0.E: Exercises
- Page ID
- 18153
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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
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Hint: use proof by contradiction.
Exercise \(\PageIndex{3}\)
Use Egyptian multiplication to calculate \(12 \times 13\).
- Answer
-
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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:
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52 + 104 = 156. 12 x 13 = 156.
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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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