36 Chapter 1 Whole Numbers These rectangular arrays help us visualize the commutative property of multiplication. For example 2 5 5 2. 2 rows of 5 5 rows of 2 2 5 10 5 2 10 Multiplication is also an associative operation. For example, (3 5) 2 3 (5 2). Associative Property of Multiplication For any numbers, a, b, and c, 1a b2 c a 1b c2 The manner in which factors are grouped under multiplication does not affect the product. 6 5 3 11 72, Answers 4. 5 6; product is 30 5. 13 12 7; product is 21 TIP: The variable “x” is commonly used in algebra and can be confused with the multiplication symbol “.” For this reason it is customary to limit the use of “” for multiplication. Applying Properties of Multiplication Example 2 a. Rewrite the expression 3 9, using the commutative property of multiplication. Then find the product. b. Rewrite the expression using the associative property of 14 22 3, multiplication. Then find the product. Solution: a. 3 9 9 3. The product is 27. b. 14 22 3 4 12 32. To find the product, we have The product is 24. 4 12 32 4 162 24 Two other important properties of multiplication involve factors of 0 and 1. Skill Practice 4. Rewrite the expression , using the commutative property of multiplication. Then find the product. 5. Rewrite the expression using the associative property of multiplication. Then find the product.
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