Verified calculation capability

Ratio Calculation Capability

Simplify, scale, and compare ratios; solve proportions; split a total; convert part-to-part ratios to fraction, decimal, and part-of-whole percent using exact rationals. · Math

Capability ID math.ratio · version 1.0.2

Open calculator REST API MCP Evidence Evidence JSON CVP Manifest Review policy

Model

Simplify

Simplify: r₁:⋯:rₙ → exact rationals; L=LCM(d₁,…,dₙ); rᵢ′=L·rᵢ; g=GCF(|r₁′|,…,|rₙ′|); (r₁′÷g):⋯:(rₙ′÷g)
Proportion: A/B = C/D → A·D = B·C
Scale: r₁:⋯:rₙ → (k·r₁):⋯:(k·rₙ)
Split total: partᵢ = total × (termᵢ / Σ terms) with every term ≥ 0 and Σ terms > 0

Solve modes: simplify · proportion · scale · split · compare · convert

Inputs / Outputs

Canonical symbols for this capability. Agent schemas remain the contract.

Symbol	Quantity	Unit	Role
`a`	First term. Integer, terminating decimal, or simple a/b. Share-URL alias: aInput	—	input
`b`	Second term. Share-URL alias: bInput	—	input
`c`	Third term, or proportion/compare C. Share-URL alias: cInput	—	input
`d`	Proportion/compare D. Share-URL alias: dInput	—	input
`k`	Scale factor. Share-URL alias: kInput	—	input / output
`total`	Total to split. Share-URL alias: totalInput	—	input
`aInput`	Share-URL alias for a	—	input
`bInput`	Share-URL alias for b	—	input
`cInput`	Share-URL alias for c	—	input
`dInput`	Share-URL alias for d	—	input
`kInput`	Share-URL alias for k	—	input
`totalInput`	Share-URL alias for total	—	input
`terms`	2 or 3 terms for simplify/scale/split	—	input / output
`termCount`	Alias for terms	—	input
`scaleOp`	Scale multiply (default) or divide	—	input / output
`scale_op`	Alias for scaleOp	—	input
`op`	Alias for scaleOp	—	input
`value`	—	—	output
`mode_label`	—	—	output
`heading`	—	—	output
`formula`	—	—	output
`inputs_summary`	—	—	output
`explainer`	—	—	output
`steps`	—	—	output
`ratio`	—	—	output
`terms_exact`	—	—	output
`gcf`	—	—	output
`clearing_factor`	—	—	output
`shares`	—	—	output
`solved`	—	—	output
`solved_for`	—	—	output
`A`	—	—	output
`B`	—	—	output
`C`	—	—	output
`D`	—	—	output
`equivalent`	—	—	output
`part_to_part`	—	—	output
`part_of_whole`	—	A	output
`part_of_whole_B`	—	—	output
`simplified`	—	—	output
`viz_terms`	—	—	output
`viz_labels`	—	—	output

Assumptions / Validity

Declared scope for this capability. Do not use it outside this domain.

Assumptions

Finite rationals: integers, terminating decimals, or simple fractions a/b.
Proportion denominators in A/B or C/D must be nonzero when used.
Simplify / proportion / compare allow negative terms. Split does not.

Example

One numerical check. The calculator page holds worked steps and FAQ.

12:18 → 2:3; 1.5:2.25 → 2:3; 3/4:5/6 → 9:10; 4:7 = x:21 → x=12

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance · all published modes. Computational verification is defined by CVP. Supplemental domain review (internal) and named expert review are defined by the Review policy and do not by themselves determine CVP conformance.

CVP: CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance · all published modes· View Manifest · CVP overview · Specification
Verified scope: all published modes
Assurance: Core
Declared partition coverage: PASS · 8/8 declared partitions (simplify, proportion, scale, split, compare, convert, three-term, invalid-domain)
Calculation version: 1.0.2
Verification: 26/26 calculation tests · 11/11 legacy golden · 7/7 legacy boundary · 8/8 legacy property
Production surface contract: 8/8
Versions: Calculation 1.0.2 · CVP protocol 1.0.0-proposed · Evidence 2026-09-16.sources-no-wolfram
Verification revision: 2026-09-16.sources-no-wolfram · 7/7 property · digest e32c91d652f9
Reference: O1 model · O2 expected_values · O2 numerical_behavior
Numerical scope: All six published Ratio modes (simplify, proportion, scale, split, compare, convert), including A:B:C where those modes support it. Independent O2 expected values; exact rational BigInt; Node is runtime host only.
Interfaces: PASS · UI (SSR) / REST / MCP
ui-ssr is query-result HTML, not a live browser session.
CVP suite: 13/13 golden · 7/7 CVP boundary · 7/7 invalid · 7/7 property · 2/2 metamorphic · 2/2 round-trip · 3/3 cross-interface · 8/8 CVP contract
Supplemental domain review: Not performed
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.0.2 (workspace artifacts agree)
Review-policy tier: Engine tested — catalog token engine_tested; supplemental; not CVP status

This calculator CURRENT · Public schema 1.0.2 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

Call this capability

Human page, REST, and MCP share the same engine and calculation_version. Build verified hashes workspace artifacts only. After deploy, attest:production GETs canonical URLs twice — the public/cached view an Agent actually hits, and origin — including every /capabilities/{id} HTML page. Public Capability HTML version must match catalog before production attestation passes. Live Trust rows above fetch /.well-known/calculatorx-production-attestation.json and the output schema const. Build hashes: release integrity. That proves currently published page / engine / schema / evidence / MCP agree — not that a historical version is independently immutable. Production surface contract 8/8.

Tool id: ratio
Engine: ratio
REST: POST /api/v1/calc/ratio
MCP: execute_calculation with capability_id: "math.ratio"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.0.2)
Versioned output schema: Immutable pin (1.0.2)

References

Human-readable sources plus CVP reference evidence classes.

Sources

OpenStax Prealgebra 2e — Ratios and Rates — 5.6 Ratios and rates; writing and simplifying A:B
OpenStax Prealgebra 2e — Solve Proportions — 6.5 Cross-multiply to solve A/B = C/D
Encyclopedia of Mathematics — Greatest common divisor — Pairwise Euclidean GCF used after clearing denominators
CalculatorX split convention — Nonnegative parts only

Reference evidence classes: O1 model · O2 expected_values · O2 numerical_behavior

Try with an agent

Inspect this capability via same-origin MCP, then call execute_calculation.

curl -sS -X POST 'https://www.calculatorx.com/mcp' \
  -H 'Content-Type: application/json' \
  -H 'MCP-Protocol-Version: 2026-07-28' \
  -H 'Mcp-Method: tools/call' \
  -H 'Mcp-Name: inspect_capability' \
  -d '{"jsonrpc":"2.0","id":1,"method":"tools/call","params":{"name":"inspect_capability","arguments":{"capability_id":"math.ratio"}}}'

Inspect the trust tier and required assurance level before execution. Pin calculation_version (1.0.2) when reproducibility matters. Full protocol notes: MCP docs.