Commutative and Associative Properties
Examples and Exercises
Answers
Solution to Example 7.5
| ⓐ | |
| \[-1+3 = \text{______}\] | |
| Use the commutative property of addition to change the order. | \[-1+3 = 3+(-1)\] |
| ⓑ | |
| \[4 \cdot 9 = \text{______}\] | |
| Use the commutative property of multiplication to change the order. | \[4 \cdot 9 = 9 \cdot 4\] |
Solution to Example 7.6
| ⓐ | |
| \((3+0.6)+0.4=\)______ | |
| Change the grouping. |
\((3+0.6)+0.4=3+(0.6+0.4)\)______ |
Notice that $$0.6+0.4$$ is $$1$$, so the addition will be easier if we group as shown on the right.
| ⓑ | |
| \(\left(-4 \cdot \frac{2}{5}\right) \cdot 15=\) _______ | |
| Change the grouping. | \(\left(-4 \cdot \frac{2}{5}\right) \cdot 15=-4 \cdot\left(\frac{2}{5} \cdot 15\right)\) |
Notice that $$\frac{2}{5} · 15$$ is $$6$$. The multiplication will be easier if we group as shown on the right.
Solution to Example 7.7
| \(6(3 x)\) | |
| Change the grouping. | \((6 \cdot 3) x\) |
| Multiply in the parentheses. | \(18 x\) |
Notice that we can multiply $$6·3$$, but we could not multiply $$3·x$$ without having a value for $$x$$.
Try It 7.9
(a) \(-4+7=7+(-4)\)
(b) \(6 \cdot 12=12 \cdot 6\)
Try It 7.10
(a) \(14+(-2)=-2+14\)
(b) \(3(-5)=(-5) 3\)