90,8 by 30,1 egyptian division

Question

I am having trouble using the Egyptian method of division.

So far I have 
1    30,1 
2    60,2 

90,8 - 90,3 -> need 5 additional units.

I know at this point I need to take parts of 30,1 but I am not sure which direction I should go from here.

I tried the 2/3 part.

1                  30,1 
2/3                20, 2/3 
1/3, 1/9           13, 2/3, 1/9

I am not sure where to go from here.

Answer 1

I have figured this out on my own. All lines that are used in the final answer are denoted by a "\" placed in front of that line.

Continuing after 2

\      1       30,1
\      2       60,2

As I stated earlier we need 5 additional units to reach 90,8 but we can decrease this by taking other parts

\      1/8      3, 1/2, 1/4, 1/8
\      1/31     1 

From here we only need an 1/8 more to reach 90,8. However the Egyptians never repeated unit fractions in their notation (1/8 was used when taking the 1/8 part). So we must change 1/8 into other unit fractions. 1/8 = .125 = .1, .025 = 1/10, 1/40

       1        30,1
\      10       300,10
\      40       1000, 200, 40

We now take the numbers on the right and reciprocate them. These form the unit fractions that sum to 1/8.

Our final answer is 3, 1/8, 1/31, 1/310, 1/1240. Checking this with your simplest method for division you will find that this equates to 98/31 or 3.161290323....