Fraction Common Denominator Plan
Plan the least positive common denominator for two canonical exact fractions and report aligned numerators.
Description
Plan the least positive common denominator for two canonical exact fractions and report aligned numerators.
A common denominator places two fractions on the same exact grid. Using their reduced denominators gives the least common denominator.
When to use this tool
Plan the least positive common denominator for two canonical exact fractions and report aligned numerators.
- 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.denominator, result.leftNumerator, result.rightNumerator. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.
Normalize both fractions. Compute denominator = b/gcd(b,d) times d and scale each numerator by that denominator divided by its own denominator.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.denominator | Positive denominator as decimal integer text, under the normalization or common-denominator convention above. |
| result.leftNumerator | The left numerator value under the stated formula or text convention. |
| result.rightNumerator | The right numerator value under the stated formula or text convention. |
{
"input": {
"leftNumerator": "2",
"leftDenominator": "3",
"rightNumerator": "1",
"rightDenominator": "6"
},
"output": {
"result": {
"denominator": "6",
"leftNumerator": "4",
"rightNumerator": "1"
}
}
}Limitations and assumptions
- The fractions are not added. The plan uses reduced inputs, so results need not preserve the original written denominators.
- 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.
- Fraction Base Termination Check
Check exact rational termination in an explicit integer radix 2–36 by removing denominator factors shared with that radix.