Verified calculation capability

Fractions Calculation Capability

Add, subtract, multiply, and divide fractions and mixed numbers using LCD/LCM for add/subtract, GCF reduction, and reciprocal division. Also simplifies and converts between fractions and decimals. · Math

Capability ID math.fractions · version 1.0.5

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

Model

Add

Add: L = LCM(b, d); a/b + c/d = [a(L/b) + c(L/d)] / L
Subtract: L = LCM(b, d); a/b − c/d = [a(L/b) − c(L/d)] / L
Multiply: a/b × c/d = (ac) / (bd)
Divide: a/b ÷ c/d = a/b × d/c
Simplify: a/b = (a÷g)/(b÷g) where g = GCF(a,b)

Solve modes: operate · simplify · to-dec · from-dec

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`op`	Operation for operate mode: + − * / (aliases add, sub, mul, div, plus, …). Share-URL alias: operator	—	input / output
`operator`	Share-URL alias for op	—	input
`aNum`	First numerator (or mixed numerator)	—	input
`aDen`	First denominator (≠ 0)	—	input
`aWhole`	Optional mixed-number whole for the first fraction	—	input
`bNum`	Second numerator	—	input
`bDen`	Second denominator (≠ 0)	—	input
`bWhole`	Optional mixed-number whole for the second fraction	—	input
`decimal`	Finite decimal for from-dec mode. Share-URL alias: decInput	—	input / output
`n`	amount of substance	—	output
`d`	—	—	output
`improper`	—	—	output
`mixed`	—	—	output
`display`	—	—	output
`formula`	—	—	output
`steps`	—	—	output

Assumptions / Validity

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

Assumptions

Integer numerators/denominators (and whole parts) for fraction modes.
Results reduced by GCF; signs normalized onto the numerator.

Example

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

3/4 + 1/6 = 11/12

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance. 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· View Manifest · CVP overview · Specification
Assurance: Core
Declared partition coverage: PASS · 2/2 declared partitions (fractions, invalid-domain)
Calculation version: 1.0.5
Verification: 32/32 calculation tests · 20/20 legacy golden · 8/8 legacy boundary · 4/4 legacy property
Production surface contract: 3/3
Versions: Calculation 1.0.5 · CVP protocol 1.0.0-proposed
CVP identity: 2/2 property · digest b258a9be030c
Reference: O1 model · O2 expected_values · O2 numerical_behavior
Interfaces: PASS · UI (SSR) / REST / MCP
ui-ssr is query-result HTML, not a live browser session.
CVP suite: 1/1 golden · 8/8 CVP boundary · 6/6 invalid · 2/2 property · 1/1 metamorphic · 1/1 round-trip · 1/1 cross-interface · 1/1 CVP contract
Supplemental domain review: Not performed
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.0.5 (workspace artifacts agree)
Review-policy tier: Engine tested — catalog token engine_tested; supplemental; not CVP status

This calculator CURRENT · Public schema 1.0.5 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. Reference Calculation Standard — Production surface contract 3/3.

Tool id: fractions
Engine: fractions
REST: POST /api/v1/calc/fractions
MCP: execute_calculation with capability_id: "math.fractions"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.0.5)
Versioned output schema: Immutable pin (1.0.5)

References

Human-readable sources plus CVP reference evidence classes.

Sources

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.fractions"}}}'

Inspect the trust tier and required assurance level before execution. Pin calculation_version (1.0.5) when reproducibility matters. Full protocol notes: MCP docs.