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Exercises Expressions, exponents and radicals

Example 7.9 from Prealgebra, 7.2 Commutative and Associative Properties

Commutative and Associative Properties: example 7.9

Evaluate each expression when $n = 17 .$

ⓐ $\frac{4}{3} (\frac{3}{4} n)$
ⓑ $(\frac{4}{3} \cdot \frac{3}{4}) n$

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

ⓐ

Substitute 17 for n.

Multiply in the parentheses first.

Multiply again.

ⓑ

Substitute 17 for n.

Multiply. The product of reciprocals is 1.

Multiply again.

What was the difference between part ⓐ and part ⓑ here? Only the grouping changed. By the Associative Property of Multiplication, $\frac{4}{3} (\frac{3}{4} n) = (\frac{4}{3} \cdot \frac{3}{4}) n .$ By carefully choosing how to group the factors, we can make the work easier.

Your turn

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

Evaluate each expression when $p = 24 :$ ⓐ $\frac{5}{9} (\frac{9}{5} p)$ ⓑ $(\frac{5}{9} \cdot \frac{9}{5}) p .$

How did it go?

PreviousCommutative and Associative Properties: example 7.8 Next Commutative and Associative Properties: example 7.10

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.