Properties of Operations: Vocabulary

• Commutative Property

• Associative Property

• Additive Identity Property

• Multiplicative Identity Property

• Multiplicative Property of Zero

• counterexample

Commutative Property

• the ORDER in which numbers are ADDED or MULTIPLIED does not change the SUM or PRODUCT

• Addition Symbols: x + y = y + x

• Addition Example:  3 + 5 = 5 + 3

• Multiplication Symbols: a * b = b * a

• Multiplication Example:  2 * 4 = 4 * 2

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Associative Property

• the way in which numbers are GROUPED when they are added or multiplied does not change the SUM or PRODUCT

• Addition Symbols: a + (b + c) = (a + b) + c

• Addition Example: 2 + (3 + 8) = (2 + 3) + 8

• Multiplication Symbols: a * (b * c) = (a * b) * c

• Multiplication Example: 3 * (4 * 5) = (3 * 4) * 5

Property

• A property is a statement that is true for any number.

Multiplicative Identity

• When any number is multiplied by 1, the product is the number.

• Symbols: x * 1 = x

• Example: 1 * 5 = 5

Multiplicative Property of Zero

• When any number is multiplied by 0, the product is 0.

• Symbols: x * 0 = 0

• Example: 3 * 0 = 0