1. P ROPERTIES AND M ENTAL M ATH #3

2. COMMUTATIVE PROPERTY (Ordering) WordsNumbers You can add or multiply numbers in any order. 18 + 9 = 9 + 18 15  2 = 2  15 Vocabulary

3. 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

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

5. Example 1: Using Properties to Add and Multiply Whole Numbers Simplify 17 + 5 + 3 + 15.

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

7. Example 3 Simplify 23 + 8 + 12 + 7. 23 + 8 + 12 + 7 = 23 + 7 + 8 + 12 = 30 + 20 = 50

8. Example 4 Simplify 49 + 17 + 51. 49 + 17 + 51 = 49 + 51 + 17 = 100 + 17 = 117

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

10. 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

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

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

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

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

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

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