How many are aware that Greeks ciphered numerals onto Ionian and Doric alphabets while scaling rational numbers n/p by LCM m/m such that mn/mp was concisely converted to a unit fraction series by finding the best divisors of denominator mp that summed to numerator mn:
http://planetmath.org/arabicnumerals
and after 800 AD Arabs taught Fibonacci to write unciphered numerals and scaled rational numbers n/p by subtracting LCM 1/m?
For example, Greek 4/13 (4/4) = 16/52 = (13 + 2 + 1)/52 = 1/4 + 1/26 + 1/52
and Arabs and Fibonacci scaled (4/13 - 1/4) = 3/52 such that a second LCM 1/18 allowed (3/52 - 1/18) = (54 -52)/936 = 1/468 meant
4/13 = 1/4 + 1/18 + 1/468, a less elegant series than Greeks and Egyptians would have written.
Taking a singular Hindu point of view ... http://arindambose.com/blog/?p=277 ,,, throws the Arab numeration baby out with Egyptian fractions. Arab-Hindu numerals only modified Egyptian fractions, the main point that I am making. But what else am I missing? Can it be said that Arabs and Fibonacci used an algorithm in their numeration system, while Greeks and Egyptians did not?
To appreciate the scope of the Arab numeration system that replaced Greek ciphered numeration with unciphered Hindu numerals (absent the Hindu zero .. since Greeks already used a zero symbol) the 1202 AD Liber Abaci http://liberabaci.blogspot.com/ should be read in great details.
To appreciate a wider scope of why and how Arabs in 800 AD continued Egyptian and Greek unit fraction scaled math used subtraction rather than multiplication Ahmes 1650 BCE rational number math needs to be studied: http://planetmath.org/anoverviewofahmespapyrus