This document discusses properties of operations in mathematics including addition and multiplication. It defines the commutative, associative, identity, and zero properties of addition and multiplication. The commutative property states that the order of numbers being added or multiplied does not change the sum or product. The associative property states that the grouping of numbers being added or multiplied does not change the sum or product. The identity properties state that adding or multiplying any number by zero or one, respectively, does not change the number. The zero property of multiplication states that multiplying any number by zero equals zero. Examples are provided to illustrate these properties.

1. CHAPTER 1
CHAPTER 1 1-9 PROPERTIES OF OPERATIONS
Properties of Addition and Multiplication
PROPERTY ADDITION MULTIPLICATION
COMMUTATIVE THE ORDER in which THE ORDER in which
PROPERTIES numbers are added does numbers are multiplied does
NOT AFFECT the sum NOT AFFECT the product
9 + 15 = 15 + 9 4 x 12 = 12 x 4
ASSOCIATIVE The way in which numbers The way in which numbers
PROPERTIES are GROUPED does NOT are GROUPED does NOT
AFFECT the sum AFFECT the product
4 + (5 + 6) = (4 + 5) + 6 (3 x 2) x 4 = 3 x (2 x 4)
IDENTITY The SUM of any number and The PRODUCT of any number
PROPERTIES ZERO is that number and ONE is that number
567 + 0 = 567 422 x 1 = 422
MULTIPLICATION The PRODUCT of any number
PROPERTY OF ZERO and ZERO is ZERO
389 x 0 = 0
TIPS COMMUTATIVE(=)Conmutareparentheses are like a BAG
TIPS ASSOCIATIVE = Think the = TO CHANGE… TO MOVE
IDENTITY = Identical
PROPERTY OF ZERO = Equals 0

2. !
FULL!
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BE
BE C AR E
C AR E

3. EXAMPLES
• Name the property or properties shown by each Expression
• a. (3 x 4) x 5 = 3 x (4 x 5)
• b. 6 + (5 + 4) = 6 + (4 + 5)
• c. (5 x 1) x 7 = 5 x 7
• d. 12 x 45 x 23 x 0 = 0
• e. (8 + 29) + 2 = (2 + 8) + 29

4. • Find each missing number. Tell what property or properties are shown
• 1. 15 + (48 + 5) = 15 + (__ + 48)
• 2. (78 + 29) + __ = 78 + 29
• 3. 84 ÷ 12 = 84 ÷ 12 x__
• 4. (26 x__) x 30 = 30 x (26 x 4)