Rational reciprocal

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

Invert a rational number given as a numerator/denominator integer-string pair.

Use when you need to: rational reciprocal · invert fraction · multiplicative inverse of a rational.

Decide before calling

Read the versioned contract and the supported scope below. Reuse rational-reciprocal@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-reciprocal@1.0.0 for rational reciprocal. 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 reciprocal
• invert fraction
• multiplicative inverse of a rational
• flip fraction

Not supported

• decimal reciprocal
• reciprocal of zero
• mixed numbers

Behavior

• Input is an object with canonical integer-string numerator and denominator fields.
• The denominator must be a positive canonical integer; zero and negative denominators are rejected.
• The input may use -0 on the numerator, canonicalized to 0.
• A zero numerator is rejected: the reciprocal of 0 is undefined.
• The output swaps numerator and denominator, with the sign normalized onto the output numerator.
• 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": "3",
  "denominator": "4"
}

Response:

{
  "result": {
    "numerator": "4",
    "denominator": "3"
  }
}

How to call it

MCP

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

{
  "id": "rational-reciprocal",
  "version": "1.0.0",
  "input": {
    "numerator": "3",
    "denominator": "4"
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/rational-reciprocal/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"numerator":"3","denominator":"4"}'

The machine-readable contract is at /v1/tools/rational-reciprocal/versions/1.0.0.

CLI

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

Get the client at /clients/cli/.

Related tools

• 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.
• Rational power: Raise a rational number to an integer exponent and return the exact reduced result.
• Rational trace check: Check a step-by-step rational calculation trace; reports the first step whose operand, operator or result disagrees.
• Array rational sum: Sum an array of canonical rationals and return the reduced total.
• Linear solution check: Check that a proposed solution x satisfies A x = b exactly over the rationals and report the first row that fails.