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2. Splash Screen

3. Objective
Use the Commutative, Associative, Identity, and Distributive Properties
Example 1-5b

4. Vocabulary
None
Example 1-5b

5. Properties Property Algebra Arithmetic Commutative a + b = b + a
6 + 1 = 1 + 6
a · b = b · a
7 · 3 = 3 · 7
Associative
a + (b + c) = (a + b) + c
2 + (3 + 8) = (2 + 3) + 8
a · (b · c) = (a · b) · c
3 · (4 · 5) = (3 · 4) · 5
Distributive
a(b + c) = ab + ac
4(6 + 2) = 4(6) + 4(2)
a(b - c) = ab - ac
3(7 - 5) = 3(7) - 3(5)
Identity Additive
a + 0 = a
9 + 0 = 9
  Multiplicative
a · 1 = a
5 · 1 = 5
Transitive
if a = b and b = c, then a = c
If = 6 and 6 = 3 · 2, then = 3 · 2
(Change position of numbers)
(Regroup numbers)
(Distribute numbers)
Example 1-5b

6. Example 1 Use the Distributive Property
Example 2 Apply the Distributive Property
Example 3 Identify Properties
Example 4 Identify Properties
Example 5 Apply Properties
Lesson 1 Contents

7. Find 6  43 using the Distributive Property
Write the problem
6  43 6
(40 + 3)
Write 43 as
Bring down 6
6(40) +
6(3)
Use the Distributive Property
Distribute the 6 to the 40
Bring down +
Distribute the 6 to the 3
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Example 1-1a

8. Find 6  43 using the Distributive Property
Follow Order of Operations
P E MD AS
6  43 6
(40 + 3)
Multiply from left to right
6(40) +
6(3)
Bring down +
240 + 18
Add
Answer:
258
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Example 1-1a

9. Find 7  33 using the Distributive Property.
Answer: 231
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Example 1-1b

10. Identify the property shown by the equation
3 + 2 = 2 + 3
Write the problem
Identify what is happening to the numbers
Answer:
Begins with 3 + 2
Commutative Property
Ends with 2 + 3
of Addition
Changed position of numbers
Identify property
Identify process
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Example 1-3a

11. Identify the property shown by the equation 9  6 = 6  9
Answer: Commutative Property of Multiplication
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Example 1-3b

12. Identify the property shown by the equation
(13  3)  4 = 13  (3  4)
Write the problem
(13  3)  4 = 13  (3  4)
Identify what is happening to the numbers
Answer:
Begins with (13  3)  4
Associative Property
Ends with 13  (3  4)
of Multiplication
Regrouping numbers
Identify property
Identify process
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Example 1-4a

13. Identify the property shown by the equation
(10 + 7) + 4 = 10 + (7 + 4)
Answer: Associative Property of Addition
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Example 1-4b

14. Now use the Associative Property by using parenthesis around the 2  4
Find 12  2  4 using the Commutative Property and the Associative Property
Write the problem
12  2  4
Since you can easily multiply 2 and 4, change the order by using the Commutative Property
2  4  12
(2  4)  12
Now use the Associative Property by using parenthesis around the 2  4
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Example 1-5a

15. Follow Order of Operations P E MD AS 12  2  4
Find 12  2  4 using the Commutative Property and the Associative Property
Follow Order of Operations
P E MD AS
12  2  4
2  4  12
Work inside parenthesis
(2  4)  12
Multiply
8  12
Answer: 96
4/4
Example 1-5a

16. Find using the Commutative Property and Associative Property*
Find using the Commutative Property and Associative Property
Answer: 117
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Example 1-5b

17. Assignment
Lesson 9:1
Properties
All
End of Lesson 1

18. Find the cost of 5 admissions and 5 meals. Then add.
THEME PARKS Suppose admission to a theme park costs $35 per person and meals cost $20 per person. What is the cost for a family of 5 people?
Find the cost of 5 admissions and 5 meals. Then add.
cost of 5 admissions
cost of 5 meals
Answer: The total cost is $275.
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Example 1-2a

19. BOWLING Suppose the cost of bowling three games at a local bowling alley is $6.50 and the cost of shoe rental is $1.50. What is the cost for a group of 6 friends to each rent a pair of shoes and bowl three games?
Answer: $48
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Example 1-2c