Mixed number to rational

mixed-number-to-rational · version 1.0.0 · Numbers & math · free, no key needed

Convert a mixed number (sign, whole part, proper-fraction numerator and denominator) into a single reduced rational.

Use when you need to: mixed number to rational · convert mixed number to fraction · mixed fraction to improper fraction.

Supported

• mixed number to rational
• convert mixed number to fraction
• mixed fraction to improper fraction

Not supported

• rational to mixed number
• decimal conversion
• negative whole or fraction fields

Behavior

• Input has a boolean negative field, and canonical non-negative integer-string whole and numerator fields, and a canonical positive integer-string denominator field.
• whole and numerator carry only magnitude; sign is expressed solely by the negative field, so -0 is rejected on those two fields (0 is required instead).
• numerator need not be less than denominator; an improper fraction part is accepted and combined normally.
• The value is (negative ? -1 : 1) * (whole * denominator + numerator) / denominator, reduced by gcd with sign only on the output numerator.
• A zero value (whole 0, numerator 0, any sign) always reduces to output numerator 0 over denominator 1.
• Each field and the output numerator and denominator may have at most 1000 digits excluding sign.

Input

• negative (boolean, required)
• whole (string, required): max length 1000
• numerator (string, required): max length 1000
• denominator (string, required): max length 1001

Output

• numerator (string, required)
• denominator (string, required)

Limits

• max digits: 1000

Example

Request input:

{
  "negative": true,
  "whole": "3",
  "numerator": "1",
  "denominator": "2"
}

Response:

{
  "result": {
    "numerator": "-7",
    "denominator": "2"
  }
}

How to call it

MCP

Connect https://computefirst.net/mcp (setup), then call execute with:

{
  "id": "mixed-number-to-rational",
  "version": "1.0.0",
  "input": {
    "negative": true,
    "whole": "3",
    "numerator": "1",
    "denominator": "2"
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/mixed-number-to-rational/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"negative":true,"whole":"3","numerator":"1","denominator":"2"}'

The machine-readable contract is at /v1/tools/mixed-number-to-rational/versions/1.0.0.

CLI

node cli.mjs run mixed-number-to-rational 1.0.0 --input input.json --base-url https://computefirst.net

Get the client at /clients/cli/.

Related tools

• Rational to mixed number: Convert a rational number into a sign, whole part, and proper-fraction numerator/denominator.
• Rational power: Raise a rational number to an integer exponent and return the exact reduced result.
• Rational simplify: Reduce a numerator/denominator pair to lowest terms with the sign normalized onto the numerator.
• Rational reciprocal: Invert a rational number given as a numerator/denominator integer-string pair.
• Angle DMS convert: Convert a signed integer angle between degrees, arcminutes, and arcseconds as an exact rational.
• Array integer clamp: Clamp an array of canonical integer strings to optional inclusive min and max bounds.