Commutative and Associative Properties
Answers
Solution to Example 7.6
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Change the grouping. |
![(3+0.6)+0.4=3+(0.6+0.4) (3+0.6)+0.4=3+(0.6+0.4)](https://learn.saylor.org/filter/tex/pix.php/1d53caf64b45c9cde618550415bfb427.svg)
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Change the grouping. |
![\left(-4 \cdot \frac{2}{5}\right) \cdot 15=-4 \cdot\left(\frac{2}{5} \cdot 15\right) \left(-4 \cdot \frac{2}{5}\right) \cdot 15=-4 \cdot\left(\frac{2}{5} \cdot 15\right)](https://learn.saylor.org/filter/tex/pix.php/50dc0ef651b6c5edd185161c35aaa798.svg) |
Notice that
is
. 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) (1+0.7)+0.3=1+(0.7+0.3)](https://learn.saylor.org/filter/tex/pix.php/d06b3abf8bc76b0d83c81551349b7452.svg)
(b) ![(-9 \cdot 8) \cdot \frac{3}{4}=-9\left(8 \cdot \frac{3}{4}\right) (-9 \cdot 8) \cdot \frac{3}{4}=-9\left(8 \cdot \frac{3}{4}\right)](https://learn.saylor.org/filter/tex/pix.php/093a4a93bed8a61d396514d309612933.svg)
Try It 7.12
(a) ![(4+0.6)+0.4=4+(0.6+0.4) (4+0.6)+0.4=4+(0.6+0.4)](https://learn.saylor.org/filter/tex/pix.php/abd2609e2465e93dcd679065cf50edb7.svg)
(b) ![(-2 \cdot 12) \cdot \frac{5}{6}=-2\left(12 \cdot \frac{5}{6}\right) (-2 \cdot 12) \cdot \frac{5}{6}=-2\left(12 \cdot \frac{5}{6}\right)](https://learn.saylor.org/filter/tex/pix.php/7df0f7e12fe03eb213c61bcf4919b074.svg)