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Chapter 0: Problem 57

Give an example to show that division does not satisfy the associative property.

Short Answer

Expert verified
For the numbers a=8, b=4, and c=2, we found that \((a/b)/c = (8/4)/2 = 1 \neq 4 = 8/(4/2) = a/(b/c)\). This demonstrates that division does not satisfy the associative property, as changing the order of operations results in different outcomes.

Step by step solution

01

Calculate (a/b)/c

Calculate the operation (8/4)/2: 1. Divide 8 by 4: \(8/4 = 2\) 2. Divide the result by 2: \(2/2 = 1\) So, \((a/b)/c = (8/4)/2 = 1\).
02

Calculate a/(b/c)

Calculate the operation 8/(4/2): 1. Divide 4 by 2: \(4/2 = 2\) 2. Divide 8 by the result: \(8/2 = 4\) So, \(a/(b/c) = 8/(4/2) = 4\).
03

Show the inequality

We found that \((a/b)/c = 1 \neq 4 = a/(b/c)\). This shows that division does not satisfy the associative property, as the rearrangement of parentheses results in different outcomes for the same numbers. The example we used clearly demonstrates that division is not associative.

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