The number system was decimal with special symbols for 1, 10, 100, 1,000, 10,000, 100,000, and 1,000,000. Addition was accomplished by grouping and regrouping. Multiplication and division were essentially based on binary multiples. Fractions were ubiquitous but only unit fractions, with two exceptions, were allowed. All other fractions were required to be written as a sum of unit fractions. Geometry was limited to areas, volumes, and similarity. Curiously, though, volume measures for the fractional portions of the hekat a volume measuring about 4.8 liters, were symbolically expressed differently from others.
Simple algebraic equations were solvable, even systems of equations in two dimensions could be solved.
Symbolic notation for numbers.
|10,000||=||a bent finger|
|100,000||=||a burbot fish|
|1,000,000||=||a kneeling figure|
Note though that there are numerous interpretations of what these hieroglyphs might represent.
Numbers are formed by grouping.
Addition is formed by grouping
Note alternate forms for these numbers.
Multiplication is basically binary.
Selecting 8 and 16 (i.e. ), we have
Division is also basically binary.
Obviously, the distributive laws for multiplication and division were well understood.
Fractions It seems that the Egyptians allowed only unit fractions, with just two exceptions, and . All other fractions must be converted to unit fractions. The symbol for unit fractions was a flattened oval above the denominator. In fact, this oval was the dign used by the Egyptians for the ``mouth." In the case of the volume measure hekat, the commonly used fractional parts of ( ,and , were denoted by parts of the symbol for the ``Horus-eye."4 For ordinary fractions, we have the following in modern notation.
All other fractions must be converted to unit fractions.
Ahmes gives a table of unit fractions.