# Rational simplify

`rational-simplify` · version 1.0.0 · Numbers & math · free, no key needed

Reduce a numerator/denominator pair to lowest terms with the sign normalized onto the numerator.

**Use when you need to: rational simplify · simplify fraction · reduce fraction to lowest terms.**

## Supported

- rational simplify
- simplify fraction
- reduce fraction to lowest terms
- normalize rational sign

## Not supported

- decimal simplify
- continued fractions
- mixed numbers

## Behavior

- Input is an object with canonical integer-string numerator and denominator fields.
- Unlike rational-add and rational-multiply, the denominator may be negative; only 0 is rejected.
- Inputs may use -0 on either field, which is canonicalized to 0 before evaluation.
- The output is numerator / gcd(|numerator|,|denominator|) over denominator / gcd(...), with the sign moved entirely onto the numerator.
- Zero is always returned as numerator 0 over denominator 1, regardless of the input denominator sign.
- Each input and output numerator and denominator may have at most 1000 digits excluding sign.

## Input

- `numerator` (string, required): max length 1001
- `denominator` (string, required): max length 1001

## Output

- `numerator` (string, required)
- `denominator` (string, required)

## Limits

- max digits: 1000

## Example

Request input:

```json
{
  "numerator": "-8",
  "denominator": "-12"
}
```

Response:

```json
{
  "result": {
    "numerator": "2",
    "denominator": "3"
  }
}
```

## How to call it

### MCP

Connect `https://computefirst.net/mcp` ([setup](/docs#connect)), then call `execute` with:

```json
{
  "id": "rational-simplify",
  "version": "1.0.0",
  "input": {
    "numerator": "-8",
    "denominator": "-12"
  }
}
```

### HTTP (no key)

```sh
curl -X POST https://computefirst.net/v1/tools/rational-simplify/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"numerator":"-8","denominator":"-12"}'
```

The machine-readable contract is at [/v1/tools/rational-simplify/versions/1.0.0](/v1/tools/rational-simplify/versions/1.0.0).

### CLI

```sh
node cli.mjs run rational-simplify 1.0.0 --input input.json --base-url https://computefirst.net
```

Get the client at [/clients/cli/](/clients/cli/).

## Related tools

- [Mixed number to rational](/tools/mixed-number-to-rational): Convert a mixed number (sign, whole part, proper-fraction numerator and denominator) into a single reduced rational.
- [Rational power](/tools/rational-power): Raise a rational number to an integer exponent and return the exact reduced result.
- [Rational to mixed number](/tools/rational-to-mixed-number): Convert a rational number into a sign, whole part, and proper-fraction numerator/denominator.
- [Rational reciprocal](/tools/rational-reciprocal): Invert a rational number given as a numerator/denominator integer-string pair.
- [Array integer clamp](/tools/array-integer-clamp): Clamp an array of canonical integer strings to optional inclusive min and max bounds.
- [Array rational mean](/tools/array-rational-mean): Return the reduced arithmetic mean of an array of canonical rationals.