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1-4
Properties of Numbers
Preview
Warm Up
California Standards
Lesson Presentation
Holt CA Course 1
1-4
Properties of Numbers
Warm Up
Evaluate.
1. 2 + 5  3 – 7
10
2. 5(3 – 1) ÷ (3 + 2) 2
3. (4 + 1)2 – 8 ÷ 2
21
4. 12 ÷ 3  6 – 20
4
Holt CA Course 1
1-4
Properties of Numbers
California
Standards
AF1.3 Apply algebraic order of
operations and the commutative,
associative, and distributive properties
to evaluate expressions; and justify each
step in the process.
Holt CA Course 1
1-4
Properties of Numbers
Vocabulary
Commutative Property- add numbers in any
order and multiply numbers in any order “switch
order”
Associative Property- add or multiply, you
can group the numbers together in any combination
“re-group”
Identity Property- the sum of 0 and any
number is the number, and the product of 1 and any
number is the number
Distributive Property- multiply numbers
mentally by “breaking apart” one of the numbers
and writing it as a sum or difference.
Holt CA Course 1
1-4
Holt CA Course 1
Properties of Numbers
1-4
Holt CA Course 1
Properties of Numbers
1-4
Holt CA Course 1
Properties of Numbers
1-4
Properties of Numbers
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.
Holt CA Course 1
1-4
Properties of Numbers
Additional Example 1: Identifying Properties of
Addition and Multiplication
Tell which property is represented.
A. (2  6)  1 = 2  (6  1)
(2  6)  1 = 2  (6  1)
Associative Property
The numbers are regrouped.
B. 3 + 0 = 3
3+0=3
Identity Property
One of the addends is 0.
C. 7 + 9 = 9 + 7
7+9=9+7
Commutative Property
Holt CA Course 1
The order of the numbers is
switched.
1-4
Properties of Numbers
Additional Example 2: Using Properties to Simplify
Expressions
Simplify each expression. Justify each step.
A. 21 + 16 + 9
21 + 16 + 9 = 16 + 9 + 21
= 16 + (9 + 21)
= 16 + 30
Commutative Property
Associative Property
Add.
= 46
B. 20  9  5
20  9  5 = 20  5  9
= 20  (5  9)
Associative Property
= 20  45
Multiply.
= 900
Holt CA Course 1
Commutative Property
1-4
Properties of Numbers
Additional Example 3: Using the Distributive
Property to Multiply Mentally
Use the Distributive Property to find 6(54).
Method 1: 6(54) = 6(50 + 4)
= 300 + 24
Rewrite 54 as 50 + 4.
Use the Distributive
Property.
Multiply.
= 324
Add.
= (6  50) + (6  4)
Method 2: 6(54) = 6(60 – 6)
= (6  60) – (6  6)
= 360 – 36
= 324
Holt CA Course 1
Rewrite 54 as 60 – 6.
Use the Distributive
Property. Multiply.
Subtract.
1-4
Properties of Numbers
Check It Out! Example 1
Tell which property is represented.
A. 7  1 = 7
71=7
Identity Property
One of the factors is 1.
B. 3 + 4 = 4 + 3
3+4=4+3
Commutative Property
The order of the numbers is
switched.
C. (5  1)  2 = 5  (1  2)
(5  1)  2 = 5  ( 1  2)
Associative Property
Holt CA Course 1
The numbers are regrouped.
1-4
Properties of Numbers
Check It Out! Example 2
Simplify each expression. Justify each step.
A. 17 + 14 + 3
17 + 14 + 3 = 14 + 17 + 3
= 14 + (17 + 3)
B. 12  3  5
= 14 + 20
= 34
12  3  5 = 3  5  12
= 3  (5  12)
= 3  60
= 180
Holt CA Course 1
Commutative Property
Associative Property
Add.
Commutative Property
Associative Property
Multiply.
1-4
Properties of Numbers
Check It Out! Example 3
Use the Distributive Property to find 8(19).
Method 1:
8(19) = 8(10 + 9)
= (8  10) + (8  9)
Method 2:
= 80 + 72
Multiply.
= 152
Add.
8(19) = 8(20 – 1)
= (8  20) – (8  1)
= 160 – 8
= 152
Holt CA Course 1
Rewrite 19 as 10 + 9.
Use the Distributive
Property.
Rewrite 19 as 20 – 1.
Use the Distributive
Property. Multiply.
Subtract.
1-4
Properties of Numbers
Lesson Quiz
Tell which property is represented.
1. 17  1 = 17
Identity Property
Associative Property
3. 2  16 = 16  2 Commutative Property
2. (12 + 14) + 5 = 12 + (14 + 5)
Simplify each expression. Justify each step.
4. 4  12  25
1,200
5. 48 + (15 + 2)
65
Use the Distributive Property to find each product.
6. 6  (12 + 5)
7. (20 – 7)  9
Holt CA Course 1
102
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