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Published byNorman Cole Modified over 8 years ago
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P ROPERTIES AND M ENTAL M ATH #3
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COMMUTATIVE PROPERTY (Ordering) WordsNumbers You can add or multiply numbers in any order. 18 + 9 = 9 + 18 15 2 = 2 15 Vocabulary
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ASSOCIATIVE PROPERTY (Grouping) WordsNumbers When you are only adding or only multiplying, you can group any of the numbers together. (17 + 2) + 9 = 17 + (2 + 9) (12 2) 4 = 12 (2 4) Vocabulary
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The Commutative and Associative Properties do not apply to subtraction or division. Caution!
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Example 1: Using Properties to Add and Multiply Whole Numbers Simplify 17 + 5 + 3 + 15.
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Example 2: Using Properties to Add and Multiply Whole Numbers Simplify 4 13 5.
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Example 3 Simplify 23 + 8 + 12 + 7. 23 + 8 + 12 + 7 = 23 + 7 + 8 + 12 = 30 + 20 = 50
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Example 4 Simplify 49 + 17 + 51. 49 + 17 + 51 = 49 + 51 + 17 = 100 + 17 = 117
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Example 5 Simplify 6 × 33 × 5. 6 × 33 × 5 = 6 × 5 × 33 = 30 × 33 = 990
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DISTRIBUTIVE PROPERTY WordsNumbers To multiply a number by a sum, multiply by each number in the sum and then add. 6 (10 + 4) = (6 10) + (6 4) = 60 + 24 = 84 Vocabulary
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When you multiply two numbers, you can “break apart” one of the numbers into a sum and then use the Distributive Property.
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Example 6: Using the Distributive Property to Multiply Use the Distributive Property to find the product. 6 35
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Example 7: Using the Distributive Property to Multiply Use the Distributive Property to find the product. 9 87
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Example 8 Use the Distributive Property to find each product. 6 71
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Example 9 Use the Distributive Property to find each product. 28 5
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Example 10 Use the Distributive Property to find each product. 8 44
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