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Q2.

Expert-verified
Found in: Page 66

### Pre-algebra

Book edition Common Core Edition
Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff
Pages 183 pages
ISBN 9780547587776

# Explain how the commutative and associative properties of multiplication can help you evaluate the product $5 · 17 · 2$ mentally

$\text{5} · 17 · 2 = 170$

See the step by step solution

## Step-1 – What are real numbers?

Real numbers are simply the combination of Whole numbers, Integers, Rational and Irrational numbers in the number system.

## Step-2 – Explain how the commutative and associative properties of multiplication can help you evaluate the product 5 x 17 x 2 mentally.

Suppose a, b, and c is three real numbers.

Associative property of Multiplication

Property: $\text{(a} · \text{b)} · \text{c}=\text{a} · \left( \text{b} · \text{c} \right)$

If you are multiplying three real numbers, the product is always the same regardless of their grouping.

Example: $\text{(6} · \text{4)} · \text{3}=\text{6} · \left( \text{4} · \text{3} \right) = 72$

Commutative Property of Multiplication:

Property: localid="1647518898866" $\text{a} · \text{b} =\text{b} · \text{a}$ or $\text{a} · \text{b} · \text{c}=\text{b} · \text{c} · \text{a}$$\text{a} · \text{b} · \text{c}=\text{b} · \text{c} · \text{a}$

If you multiply two or three real numbers in any order, their product will always be the same.

Example: $\text{12} · \text{4} =\text{4} · \text{12} = 48$ or $\text{5} · \text{6} · \text{4}=\text{6} · \text{4} · \text{5} \text{=} \text{120}$

## Step-3 – Explain how the commutative and associative properties of multiplication can help you evaluate the product 5 x 17 x 2 mentally.

Commutative Property of Multiplication states that if you multiply two or three real numbers in any order, their product will always be the same.

Property: $\text{a} · \text{b} =\text{b} · \text{a}$ or $\text{a} · \text{b} · \text{c}=\text{b} · \text{c} · \text{a}$

Example: $\text{12} · \text{4} =\text{4} · \text{12} = 48$ or $\text{5} · \text{6} · \text{4}=\text{6} · \text{4} · \text{5} \text{=} \text{120}$

Associative property of Multiplication states that if you are multiplying three real numbers, the product is always the same regardless of their grouping.

Property:$\text{(a} · \text{b)} · \text{c}=\text{a} · \left( \text{b} · \text{c} \right)$

Example: $\text{(6} · \text{4)} · \text{3}=\text{6} · \left( \text{4} · \text{3} \right) = 72$

In short we can write:

Commutative Property of Multiplication: $\text{a} · \text{b} =\text{b} · \text{a}$ or $\text{a} · \text{b} · \text{c}=\text{b} · \text{c} · \text{a}$

Associative Property of Multiplication: $\text{(a} · \text{b)} · \text{c}=\text{a} · \left( \text{b} · \text{c} \right)$

So, we can multiply the numbers in any order.

localid="1649347774162" $\begin{array}{l}\text{5}·17·2=170\\ =5\left(17·2\right)\left(\text{by Associative Property)}\\ =5\left(2·17\right)\left(\text{by Commutative Property}\right)\\ =5·34=170\end{array}$

$\text{5} · 17 · 2 = 170$