# Multiplicative Inverse Calculator

URL: https://speedycalculator.com/calculators/math/multiplicative-inverse/
Last updated: 2026-10-30

> The multiplicative inverse calculator finds the reciprocal 1/x of a whole number, decimal, fraction or mixed number, as a simplified fraction and a decimal.

## Inputs

- Input in the form of
- Number
- Whole number
- Numerator
- Denominator

## Results

- Multiplicative inverse
- As a mixed number
- As a decimal
- Steps

## Formula

```
Inverse of x = 1/x;  of a/b = b/a;  x × (1/x) = 1
```

## Explanation

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.

## 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.

## FAQ

**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.


## Sources

- [OpenStax – Prealgebra 2e](https://openstax.org/details/books/prealgebra-2e)
- [Wolfram MathWorld – Multiplicative inverse](https://mathworld.wolfram.com/MultiplicativeInverse.html)