Description
Return crossResidual=roundedNumerator*denominator-numerator*roundedDenominator, requiring nonzero original and rounded denominators and integer rounded components.
A ratio compares quantities under a stated numerator and denominator. Fractions, percentage numerals, and percentage-point changes use different conventions, and changing a part can also change its whole. Unit consistency, zero denominators, rounding, and the order of adjustments determine the result.
Return crossResidual=roundedNumerator*denominator-numerator*roundedDenominator, requiring nonzero original and rounded denominators and integer rounded components.
When to use this tool
Use Ratio Preserving Integer Rounding Residual when you need this specific ratio, allocation, transformation, interval, or adjustment-order calculation with an explicit base.
How to use the tool and how it works
- Enter numerator, denominator, roundedNumerator, roundedDenominator. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read crossResidual. Use the output convention below.
Return crossResidual=roundedNumerator*denominator-numerator*roundedDenominator, requiring nonzero original and rounded denominators and integer rounded components.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| numerator | Numerator | Required. Finite number. |
| denominator | Denominator | Required. Finite number. |
| roundedNumerator | Supplied integer rounded component; no rounding is performed. | Required. Safe integer. |
| roundedDenominator | Rounded Denominator | Required. Safe integer. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| crossResidual | Cross Residual | Required. Finite number. |
{
"input": {
"numerator": 2,
"denominator": 3,
"roundedNumerator": 3,
"roundedDenominator": 5
},
"output": {
"crossResidual": -1
}
}Limitations and assumptions
- The rounded values are supplied, not calculated or verified. Residual is a cross-product discrepancy rather than direct ratio error and can lose precision in large intermediate products.
- The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.
Alternative or Complementary methods
Check numerator, denominator, units, and adjustment order before comparing results. Use a complete allocation or physical mixture model when a single arithmetic term leaves relevant constraints unspecified.
References
Similar or alternative tools
- Reciprocal Ratio Rounding Envelope
Invert a strictly positive closed ratio interval; no decimal display rounding.
- Mixture Target Share Residual
Calculate actualFraction=(firstAmount*firstFraction+secondAmount*secondFraction)/(firstAmount+secondAmount) and residual=actualFraction-targetFraction.