Six Fraction Calculator
A high-performance arithmetic tool for summing and reducing sequences of six fractions. Features LCD calculation for large denominators and detailed solution steps.
About
When arithmetic expressions scale beyond simple pairs, finding the Least Common Denominator (LCD) becomes computationally intensive and prone to human error. This calculator is engineered for complex sequences involving six distinct fractions. It targets advanced academic scenarios and technical resource allocation problems where multiple ratios must be aggregated into a single net value.
Unlike standard calculators that convert fractions to decimals (losing precision with repeating decimals like 0.333...), this tool maintains exact rational forms throughout the calculation. It handles the heavy lifting of finding the Least Common Multiple (LCM) for up to six denominators, which can frequently result in values exceeding standard integer limits, handled here via robust 64-bit integer logic.
Formulas
The summation of six fractions requires transforming all terms to a common base L (the LCD). For a set of fractions nidi where i goes from 1 to 6:
Each numerator is then scaled:
The final result is the sum of scaled numerators over L, reduced to lowest terms.
Reference Data
| N | Denominator Sequence | Resulting LCD |
|---|---|---|
| 1 | 2, 3, 4, 5, 6, 7 | 420 |
| 2 | 10, 20, 30, 40, 50, 60 | 600 |
| 3 | 12, 15, 18, 20, 24, 30 | 360 |
| 4 | Prime Numbers (2, 3, 5, 7, 11, 13) | 30,030 |
| 5 | Fibonacci (1, 2, 3, 5, 8, 13) | 3120 |
| 6 | Powers of 2 (2, 4, 8, 16, 32, 64) | 64 |