Multiplicative Inverse Calculator
Find the multiplicative inverse (reciprocal) of numbers, fractions, and mixed numbers with step-by-step solutions
Calculate Multiplicative Inverse
Enter any non-zero integer or decimal number
Multiplicative Inverse Result
Why? The multiplicative inverse of a number a is a value b such that a × b = 1. Since any number multiplied by zero equals zero (never 1), zero has no multiplicative inverse.
Example Calculations
Integer Example
Multiplicative inverse of 5
Decimal Example
Multiplicative inverse of 2.5
Fraction Example
Multiplicative inverse of 3/4
Mixed Number Example
Multiplicative inverse of 2 1/3
Key Properties
Definition
The multiplicative inverse of a is b such that a × b = 1
For Fractions
Inverse of a/b is b/a (flip numerator and denominator)
Special Cases
1 and -1 are their own multiplicative inverses
Zero Exception
Zero has no multiplicative inverse
Quick Tips
Multiplicative inverse is also called reciprocal
For integer n: inverse = 1/n
For fraction a/b: inverse = b/a
Sign of inverse matches original number
Inverse of inverse equals original number
Understanding Multiplicative Inverse
What is Multiplicative Inverse?
The multiplicative inverse (or reciprocal) of a number a is another number b such that when they are multiplied together, the result equals 1. Mathematically: a × b = 1.
Key Properties
- Uniqueness: Every non-zero number has exactly one multiplicative inverse
- Sign preservation: Positive numbers have positive inverses, negative have negative
- Special cases: 1 and -1 are their own inverses
- Zero exception: Zero has no multiplicative inverse
How to Find Multiplicative Inverse
For Integers
Inverse of n = 1/n
Example: Inverse of 5 = 1/5 = 0.2
For Fractions
Inverse of a/b = b/a
Example: Inverse of 3/4 = 4/3
For Decimals
Convert to fraction, then flip
Example: 0.25 = 1/4, inverse = 4/1 = 4
Converting Mixed Numbers
Steps:
- Convert mixed number to improper fraction
- Use formula: (whole × denominator + numerator) / denominator
- Find inverse by flipping numerator and denominator
Example: 2¼ = (2×4 + 1)/4 = 9/4
Inverse = 4/9
Applications
Division
a ÷ b = a × (multiplicative inverse of b)
Solving Equations
Isolate variables by multiplying by inverse
Complex Fractions
Simplify by multiplying by inverse