Rational Unit Fraction Complement Term Tool

Description

For positive decimal-integer denominator n return numerator=n-1 and denominator=n as exact decimal strings.

A rational number is represented by an integer numerator and a nonzero integer denominator. Sign placement, reduction by a greatest common divisor, and the chosen division or rounding convention affect intermediate representations. Exact integer text preserves arithmetic that could be lost in a floating-point conversion.

For positive decimal-integer denominator n return numerator=n-1 and denominator=n as exact decimal strings.

When to use this tool

Use Rational Unit Fraction Complement Term when you need this particular exact fraction comparison, reduction, sign, denominator, or rounding component.

How to use the tool and how it works

Enter denominator. Use the units and conventions below.
Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
Read numerator, denominator. Use the output convention below.

For positive decimal-integer denominator n return numerator=n-1 and denominator=n as exact decimal strings.^[1]

Input field	Meaning and units	Accepted input
denominator	Denominator or exact integer denominator text under the stated sign restriction.	Required. Text; maximum UTF-16 length 8192. Integer syntax: optional + or - and 1-128 decimal digits; leading zeros accepted. Apply the sign restriction above.

Output field	Interpretation	Returned shape
numerator	Numerator in the numeric or exact integer-text representation declared below.	Required. Text; maximum UTF-16 length 8192.
denominator	Denominator or exact integer denominator text under the stated sign restriction.	Required. Text; maximum UTF-16 length 8192.

json

{
  "input": {
    "denominator": "5"
  },
  "output": {
    "numerator": "4",
    "denominator": "5"
  }
}

Limitations and assumptions

This represents 1-1/n without reducing the fraction. At n=1 the result is 0/1; negative or zero denominators are unsupported.
Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.

Alternative or Complementary methods

Reduce fractions where the interpretation requires it and choose a consistent denominator-sign and division convention. Use a complete rational operation when one denominator or determinant term is insufficient.

References

Calculation and input contract: number/rational-unit-fraction-complement-term — tool.io

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