Middle Kingdom (MK) economics provided a rigorous foundation for Egyptian mathematics. Scribes solved economic problems by generally converting rational numbers to equivalent unit fraction series within finite arithmetic. The exacting weights and measures units facilitated a a decentralized commodity based monetary system. Exacting Egyptian fraction commodity units eliminated an awkward Old Kingdom 'command economy' practice of rounding off binary numbers within a binary balance beam created measuring system. Egyptian MK mathematics was finite and discrete by generally factoring composite numbers into prime components by creating LCM 2/n tables and exacting weights and measures units.

Inside th Egyptian economy the Heqanakht Papers discuss two absentee landlords' family and estate production and profit concerns in four letters. Accounting for Private Estates and the Household in the 20th Century BC Middle Kingdom by Mahmoud Ezzamel appeared in the journal Abacus, Vol. 38, No. 2 (2002), pp.235-262. Ezzamel, an accountant, shows that absentee landlords relied on theoretical commodities and metals units that summed to a monetary system. Practical measurements issued payments to workers and implemented other management controls within rational number remainders written in Egyptian fractions. An abstract of Ezzamel's article follows: 2,000 BCE Accounting Article.

The Ahmes Papyrus (AP) and the Moscow Mathematical Papyrus(MMP) scaled grain inventories producing bread, beer and other products. Pesu and sub-units (i.e besha, des-jugs) further scaled bread, beer and other products for distribution. Gillings showed that alternando and dividendo, modern proportions, and a harmonic mean was used in bread and beer recipes. Several AP and MMP problems discuss 15 to 16 hekats of grain producing 200 loaves of bread, with 5 hekats, with the balance of hekats producing beer. Each hekat produced one, two, and three types of beer, labeled from 8/3 pesu to 6 pesu, denoted initial grain content by an inverse to the final product. A product with 3/8 hekat of grain was reported as 8/3 pesu, written as 2 2/3 pesu.

Equally important, in 2002 James P. Allen wrote a book on the The Heqanakht Papers. Around 2,000 BCE a political compromise encouraged middle class Egyptians to accumulate wealth. Egyptology and economic historians debate the implications of the Heqanakht Papers, often without stressing the role of Egyptian fractions. Egyptian fractions unified a decentralized Egyptian economy method that created verifiable weights and measures units. Morris Silver, Professor Emeritus, Department of Economics, City College of the City University of New York, reviewed Allen's book, adding several discussion points. Professor Silver also reviewed "The Invention of Coinage and the Monetization of Ancient Greece" by David M. Schaps in the same manner, adding meta and micro economic considerations to the discussion. For example, Morris Silver aptly cited Babylonian (and Egyptian) monetary systems that spread across the Ancient Near East using 'bags of coins' well before Lydia and Greeks were improperly reported to have created coinage.

Outside the economy a 1990s paradigm conclude that Middle Kingdom (MK) Egyptian contacts with Babylonian included the use of algorithms by both cultures, a situation that existed in both cultures prior to 2,000 BCE. The post-2,000 BCE bi-cultural algorithm suggestions excludes impacts of non-algorithmic MK Egyptian fraction methods. A 2001 publication by Jens Hoyrup, noted Babylonian scholar, diverts attention away from Egyptian fraction issues by raising algorithm issues. Egyptians likely used no algorithm after replacing its Old Kingdom's binary numeration system with a finite Egyptian fraction system. Finite Egyptian fraction arithmetic was based in methodologies, one being optimized least common multiples to wrote exact remainders.

Hoyrup, Marshall Clagett, Ancient Egyptian Science, Vol III,1999, and by Joran Friberg, Unexpected links of Egyptian and Babylonian Mathematics, 2005 and others omitted discussions of the Akhmim Wooden Tablet. The incomplete position of 1920's scholars offerred potential algorithmic aspects of the RMP, and the MMP. Hoyrup, Clagett and Friberg improperly conclude that additive views of Middle Kingdom Egyptian arithmetic were sufficient to parse aspects of the RMP 2/n table. That is, additive views of Egyptian fraction arithmetic oddly exclude theoretical aspects of scribal subtraction, multiplication, division, and Egyptian fraction mathematics reported in RMP problems and other mathematical texts.

Algorithm adherents discuss a wider range of theoretical arithmetic issues. One is connected to 'red auxiliary numbers used in multiplication and the conversion of rational numbers to optimized unit fraction series. Another idea includes aspects of the EMLR, the Akhmim Wooden Tablet (AWT), and 2/n tables. One a third level the Kahun Papyrus) includes its own set of theoretical issues. Taken as a whole Egyptian fraction 2/n tables and red auxiliary LCMs jump-started scribal finite arithmetic methods during the Middle Kingdom. Scribal finite arithmetic generally created quotient and exact remainder division statements. Quotient and remainder division methods combined LCM red auxiliary numbers with other theoretical methods that generally converted rational numbers to unit fraction series in the RMP and the EMLR; in the AWT and RMP, a hekat unity(64/64), and 320 ro for a hekat, that allowed volume units to be exactly divided into quotients and remainders.

'Red auxiliary' numbers used in RMP 36 defined one of several theoretical methods that created scaled 2/n tables and the Egyptian fraction numeration system. Prime numbers were used within the Egyptian fraction notation to write exact quotient and remainder division statements in the AWT and other hieratic texts. Ahmes' bird-feeding rate method, for example, wrote out practical ways to monitor inventories. Merging the unit fraction mathematics that created 2/n tables and inventory monitoring systems, 2,050 BCE to 1500 BCE Egyptian arithmetic contained theoretical and practical sides. Neither side, but itself, provided a sufficient description of the Egyptian fraction system.

Conflicting Old Kingdom binary numeration issues, that may be obvious to several PM readers, were resolved by scribes around 2,000 BCE in favor of Egyptian fraction methods. A new Egyptian fraction system created a decentralized Egyptian economy managed within scaled theoretical commodity/monetary units. Practical recording of commodity/monetary accounts was included in a double entry accounting system. Middle Kingdom scribes created an exact weights and measures system beyond the monetary system. For example, units were used by absentee landlords to manage estates, paying a 10 percent political tax rate to Pharaoh, as well as creating contracts of various types. In other words, the Egyptian economy fully integrated the Egyptian fraction system and its finite notation system in all phases of their math education and their economic lives. The system spread across Egypt, and the ancient Near East, to Greece and elsewhere, carrying commodities and bags of 'coins' to buy and sell goods within the region's decentralized and centralized economies.

In conclusion, economic considerations improved MK weights and measures units, allowing prime number divisors and prime number weights facilitating Pharaoh and absentee landlord inventory controls 0ver commodities. Exact Egyptian fraction weights and measure units formed one of several building block of the Egyptian economy by creating the Western Tradition's first commodity based monetary system. Weights and measures units created double entry accounting entries that compared expected to actual usages of commodities inventories, with managers resolving each major difference. Expected (theoretical) daily usages were created by setting rates based on dividing a hekat unity (64/64), and other substitions (like one hekat = 320 ro) by rational numbers. The first formal state of hekat unities is recorded in the Akhmim Wooden Tablet, and later in other double checked volume based systems that allowed profits, losses, taxes, and business contracts to be recorded and managed.