P ROPERTIES AND M ENTAL M ATH #3

COMMUTATIVE PROPERTY (Ordering) WordsNumbers You can add or multiply numbers in any order =  2 = 2  15 Vocabulary

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

The Commutative and Associative Properties do not apply to subtraction or division. Caution!

Example 1: Using Properties to Add and Multiply Whole Numbers Simplify

Example 2: Using Properties to Add and Multiply Whole Numbers Simplify 4  13  5.

Example 3 Simplify = = = 50

Example 4 Simplify = = = 117

Example 5 Simplify 6 × 33 × 5. 6 × 33 × 5 = 6 × 5 × 33 = 30 × 33 = 990

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) = = 84 Vocabulary

When you multiply two numbers, you can “break apart” one of the numbers into a sum and then use the Distributive Property.

Example 6: Using the Distributive Property to Multiply Use the Distributive Property to find the product. 6  35

Example 7: Using the Distributive Property to Multiply Use the Distributive Property to find the product. 9  87

Example 8 Use the Distributive Property to find each product. 6  71

Example 9 Use the Distributive Property to find each product. 28  5

Example 10 Use the Distributive Property to find each product. 8  44