Fraction Reciprocal Pair
Return the exact reciprocal of a nonzero rational in canonical integer text; zero reciprocal is rejected.
Description
Return the exact reciprocal of a nonzero rational in canonical integer text; zero reciprocal is rejected.
Taking a reciprocal exchanges numerator and denominator, but zero has no reciprocal.
When to use this tool
Return the exact reciprocal of a nonzero rational in canonical integer text; zero reciprocal is rejected.
- Prepare the supplied numerator, denominator 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 numerator, denominator. 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.numerator, result.denominator. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.
Normalize the fraction, require nonzero numerator, swap numerator and denominator, then reduce again with a positive denominator.1
| Input field | Meaning and representation | Accepted input |
|---|---|---|
| numerator | Exact signed decimal integer text; denominator fields must be nonzero. | Optional + or - and 1 to 256 decimal digits |
| denominator | 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.numerator | Reduced signed numerator as decimal integer text. |
| result.denominator | Positive denominator as decimal integer text, under the normalization or common-denominator convention above. |
{
"input": {
"numerator": "-2",
"denominator": "3"
},
"output": {
"result": {
"numerator": "-3",
"denominator": "2"
}
}
}Limitations and assumptions
- Inputs and outputs are exact decimal integer strings. The tool does not represent infinity or perform floating-point division.
- 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
- Canonical Fraction Pair
Canonicalize an exact integer fraction into coprime numerator and positive denominator text; zero denominator is rejected.
- Fraction Mediant Pair
Exact rational mediant of canonical positive-denominator pairs using decimal integer text and coprime output; no IEEE-754 precision loss.