Properties of Real Numbers and Equality

Identify the example that represents the Multiplicative Property of Zero.

• -9 x 0 = 0

• -9 + 9 = 0

• 9 - 9 = 0

• 9 + 0 = 9

What property is this?
1a = a

• Commutative Property of Multiplication

• Multiplicative Inverse

• Multiplicative Identity

• Distributive Property

Identify this property.

• Commutative

• Associative

• Additive Identity

• Distributive

The Commutative Property states that when adding or multiplying two or more numbers or terms, order is not important. That is:

The Additive Inverse Property states that for every number a there is a number −a such that a + (−a) = 0.

• 5 + (-5) = 0

• 6 + (-6) = -12

• 2 + (-2) = 0

• 8 + (-7) = 0

The Additive Property of Equality states that equality is maintained if the same amount is added to both sides of an equation. That is, if a = b, then a + c = b + c

• 5x = 10 then 5x + 2 = 12

• 3x = 9 then 3x + 3 = 9

• 4x = 8 then 4x - 4 = 4

• 6x = 12 then 6x - 3 = 6

The Multiplicative Property of Equality states that equality is maintained if both sides of an equation are multiplied by the same amount. That is, if a = b, then a · c = b · c

• y = 3 then 4y = 4(3)

• x = 2 then 2x = 22

• y = 6 then 3y = 3

• x = 4 then 2x = 8

The Associative Property states that when adding or multiplying three or more numbers or terms together, grouping is not important. That is:

Which property justifies the work in solving this equation?

• Addition Property of Equality

• Additive Inverse Property

• Identity Property of Addition

• Subtraction Property of Equality

Which property of real numbers justifies the work shown from Step 1 to Step 2?

• Distributive Property

• Commutative Property

• Identity Property

• Associative Property