Since the 1880s, formalized in the 1920s, an incomplete and muddled view defined ancient Egyptian multiplication and division operations. Springer's on-line encyclopedia also summarizes the 1920s view on Wikpedia:

"The art of computation arose and developed long before the times of the oldest written records extant. The oldest mathematical records are the Cahoon papyri and the famous Rhind papyrus, which is believed to date back to about 2000 BCE. Additive hieroglyphic methods representation numbers (cf. Numbers, representations of) in ways that Old Kingdom Egyptians had perform addition and subtraction operations on natural numbers in relatively simple ways. For example, multiplication was carried out by doubling, i.e. the factors were decomposed into sums of powers of two, the individual summands were multiplied, and the components added. Operations on fractions (cf. Fraction) were reduced in Ancient Egypt to operations on aliquot fractions, i.e. on fractions of the type. More complicated fractions were decomposed with the aid of tables into a sum of aliquot fractions."

The 1920's conclusions transliterated an incomplete additive version of Egyptian multiplication. The 1920's historians had not followed up a 1895 report that suggested a second form of multiplication method was present in Ahmes' 2/n table, and other RMP problems (i.e. RMP 38). The second method included aliquot parts, as Springer suggests above. Aliquot part were reported by F. Hultsch in 1895. Hultsch parsed Ahmes' 2/n table revealing aliquot part patterns for that closely parsed 2/n table data. Yet, Springer's Egyptian multiplication encyclopedia entry did not specify critical aliquot part operational details. Sadly, 1920s math historians had also skipped over operational details of F. Hultsch's 1895 aliquot part discussion points by falsely concluding that aliquot part patterns had not been seen in Ahmes' 2/n table.

The aliquot part story line remained unsolved until the 21st century. Shortly after 2002 the Kahun Papyrus and the Rhind Papyrus 2/n table were decoded revealing two aliquot part operational methods: (1) new inverse multiplication and division methods, and (2) a LCM number method written in red. The multiplication and division methods had been hidden in same set of aliquot part operational steps, including red auxiliary numbers steps. In 2006, the 1895 Hultsch-Bruins method was confirmed from a second direction, detailing a common aliquot method used in the RMP and Egyptian Mathematical Leather Roll.

It has been clear since 2006 that Ahmes' aliquot part division steps, sensed in the 19th century, were not decoded during the 20th century. Two reasons misdirected 1920s math historians. The first prematurely closed the subject of Egyptian fraction arithmetic operations by concluding Egyptian multiplication contained only additive steps. Second, scribal division was suggested have followed an non-inverse process called 'single false position'.

Moreover, Springer followed the misleading 1920's definition of Egyptian division by suggesting: "Division was carried out by subtracting from the number to be divided the numbers obtained by successive doubling of the divisor." Math historians call the 1920's proposed Egyptian division method 'single false position'. Ironically, 'single false position' was first documented in 800 AD, and at no earlier data. Later Arab texts improved up its root finding 'double false position ', method.

Springer's definition of Egyptian division was historically incomplete. To complete a definition of Egyptian division the first six RMP problems, a division by 10 labor rate (defined earlier in the Reisner Papyrus) set of problems are consulted. In addition, RMP algebra problems and methods are consulted. For example, Ahmes divided 28 by 97, in RMP 31(confirmed in RMP 34) by solving: x + (2/3 + 1/2 + 1/7)x = 33 and x + (2/3 + 1/2 + 1/7)x = 37 as other vulgar fraction problems were solved in the Kahun Papyrus and Rhind Papyrus 2/n tables. Aliquot part steps were hidden in theoretical multiplication and division operations for over 100 years.

Ahmes did not use 'single false position' in any arithmetic operation, a valid point made by Robins-Shute in 1987. The 1920s 'false position' idea was a false supposition. For example, 28/97, in RMP 31, and RMP 23 expose Ahmes' LCM method. In RMP 23 where 45 was introduced solving most of the problem, but 360 was needed to Ahmes to complete the problem as all other algebra problems were solved.

In the 21st century, Ahmes is reported as converting vulgar fractions into optimized unit fractions series within a LCM multiplication method. The LCM method replaced the aliquot parts of the denominator in the numerator. To convert 2/97 in RMP 31, and the 2/n table. Ahmes converted 28/97 into two problems, 2/97 and 26/97, such that:

1. To convert 2 by 97: As Ahmes' 2/n table wrote for all 2/n conversions less than 2/101, he first selected a highly divisible number m as an optimizing multiplier m/m. In the 2/97 case 56 was selected, creating a multiplier 56/56 such that the aliquot parts of 56 (28, 14, 8, 7, 4, 2, 1) were introduced into the solution by writing:

2/97*(56/56) = 112/(56*97) = (97 + 8 + 7)/56*97)

and,

2/97 = 1/56 + 1/679 + 1/776

2. To convert 26/97 Ahmes looked for a multiplier m/m that would increase the numerator to greater than 97. Ahmes found 4/4. By considering the aliquot parts of 4 (4 , 2, 1) Ahmes wrote out:

26/97*(4/4) = 104/(4*97)= (97 + 4 + 2 + 1)/(4*97)

such that:

26/97 = 1/4 + 1/97 + 1/194 + 1/388

and,

3. Ahmes combined steps 2/97 and 26/97 into one Egyptian fraction series by writing:

28/97 = 1/4 + 1/56 + 1/97 + 1/194 + 1/388 + 1/679 + 1/77

'Single false position' was false 20th century supposition that failed to parse Ahmes' actual division operation. Ahmes division operation is correctly parsed as inverse to Egyptian multiplication. Egyptian scribes applied theoretical ideas in Ahmes math tool box to convert rational numbers to Egyptian fractions.

In, RMP 35-RMP 38 and RMP 66 a hekat was replaced by its 1/320 unit equivalent, 320 ro. In RMP. 10 hekat, 3200 ro, was divided by 365, the number of civil days in the year obtaining:

8 + 280/365

the expected daily use of fat.

The quotient 8 was proven by the binary steps 1 - 365, 2 - 730, 4 - 1460, and 8 - 2920. The remainder 280 (3200 - 2920 = 280). Translated to modern notation Ahmes' proof multiplied the initial divisor 365 by (8 + 2/3 + 1/10 + 2190) summing (2920 + 243 1/3 + 36 1/2 + 1/6) obtaining 3200 ro, the exact initial value of 10 hekat of fat.

RMP 38 reported Ahmes multiplying 320 ro, one hekat, by 7/22, obtaining 101 9/11. The 101 9/11 answer was proven by multiplying 101 9/11 by 22/7, with the initial divisor 7/22 parsed by binary steps 34/11 times 1/10 = 7/22.

Egyptian division was an inverse of Egyptian multiplication, reported in the RMP and the 1900 BCE Akhmim Wooden Tablet (AWT) and other Middle Kingdom texts.

Conclusion: To parse ancient Egyptian multiplication and division written with a weights and measures context , Ahmes' 2/n table and other arithmetic operations must be stripped away to reveal rational numbers. Ahmes multiplication and division of rational numbers were inverse to each other.

Egyptian multiplication contained two aspects, a theoretical side, and a practical side. Egyptian division was an inverse of Egyptian multiplication, and visa verse. Prior to the 21st century AD Egyptian math scholars had not considered theoretical aspects of the RMP and other Egyptian texts. Theoretical definitions hid an aliquot part and other arithmetic definitions, two being a hekat unity stated as (64/64), and a hekat stated as 320 ro. Egyptian division was quotient and exact remainder based, aspects that scholars are increasingly studying, linked to aliquot parts, 2/n tables, and other ancient scribal applications, such as weights and meaures, after 2005.