Print this chapterPrint this chapter

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