1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Warm Up
Find each sum or product.
3. 8(24)
4. 7(12)
5. 3(91)
6. 6(15) 32 68
192 84
273 90

3. Problem of the Day
Determine the secret number from the following clues:
The number is a multiple of 5.
It is divisible by 3.
It is less than 200.
Its tens digit equals the sum of its other two digits.
165

4. Sunshine State Standards
MA.6.A.3.5 Apply the Commutative, Associative, and Distributive Properties to show that two expressions are equivalent.

5. Vocabulary Commutative Property Associative Property
Distributive Property

6. 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.

7. COMMUTATIVE PROPERTY (Ordering)
Words
Numbers
You can add or multiply numbers in any order. =
15  2 = 2  15

8. ASSOCIATIVE PROPERTY (Grouping)
Words
Numbers
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)

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

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

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

12. The expressions in each row of example 1B are equivalent because they have the same value.
Helpful Hint

13. Check It Out: Example 1A
Simplify = =
= 50

14. Check It Out: Example 1B
Simplify = =
= 117

15. Check It Out: Example 1C
Simplify 6 × 33 × 5.
6 × 33 × 5
= 6 × 5 × 33
= 30 × 33
= 990

16. Check It Out: Example 1D
Simplify 2 × 69 × 5.
2 × 69 × 5
= 2 × 5 × 69
= 10 × 69
= 690

17. DISTRIBUTIVE PROPERTY
Words
Numbers
To multiply a number by a sum, multiply by each number in the sum and then add.
6  (10 + 4) = (6  10) + (6  4) = =

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

19. Additional Example 2A: Using the Distributive Property to Multiply
Use the Distributive Property to find the product.
6  35
“Break apart” 35 into
6  35 = 6  (30 + 5)
Use the Distributive Property.
= (6  30) + (6  5)
Use mental math to multiply. = =
Use mental math to add.

20. Additional Example 2B: Using the Distributive Property to Multiply
Use the Distributive Property to find the product.
9  87
“Break apart” 87 into
9  87 = 9  (80 + 7)
Use the Distributive Property.
= (9  80) + (9  7)
Use mental math to multiply. = =
Use mental math to add.

21. Check It Out: Example 2A
Use the Distributive Property to find each product.
6  71
6  71 = 6  (70 + 1)
= 6   1 =
= 426

22. Check It Out: Example 2B
Use the Distributive Property to find each product.
28  5
28  5 = (20 + 8)  5
= 20   5 =
= 140

23. Check It Out: Example 2C
Use the Distributive Property to find each product.
8  44
8  44 = 8  (40 + 4)
= 8   4 =
= 352

24. Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems

25. Lesson Quiz
Simplify.
 5  3
Use the Distributive Property to find each product.
4. 8   15
6. 5   71 50
150 70 96 90
170
213

26. Lesson Quiz for Student Response Systems
1. Evaluate
A. 50
B. 40
C. 30
D. 20

27. Lesson Quiz for Student Response Systems
2. Evaluate 3  7  10.
A. 140
B. 170
C. 190
D. 210

28. Lesson Quiz for Student Response Systems
3. Evaluate
A. 86
B. 80
C. 77
D. 70

29. Lesson Quiz for Student Response Systems
4. Use the Distributive Property to find the product.
7  15
A. 135
B. 125
C. 115
D. 105

30. Lesson Quiz for Student Response Systems
5. Use the Distributive Property to find the product.
4  73
A. 292
B. 282
C. 272
D. 262