Commutative and Associative Properties

Read this section on the communitive and associative properties. Complete the practice questions and check your answers.

Answers

Solution to Example 7.6

ⓐ  
  (3+0.6)+0.4=______
Change the grouping.

(3+0.6)+0.4=3+(0.6+0.4)


ⓑ  
  \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.


Try It 7.11

(a) (1+0.7)+0.3=1+(0.7+0.3)

(b) (-9 \cdot 8) \cdot \frac{3}{4}=-9\left(8 \cdot \frac{3}{4}\right)


Try It 7.12

(a) (4+0.6)+0.4=4+(0.6+0.4)

(b) (-2 \cdot 12) \cdot \frac{5}{6}=-2\left(12 \cdot \frac{5}{6}\right)