1. 1-5 Properties and Mental Math I CAN use the commutative and associative properties to add and multiply whole numbers. I CAN use the distributive property to multiply whole numbers.

2. 1-5 Properties and Mental Math Vocabulary Commutative Property Associative Property Distributive Property

3. 1-5 Properties and Mental Math Mental math means “doing math in your head.” Many mental math strategies use number properties that you already know to make equivalent expressions that may be easier to simplify.

4. 1-5 Properties and Mental Math COMMUTATIVE PROPERTY (Ordering) WordsNumbers You can add or multiply numbers in any order. 18 + 9 = 9 + 18 15  2 = 2  15

5. 1-5 Properties and Mental Math 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)

6. 1-5 Properties and Mental Math The Commutative and Associative Properties do not apply to subtraction or division. Caution!

7. 1-5 Properties and Mental Math Example 1: Using Properties to Add and Multiply Whole Numbers A. Simplify 17 + 5 + 3 + 15. 17 + 5 + 3 + 15 Look for sums that are multiples of 10 4) 40 Use the Commutative Property. 1) 17 + 3 + 5 + 15 2) (17 + 3) + (5 + 15) Use mental math to add. 3) 20 + 20 Use the Associative Property to make groups of compatible numbers.

8. 1-5 Properties and Mental Math Example 1: Using Properties to Add and Multiply Whole Numbers B. Simplify 4  13  5. 4  13  5 Look for products that are multiples of 10 4) 260 Use the Commutative Property. 1) 13  4  5 2) 13  (4  5) Use mental math to multiply. 3) 13  20 Use the Associative Property to group compatible numbers.

9. 1-5 Properties and Mental Math You Try! Example 1 A. Simplify 12 + 5 + 8 + 5. 12 + 5 + 8 + 5 Look for sums that are multiples of 10 4) 30 Use the Commutative Property. 1) 12 + 8 + 5 + 5 2) (12 + 8) + (5 + 5) Use mental math to add. 3) 20 + 10 Use the Associative Property to make groups of compatible numbers.

10. 1-5 Properties and Mental Math You Try! Example 1 B. Simplify 8  3  5. 8  3  5 Look for products that are multiples of 10. 4) 120 Use the Commutative Property. 1) 3  8  5 2) 3  (8  5) Use mental math to multiply. 3) 3  40 Use the Associative Property to group compatible numbers.

11. 1-5 Properties and Mental Math 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

12. 1-5 Properties and Mental Math When you multiply two numbers, you can “break apart” one of the numbers into a sum and then use the Distributive Property.

13. 1-5 Properties and Mental Math Example 2: Using the Distributive Property to Multiply Use the Distributive Property to find the product. A. 6  35 1) 6  (30 + 5) “Break apart” 35 into 30 + 5. 4) 210 Use the Distributive Property. 2) (6  30) + (6  5) Use mental math to add. 3) 180 + 30 Use mental math to multiply.

14. 1-5 Properties and Mental Math Example 2: Using the Distributive Property to Multiply Use the Distributive Property to find the product. B. 9  87 1) 9  (80 + 7) “Break apart” 87 into 80 + 7. 4) 783 Use the Distributive Property. 2) (9  80) + (9  7) Use mental math to add. 3) 720 + 63 Use mental math to multiply.

15. 1-5 Properties and Mental Math You Try! Example 2 Use the Distributive Property to find the product. A. 4  27 1) 4  (20 + 7) “Break apart” 27 into 20 + 7. 4) 108 Use the Distributive Property. 2) (4  20) + (4  7) Use mental math to add. 3) 80 + 28 Use mental math to multiply.

16. 1-5 Properties and Mental Math You Try! Example 2 Use the Distributive Property to find the product. B. 6  43 1) 6  (40 + 3) “Break apart” 43 into 40 + 3. 4) 258 Use the Distributive Property. 2) (6  40) + (6  3) Use mental math to add. 3) 240 + 18 Use mental math to multiply.

17. 1-5 Properties and Mental Math CAN YOU use the commutative and associative properties to add and multiply whole numbers? CAN YOU use the distributive property to multiply whole numbers?

18. 1-5 Properties and Mental Math Lesson Quiz Use the Commutative and Associative Properties to find each sum or product. 1. 18 + 24 + 2 + 6 2. 25 5  4 Use the Distributive Property to find each product. 3. 8  12 4. 5  34 500 50 96 170

19. 1-5 Properties and Mental Math HOMEWORK p. 28: 1-29 odd