The multiplicative inverse of a number is the number you multiply it by to get 1. Dividing by a fraction is multiplying by its inverse, which is why “flip and multiply” works.
How to use the Multiplicative Inverse Calculator
- Input in the form of
- Number
- Whole number
- Numerator
- Denominator
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
The input is written as an exact fraction, then numerator and denominator are swapped and the result simplified. Zero has no multiplicative inverse.
Formula
Inverse of x = 1/x; of a/b = b/a; x × (1/x) = 1
Worked example
Inputs — Input in the form of: A simple fraction; Numerator: 3; Denominator: 4.
Results — Multiplicative inverse = 4/3; As a mixed number = 1 1/3; As a decimal = 1.33333333333; Steps = 1. Write the number as a fraction: 3/4
2. Swap numerator and denominator: 4/3
3. Check: 3/4 × 4/3 = 1.
Key terms
- Reciprocal
- 1 divided by a number.
Frequently asked questions
What is the multiplicative inverse of 3/4?
4/3.
What is the inverse of a mixed number such as 2 3/4?
Convert to 11/4, then flip: 4/11.
Does zero have an inverse?
No – nothing times zero equals 1.
Is the inverse the same as the reciprocal?
Yes, for multiplication the two terms mean the same.