Reciprocal Calculator – Find 1/x
Calculate the reciprocal of any number
Table of Contents
How to Use
- Enter any non-zero number
- Click calculate to find the reciprocal
- View the result as a decimal and fraction
- Check the verification that shows x × (1/x) = 1
What is a Reciprocal?
The reciprocal of a number is also called its multiplicative inverse. For any non-zero number x, the reciprocal is 1/x. When you multiply a number by its reciprocal, the result is always 1.
Formula: Reciprocal of x = 1/x, where x × (1/x) = 1
Examples
- Reciprocal of 2 = 1/2 = 0.5
- Reciprocal of 5 = 1/5 = 0.2
- Reciprocal of 1/3 = 3
- Reciprocal of -4 = -1/4 = -0.25
- Reciprocal of 0.25 = 4
Properties of Reciprocals
- The reciprocal of a reciprocal is the original number: 1/(1/x) = x
- Zero has no reciprocal (division by zero is undefined)
- The reciprocal of 1 is 1
- The reciprocal of -1 is -1
- Reciprocals of positive numbers are positive
- Reciprocals of negative numbers are negative
Applications
- Division: Dividing by a number is the same as multiplying by its reciprocal
- Fractions: To divide fractions, multiply by the reciprocal of the divisor
- Algebra: Solving equations often involves using reciprocals
- Physics: Many formulas use reciprocals (e.g., resistance, focal length)
Frequently Asked Questions
- Why doesn't zero have a reciprocal?
- Zero has no reciprocal because 1/0 is undefined. There is no number that, when multiplied by zero, gives 1. This is why division by zero is not allowed in mathematics.
- What is the reciprocal of a fraction?
- The reciprocal of a fraction a/b is b/a (flip the fraction). For example, the reciprocal of 3/4 is 4/3. This is why dividing by a fraction is the same as multiplying by its reciprocal.
- Is the reciprocal the same as the inverse?
- The reciprocal is specifically the multiplicative inverse. There's also an additive inverse (the negative of a number). For example, the multiplicative inverse of 5 is 1/5, while the additive inverse of 5 is -5.
- How do reciprocals help with division?
- Dividing by a number is equivalent to multiplying by its reciprocal. For example, 6 ÷ 2 = 6 × (1/2) = 3. This property is especially useful when dividing fractions.