is 4/3 ≈ 1.333. Verification: (3/4) × (4/3) = 12/12 = 1.
How do you find the inverse of a mixed number?
First convert the mixed number to an improper fraction: for a b/c, the improper fraction is (ac + b)/c. Then invert it: the inverse is c/(ac + b).
Example: 2 and 1/3 = 7/3. Inverse = 3/7 ≈ 0.429.
Does every number have a multiplicative inverse?
No. Zero has no multiplicative inverse, because no number multiplied by zero equals 1 (n × 0 = 0 for any n). All other non-zero real numbers have a multiplicative inverse.
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