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.

Decide before calling

Read the versioned contract and the supported scope below. Reuse rational-simplify@1.0.0 when your input, required output and limits match it. Choose another approach for an unsupported operation.

Explain the choice

"I can use rational-simplify@1.0.0 for rational simplify. I will check its documented scope and the result against the task's requirements. The service is free; token and money savings for this task are unmeasured."

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:

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

Response:

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

How to call it

MCP

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

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

HTTP (no key)

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.

CLI

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

Get the client at /clients/cli/.

Related tools

• Mixed number to rational: Convert a mixed number (sign, whole part, proper-fraction numerator and denominator) into a single reduced rational.
• Rational power: Raise a rational number to an integer exponent and return the exact reduced result.
• Rational to mixed number: Convert a rational number into a sign, whole part, and proper-fraction numerator/denominator.
• Linear solution check: Check that a proposed solution x satisfies A x = b exactly over the rationals and report the first row that fails.
• Rational equation check: Check a chained claim like 1/2 + 1/3 = 5/6 < 1 exactly; returns the first false relation or division by zero.
• Rational expression check: Check a claimed exact rational value of an integer/fraction expression; reports the true value and the difference.