Purpose and steps
Fraction Calculator validates first numerator, first denominator, operation, second numerator, second denominator before applying the displayed equation. Fractional numerators or denominators are rejected rather than truncated.
- Add, subtract, multiply or divide two integer fractions. The rational result is reduced exactly using integer arithmetic; a decimal approximation is also displayed.
- Enter First numerator, First denominator, Operation, Second numerator, Second denominator in the stated format. Baseline values are for reproduction.
- Check the output unit and convention: Read simplified fraction with its stated unit and convention. The default example and the independent worked scenario use different inputs, so compare the assumptions before comparing the numbers.
- Change one input and compare the result. Fractional numerators or denominators are rejected rather than truncated. Denominators and a divisor fraction must be nonzero; decimal output is approximate.
Input reference and units
These values reproduce the model’s demonstration. Replace them with your own records or measurements; they are not recommended targets.
On a small screen, swipe the table horizontally to see all columns.
| Parameter | Demonstration value | How to enter it |
|---|---|---|
| First numerator | 1 | Enter first numerator without adding a unit suffix. Scope: Fractional numerators or denominators are rejected rather than truncated. |
| First denominator | 2 | Enter first denominator without adding a unit suffix. Scope: Fractional numerators or denominators are rejected rather than truncated. |
| Operation | + | Select the explicitly labeled convention before interpreting the numerical input. |
| Second numerator | 1 | Enter second numerator without adding a unit suffix. Scope: Fractional numerators or denominators are rejected rather than truncated. |
| Second denominator | 3 | Enter second denominator without adding a unit suffix. Scope: Fractional numerators or denominators are rejected rather than truncated. |
Model-specific method
How this calculator produces its result
Fraction Calculator: a/b + c/d = (ad + bc)/bd; reduced numerator = numerator / gcd(numerator, denominator). Input definitions: a = First numerator; b = First denominator; mode = Operation; c = Second numerator; d = Second denominator. Use the selected convention throughout the calculation.
Fraction Calculator: calculation relationships
Add, subtract, multiply or divide two integer fractions. The rational result is reduced exactly using integer arithmetic; a decimal approximation is also displayed. Fractional numerators or denominators are rejected rather than truncated. Denominators and a divisor fraction must be nonzero; decimal output is approximate.
Addition requires a common denominator. One quarter plus two thirds becomes (1×3 + 2×4)/(4×3) = 11/12. Reduce numerator and denominator by their GCD after the operation. Multiplication instead multiplies numerators and denominators directly; division inverts the nonzero second fraction. The fraction string is exact even when its displayed decimal repeats.
a/b + c/d = (ad + bc)/bd; reduced numerator = numerator / gcd(numerator, denominator)
- a: First numerator. Enter first numerator without adding a unit suffix. Scope: Fractional numerators or denominators are rejected rather than truncated.
- b: First denominator. Enter first denominator without adding a unit suffix. Scope: Fractional numerators or denominators are rejected rather than truncated.
- mode: Operation. Select the explicitly labeled convention before interpreting the numerical input.
- c: Second numerator. Enter second numerator without adding a unit suffix. Scope: Fractional numerators or denominators are rejected rather than truncated.
- d: Second denominator. Enter second denominator without adding a unit suffix. Scope: Fractional numerators or denominators are rejected rather than truncated.
- Result units: stated beside each output
- Calculation relationship: a/b + c/d = (ad + bc)/bd; reduced numerator = numerator / gcd(numerator, denominator)
- Supported domain: see the limits below
Worked example
Fraction Calculator baseline input: First numerator: 1; First denominator: 2; Operation: +; Second numerator: 1; Second denominator: 3. Output: Simplified fraction = 5/6; Decimal = 0.833333333333. Substitute these values into the displayed equation to reproduce the result.
Reproduce the default scenario
This reproduces the default inputs in the reference table above; it is not an additional independent example. Displayed rounding may differ from intermediate precision.
- Simplified fraction
- 5/6
- Decimal
- 0.833333333333
Reading results without overstating them
- Read simplified fraction with its stated unit and convention. The default example and the independent worked scenario use different inputs, so compare the assumptions before comparing the numbers.
- Change one input at a time and use the equation to explain the result; do not mix unit, grade-scale, time-zone or rounding conventions across comparisons.
Assumptions and exclusions
- Fractional numerators or denominators are rejected rather than truncated.
- Denominators and a divisor fraction must be nonzero; decimal output is approximate.
Sources and content notes
Toolify describes the implemented algorithm and its assumptions. Sources below support the topic or applicable rules; they do not endorse this calculator. Examples are illustrative, and published rules take precedence over simplified estimates.
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