# Free online mixed number calculator

> A mixed number combines a whole number and a proper fraction, like 1 1/2 or 3 2/5. This calculator adds, subtracts, multiplies, or divides any two mixed numbers and gives the.

Add, subtract, multiply, and divide mixed numbers. Converts each mixed number to an improper fraction, performs the operation, simplifies by GCD, and converts the result back to a mixed number with a decimal equivalent.

**Interactive version:** https://onlinecalculator.me/math/mixed-number/
**Category:** Math

## How to use

1. Select an operation — Add (+), Subtract (−), Multiply (×), or Divide (÷).
2. Enter the whole number, numerator, and denominator for the first mixed number.
3. Enter the whole number, numerator, and denominator for the second mixed number.
4. Read the result as a mixed number, improper fraction, and decimal.

## Converting mixed numbers to improper fractions

For a mixed number W n/d:

```
improperNumerator = W × d + n
improperFraction  = improperNumerator / d
```

Example: 1 1/2 → (1 × 2 + 1) / 2 = 3/2

## The four operations

After converting both numbers to improper fractions a/b and c/d:

**Addition:** (a×d + c×b) / (b×d)

**Subtraction:** (a×d − c×b) / (b×d)

**Multiplication:** (a×c) / (b×d)

**Division:** (a×d) / (b×c)  ← multiply by the reciprocal

Then reduce by GCD to get the final simplified result.

## Worked examples

**1 1/2 + 2 1/3:** 3/2 + 7/3 = (9 + 14)/6 = 23/6 = **3 5/6** ≈ 3.833

**3 1/2 − 1 1/4:** 7/2 − 5/4 = (14 − 5)/4 = 9/4 = **2 1/4** = 2.25

**1 1/2 × 2 2/3:** 3/2 × 8/3 = 24/6 = **4**

**3 1/2 ÷ 1 3/4:** 7/2 ÷ 7/4 = 7/2 × 4/7 = 28/14 = **2**

## Notes

- Entering 0 as the whole number gives a pure fraction (e.g., 0 3/4 = 3/4).
- The denominator cannot be zero — the calculator will show an error.
- Negative results are supported; enter a negative whole number.

## Frequently asked questions

### How does the calculator handle mixed numbers?

Each mixed number is first converted to an improper fraction. For example, 1 1/2 becomes 3/2 (whole × denominator + numerator, over denominator). The chosen operation is then performed on the two improper fractions, and the result is simplified and converted back.

### How is the result simplified?

The calculator divides both the numerator and denominator of the result by their Greatest Common Divisor (GCD), found with the Euclidean algorithm. This gives the fully reduced fraction.

### How is mixed number addition calculated?

Convert both to improper fractions (a/b and c/d), then compute (a×d + c×b) / (b×d), and reduce. Example: 1 1/2 + 2 1/3 = 3/2 + 7/3 = (9 + 14)/6 = 23/6 = 3 5/6.

### How is mixed number multiplication calculated?

Convert both to improper fractions, then multiply numerators and denominators: (a×c) / (b×d), then reduce. Example: 1 1/2 × 2 2/3 = 3/2 × 8/3 = 24/6 = 4.

### Can I enter a mixed number with just a fraction (no whole number)?

Yes. Enter 0 in the whole number field and the desired numerator and denominator. For example, 0 whole, numerator 3, denominator 4 represents 3/4.

## Sources

- [Fraction (mixed numbers)](https://en.wikipedia.org/wiki/Fraction) — Wikipedia
- [Mixed Fraction](https://mathworld.wolfram.com/MixedFraction.html) — Wolfram MathWorld

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