```Date: Oct 18, 2012 10:47 AM
Author: Milo Gardner
Subject: Re: Why study Egyptian fraction math?

MODERN TRANSLATIONS: Most 20th century transliterations and translations of Middle Kingdom arithmetic texts have been incomplete and misleading. Ahmes' actual Middle Kingdom arithmetic was finite. The arithmetic used LCM m, a number theory concept. Egyptian scribes scaled rational number by LCM m within (n/p)(m/m) = mn/mp that recorded concise unit fraction series in a multiplication context. Egyptian scribes selected the best divisors of denominator mp (a GCD) that best summed to numerator mn by following the implicit algebraic context:a. n/p = n/p(m/m) = mn/mqexample: 4/13 = 4/13(4/4) = 16/52 = (13 + 2 + 1)/52 = 1/4 + 1/26 + 1/52with the divisors of mp often recorded in red that best summed to numerator mn created concise unit fraction series.A second algebraic context was recorded in RMP 37. The subtraction context was emulated by Arabs and Fibonacci per:b. (n/pq - 1/m)= (mn -pq)/mpexample: (4/13 - 1/4)= (16 - 13)/52 = (2 + 1)/52 = 1/26 + 1/52also meant 4/13 = 1/4 + 1/26 + 1/52
```