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Chapter 0: Problem 43

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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Most popular questions from this chapter

The intersection of two sets of numbers consists of all numbers that are in both sets. If \(A\) and \(B\) are sets, then their intersection is denoted by \(A \cap B .\) In Exercises \(31-40,\) write each intersection as a single interval. $$ [-8,-3) \cap[-6,-1) $$

Explain why $$ |a b|=|a||b| $$ for all real numbers \(a\) and \(b\).

Give an example of an open interval and a closed interval whose union equals the interval (2,5) .

Give an example of two irrational numbers whose product is a rational number.

In Exercises \(7-16,\) write each union as a single interval. $$ [-2,8] \cup(-1,4) $$
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