Properties

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1-6
Properties
Warm Up
Problem of the Day
Lesson Presentation
Course 2
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Warm Up Evaluate. 1. 2 5 ? 3 7 2. 5(3 1)
(3 2) 3. (4 1)2 8 2 4. 12 3 ? 6 20
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21
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Problem of the Day Daniel usually buys 6 bottles
of water and 3 apples when he goes to the grocery
store. Next time he goes, he will buy three times
as many of each. How many items will Daniel buy?
27
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Learn how to identify properties of rational
numbers and use them to simplify numerical
expressions.
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Vocabulary
Commutative Property Associative
Property Identity Property Distributive Property
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Additional Example 1 Identifying Properties of
Addition and Multiplication Tell which property
is represented. A. (2 ? 6) ? 1 2 ? (6 ? 1) B.
3 0 3 C. 7 9 9 7
(2 ? 6) ? 1 2 ? (6 ? 1)
The numbers are regrouped.
Associative Property
3 0 3
One of the factors is 0.
Identity Property
7 9 9 7
The order of the variables is switched.
Commutative Property
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Check It Out Example 1 Tell which property is
represented. A. 7 ? 1 7 B. 3 4 4 3 C.
(5 ? 1) ? 2 5 ? (1 ? 2)
7 ? 1 7
One of the factors is 1.
Identity Property
3 4 4 3
The order of the numbers is switched.
Commutative Property
(5 ? 1) ? 2 5 ? ( 1 ? 2)
The numbers are regrouped.
Associative Property
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Additional Example 2 Using Properties to
Simplify Expressions Simplify each expression.
Justify each step. A. 21 16 9 B. 20 ? 9 ?
5
21 16 9 16 9 21
Commutative Property.
16 (9 21)
Associative Property.
Add.
16 30
46
20 ? 9 ? 5 20 ? 5 ? 9
Commutative Property.
20 ? (5 ? 9)
Associative Property.
Multiply.
20 ? 45
900
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Check It Out Example 2A B Simplify each
expression. Justify each step. A. 17 14
3 B. 12 ? 3 ? 5
17 14 3 14 17 3
Commutative Property.
14 (17 3)
Associative Property.
Add.
14 20
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12 ? 3 ? 5 3 ? 5 ? 12
Commutative Property.
3 ? (5 ? 12)
Associative Property.
Multiply.
3 ? 60
180
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You can use the Distributive Property to multiply
numbers mentally by breaking apart one of the
numbers and writing it as a sum or difference.
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Additional Example 3 Using the Distributive
Property to Multiply Mentally Use the
Distributive Property to find 6(54). Method
1 Method 2
6(54) 6(50 4)
Rewrite 54 as 50 4.
Use the Distributive Property.
(6 ? 50) (6 ? 4)
300 24
Multiply.
324
Add.
6(54) 6(60 6)
Rewrite 54 as 60 6.
(6 ? 60) (6 ? 6)
Use the Distributive Property. Multiply.
360 - 36
Subtract.
324
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Check It Out Example 3 Use the Distributive
Property to find 8(19). Method 1 Method 2
Rewrite 19 as 10 9.
8(19) 8(10 9)
Use the Distributive Property.
(8 ? 10) (8 ? 9)
80 72
Multiply.
152
Add.
8(19) 8(20 1)
Rewrite 19 as 20 1.
(8 ? 20) (8 ? 1)
Use the Distributive Property. Multiply.
160 8
Subtract.
152
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Lesson Quiz
Tell which property is represented. 1. 17 ? 1
17 2. (12 14) 5 12 (14 5) 3. 2 ? 16
16 ? 2 Simplify each expression. Justify each
step. 4. 4 ? 12 ? 25 5. 48 (15 2) Use the
Distributive Property to find each product. 6. 6
? (12 5) 7. (20 7) ? 9
Identity Property
Associative Property
Commutative Property
1,200
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102
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