0.E: Exercises

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May 13, 2022
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- 0.4: Egyptian Multiplication and Division (optional)
- 1: Binary operations

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Exercise $\PageIndex{1}$

Solve the following:

$\frac{2 \times 5}{2+3}$

Answer: $2$ .

Exercise $\PageIndex{2}$

Prove or disprove: There is a largest integer.

Answer: Hint: use proof by contradiction.

Exercise $\PageIndex{3}$

Use Egyptian multiplication to calculate $12 \times 13$ .

Answer

List powers of two in increasing order in a column without going over one chosen factor (12 in this exercise):
List the other factor (13 in this exercise) next to the 1, and double for each cell underneath:
Choose the rows that add up to the first, chosen, factor (12 in this exercise):

1	13
2	26
4	52
8	104

Add the two numbers in the right-hand column to get the answer:
- 52 + 104 = 156. 12 x 13 = 156.
- This is because of the distributive property of multiplication. Since 12 x 13 = (4 + 8) x 13 = (4 x 13) + (8 x 13), this all works out. Also, the right-hand column is just saving time: doubling a quantity is much easier than multiplying it by 4 or 8 or 16 etc.

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