Chapter 5.1, Problem 77E

Invent an Egyptian type of numeration system using the following symbols:

, where these symbols represent units, tens, hundreds, and so on, respectively.

a. Write $3,142$ and $7,203$ using this notation.

b. Find $3,142+7,203$ similar to the way we added in Example 2.

c. Find $7,203-3,142$ similar to the way we subtracted in Example 2.

Example 2 Adding and Subtracting in the Egyptian System

a. Add and

b. Subtract from using Egyptian notation.

Solution:

a. We add these two numbers by simply grouping all the symbols together (the addition sign is not part of the Egyptian notation). After obtaining the sum, we regroup $10$ heel bones as one scroll.

We can now rewrite this answer as .

b. We have the reverse problem from part a). Although we can subtract two strokes from four strokes, we cannot subtract six heel bones from three heel bones unless we “borrow.” That is, we convert one scroll to $10$ heel bones.

c. Rewrite