Exact Fraction Order
Compare exact rational values by cross products, preserving large integer precision and normalizing negative denominators.
Description
Compare exact rational values by cross products, preserving large integer precision and normalizing negative denominators.
Fraction ordering can be decided exactly with cross multiplication when both denominators are positive.
When to use this tool
Compare exact rational values by cross products, preserving large integer precision and normalizing negative denominators.
- Prepare the supplied leftNumerator, leftDenominator, rightNumerator, rightDenominator fields for this operation.
- Compare the complete example with the representation used by your own input before carrying the result into another step.
How to use the tool and how it works
- Enter leftNumerator, leftDenominator, rightNumerator, rightDenominator. Use the exact text syntax, units and index conventions explained below.
- Run the tool. If input validation fails, correct the supplied fields before interpreting any result.
- Read result.order. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.
Normalize a/b and c/d, compare a*d with c*b and return order -1, 0 or 1.1
| Input field | Meaning and representation | Accepted input |
|---|---|---|
| leftNumerator | Exact signed decimal integer text; denominator fields must be nonzero. | Optional + or - and 1 to 256 decimal digits |
| leftDenominator | Exact signed decimal integer text; denominator fields must be nonzero. | Optional + or - and 1 to 256 decimal digits |
| rightNumerator | Exact signed decimal integer text; denominator fields must be nonzero. | Optional + or - and 1 to 256 decimal digits |
| rightDenominator | Exact signed decimal integer text; denominator fields must be nonzero. | Optional + or - and 1 to 256 decimal digits |
| Output field | Interpretation |
|---|---|
| result | Object containing the named outputs below. |
| result.order | Comparison result under the exact convention above; -1 means left before right, 0 equal, +1 after. |
{
"input": {
"leftNumerator": "2",
"leftDenominator": "3",
"rightNumerator": "1",
"rightDenominator": "6"
},
"output": {
"result": {
"order": 1
}
}
}Limitations and assumptions
- The tool compares exact input rationals, without measurement tolerance, approximate equality or floating-point conversion.
- Numerator and denominator fields use exact decimal integer strings of at most 256 digits with an optional sign. Fractions are reduced with a positive denominator before the stated operation.
- All declared input fields are required and unexpected top-level fields are rejected. Numbers must be finite; lists are limited to 128 entries and ordinary text fields to 8,192 UTF-16 code units, with tighter limits where stated.
- JSON text inputs must parse within bounded nesting and size limits. Numeric outputs outside the safe finite range are rejected; large exact integer results use decimal strings. Indexes and half-open spans are zero-based unless a rank is explicitly described as one-based.
Alternative or Complementary methods
Use exact numerator/denominator operations when equality and boundary decisions matter. Convert to a decimal display only with an explicit rounding policy; a rounded display should not replace the exact result.
References
Similar or alternative tools
- Exact Fraction Addition
Exact rational addition using decimal integer text and coprime output; no IEEE-754 precision loss.
- Exact Fraction Division
Exact rational division using decimal integer text and coprime output; no IEEE-754 precision loss.