# Fraction Simplifier

> Reduces a fraction to lowest terms by dividing by the GCD and converts it to a mixed number, a decimal and a percentage.

- Calculator id: `fraction-simplifier` · Category: Math (`math`) · Tool name: `calculate_simplified_fraction`
- Canonical page: https://tttkmbb.com/math/fraction-simplifier · This document: https://tttkmbb.com/math/fraction-simplifier.md · JSON definition: https://tttkmbb.com/math/fraction-simplifier.json

## Purpose

Reduces a fraction to lowest terms by dividing by the GCD and converts it to a mixed number, a decimal and a percentage.

**Use when:** You have a numerator and denominator and want the reduced fraction, its mixed-number form, decimal value or percent.

**Do not use when:** You need to add or multiply fractions (reduce each result with this tool afterwards) or to simplify a ratio of non-integers (use ratio).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `numerator` | integer |  | required | Top number of the fraction (may be negative). (min -1000000000000000, max 1000000000000000) |
| `denominator` | integer |  | required | Bottom number of the fraction; must not be 0. (min -1000000000000000, max 1000000000000000) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `simplified` | string |  | Lowest-terms fraction with the sign in the numerator, e.g. '3/4' (a whole number when the denominator reduces to 1). |
| `simplified_numerator` | integer |  | Numerator after reduction. |
| `simplified_denominator` | integer |  | Denominator after reduction (always positive). |
| `mixed_number` | string |  | Whole part plus proper fraction, e.g. '2 1/2'. |
| `decimal` | number |  | numerator / denominator. |
| `percent` | number | % | numerator / denominator × 100. |
| `gcd` | integer |  | Greatest common divisor the fraction was divided by. |

## Formula

`simplified = (numerator / g) / (denominator / g) with g = gcd(|numerator|, |denominator|); decimal = numerator / denominator; percent = decimal × 100`

## Data Sources

- Wikipedia – Irreducible fraction — https://en.wikipedia.org/wiki/Irreducible_fraction (reference, retrieved 2026-09-23)
- Wikipedia – Fraction — https://en.wikipedia.org/wiki/Fraction (reference, retrieved 2026-09-23)
- Wolfram MathWorld – Fraction — https://mathworld.wolfram.com/Fraction.html (reference, retrieved 2026-09-23)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/fraction-simplifier?numerator=…&denominator=…`
- `POST https://tttkmbb.com/api/v1/calculate/fraction-simplifier` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/fraction-simplifier · OpenAPI operationId `calculate_simplified_fraction` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "fraction-simplifier", "inputs": {…}}`

## Example

- 6/8: inputs `{"numerator":6,"denominator":8}` → `{"simplified":"3/4","simplified_numerator":3,"simplified_denominator":4,"mixed_number":"3/4","decimal":0.75,"percent":75,"gcd":2}`
- 10/4: inputs `{"numerator":10,"denominator":4}` → `{"simplified":"5/2","mixed_number":"2 1/2","decimal":2.5,"percent":250,"gcd":2}`

```
GET https://tttkmbb.com/api/v1/calculate/fraction-simplifier?numerator=6&denominator=8
```

## Limitations

You need to add or multiply fractions (reduce each result with this tool afterwards) or to simplify a ratio of non-integers (use ratio). All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**How is a negative fraction written?**

The sign is moved to the numerator: 6/−8 becomes −3/4, and the mixed form of −5/4 is '-1 1/4'.

**Can I enter decimals?**

No, both parts must be integers. Convert a decimal such as 0.75 to 75/100 first (or use ratio for non-integer pairs).

## Related

- [GCD and LCM Calculator](https://tttkmbb.com/math/gcd-lcm.md) — The GCD used to reduce the fraction.
- [Ratio Calculator](https://tttkmbb.com/math/ratio.md) — Simplify a ratio (also works with decimals).
- [Percentage Calculator](https://tttkmbb.com/math/percentage.md) — Percent arithmetic on the resulting value.