Book edition Common Core Edition

Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff

Pages 183 pages

ISBN 9780547587776

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Short Answer

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

$5 \cdot 17 \cdot 2 = 170$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

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: $(a \cdot b) \cdot c = a \cdot (b \cdot c)$

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

Example: $(6 \cdot 4) \cdot 3 = 6 \cdot (4 \cdot 3) = 72$

Commutative Property of Multiplication:

Property: localid="1647518898866" $a \cdot b = b \cdot a$ or $a \cdot b \cdot c = b \cdot c \cdot a$ $a \cdot b \cdot c = b \cdot c \cdot a$

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

Example: $12 \cdot 4 = 4 \cdot 12 = 48$ or $5 \cdot 6 \cdot 4 = 6 \cdot 4 \cdot 5 = 120$

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: $a \cdot b = b \cdot a$ or $a \cdot b \cdot c = b \cdot c \cdot a$

Example: $12 \cdot 4 = 4 \cdot 12 = 48$ or $5 \cdot 6 \cdot 4 = 6 \cdot 4 \cdot 5 = 120$

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

Property: $(a \cdot b) \cdot c = a \cdot (b \cdot c)$

Example: $(6 \cdot 4) \cdot 3 = 6 \cdot (4 \cdot 3) = 72$

In short we can write:

Commutative Property of Multiplication: $a \cdot b = b \cdot a$ or $a \cdot b \cdot c = b \cdot c \cdot a$

Associative Property of Multiplication: $(a \cdot b) \cdot c = a \cdot (b \cdot c)$

So, we can multiply the numbers in any order.

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

$5 \cdot 17 \cdot 2 = 170$

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Pre-algebra

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Short Answer

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

Step by Step Solution

Step-1 – What are real numbers?

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

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

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

Step by Step Solution

Step-1 – What are real numbers?

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

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

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