Reciprocal Calculator
Find the multiplicative inverse of numbers and fractions with step-by-step solutions
Calculate Reciprocal
Enter any non-zero number (integers, decimals, negative numbers)
Reciprocal Result
Step-by-Step Solution:
Mathematical Property:
The product of a number and its reciprocal equals 1
Alternative Notation:
1/x or x⁻¹
Reciprocal Properties
Definition
The reciprocal (or multiplicative inverse) of x is 1/x
For Fractions
Reciprocal of a/b is b/a (swap numerator and denominator):
Special Cases
- • Reciprocal of 1 = 1
- • Reciprocal of -1 = -1
- • Reciprocal of 0 is undefined
- • Reciprocal of reciprocal = original number
Quick Examples
Common Reciprocals
Mathematical Rules
(1/x)⁻¹ = x
1/(a/b) = b/a
1/(1/x) = x
x⁻¹ = 1/x
Understanding Reciprocals
What is a Reciprocal?
A reciprocal, also called the multiplicative inverse, is a number that when multiplied by the original number gives a product of 1. For any non-zero number x, its reciprocal is 1/x.
How to Find Reciprocals
- •For whole numbers: Divide 1 by the number
- •For fractions: Flip the numerator and denominator
- •For decimals: Divide 1 by the decimal
Etymology
The word "reciprocal" comes from Latin "reciprocus," meaning "returning the same way" or "alternating," which perfectly describes the mathematical relationship.
Key Points
- • Zero has no reciprocal (undefined)
- • The reciprocal of 1 is 1
- • The reciprocal of -1 is -1
- • Reciprocals preserve signs
- • Taking the reciprocal twice returns the original number
Applications of Reciprocals
Algebra
Solving equations involving fractions and rational expressions.
Physics
Calculating inverse relationships in physics formulas and electrical circuits.
Finance
Interest rate calculations, currency conversions, and investment ratios.