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) \(3(-5)=(-5) 3\)

Back to '1.1 Commutative Law of Addition and Multiplication\'