Page 67 - Math Course 2 (Book 1)

Commutative and Associative Properties

Mo. 2

Lesson 5 Let’s Begin

KEY CONCEPTS:
1. Recognize the Commutative and Use Addition Properties
Associative Properties.
2. Use the Commutative and Associative Example
Properties to simplify algebraic
expressions.
TRANSPORTATION
Find the distance between
MO. 2 - L5a Lakewood/ Ft. McPherson
and Five Points. Explain
Recognize the Commutative how the Commutative
Property makes calculating
and Associative Properties the answer unnecessary.

Key Concept

Associative Property

Words The way you group three or more Lakewood/Ft.
Garnett to
numbers when adding or multiplying McPhersonto Oakland City West End to Five Points
Oakland City to West End
Garnett
does not change their sum or product.
Symbols For any numbers a, b, and c 1.1 + 1.5 + 1.5 + 0.4
(a+b)+c = a+(b+c) and (ab)c = a(bc).

Examples (2+4)+6 = 2+(4+6), (3•5)•4 = 3•(5•4) 1.1 + 1.5 + 1.5 + 0.4 = 1.1 + 0.4 + 1.5 + 1.5
Commutative (+)

Commutative Property = (1.1 + 0.4) + (1.5 + 1.5)
Associative (+)

Words The order in which you add or multiply = 1.5 + 3.0 Add.
number does not change their sum or
product. = 4.5 Add.
Symbols For any numbers a and b, a + b = b + a
and a • b = b • a
Answer The distance is 4.5 miles
Examples 5 + 6 = 6 + 5, 3 • 2 = 2 • 3

Concept Summary
Properties of Numbers
The following properties are true for any numbers a, b, and c.
Properties Addition Multiplication
Commutative a + b = b + a ab = ba
Associative (a + b) + c = a + (b + c) (ab)c = a(bc)
Identity 0 is the identity a + 0 = 0 + a = a 1 is the identity a • 1 = 1 • a = a
Zero – a • 0 = 0 • a = 0
Distributive a (b + c) = ab + ac and (b + c) a = ab + ca
Substitution If a = b, then a may be substituted for b.

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