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Exercises Expressions, exponents and radicals

Example 7.6 from Prealgebra, 7.2 Commutative and Associative Properties

Commutative and Associative Properties: example 7.6

Use the associative properties to rewrite the following:

ⓐ $(3 + 0.6) + 0.4 =__________$
ⓑ $(−4 \cdot \frac{2}{5}) \cdot 15 =__________$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution

ⓐ

$(3 + 0.6) + 0.4 =__________$

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.

ⓑ

$(−4 \cdot \frac{2}{5}) \cdot 15 =__________$

Change the grouping. $(−4 \cdot \frac{2}{5}) \cdot 15 = −4 \cdot (\frac{2}{5} \cdot 15)$

Notice that $\frac{2}{5} \cdot 15$ is $6 .$ The multiplication will be easier if we group as shown on the right.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Use the associative properties to rewrite the following:
ⓐ $(1 + 0.7) + 0.3 =__________$ ⓑ $(−9 \cdot 8) \cdot \frac{3}{4} =__________$

How did it go?

PreviousCommutative and Associative Properties: example 7.5 Next Commutative and Associative Properties: example 7.7

From Prealgebra (1st edition) by OpenStax (Rice University), section 7.2, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.