Algebraic Properties

Commutative PropertiesAre the two expressions equivalent?

Commutative Property of Addition: When adding two or more numbers together, order is not important

5 1 7 3

1 35 7

ab b aCommutative Property of Multiplication: When multiplying

two or more numbers together, order is not important

ab baThere are no Commutative Properties for Subtraction and Division.

5173

1357

Associative PropertiesAre the two expressions equivalent?

Associative Property of Addition: When adding more than two numbers the grouping of the numbers does not change the sum.

5 1 7 5 1 7

a b c a b c Associative Property of Multiplication: When multiplying

more than two numbers the grouping of the numbers does not change the product.

a b c a b c Are there Associative Properties for Subtraction and Division?

5 2 7 5 2 7

Identity PropertiesWhat number can you add to a number to not change its value?

Identity Property of Addition: The sum of any expression and zero is itself:

0a a Identity Property of Multiplication: The product of any

expression and one is itself:

1a a There are no Identity Properties for Subtraction and Division.

What number can you multiply a number by to not change its value?

Inverse PropertiesWhat number can you add to a number to get 0 (the additive identity)?

Additive Inverse Property: The additive inverse of any number “a” is the opposite of “a.” The sum of a number and its additive inverse is 0.

0a a Multiplicative Inverse Property: The multiplicative inverse of

any number “a” is the reciprocal of “a.” The product of a number and its multiplicative inverse is 1.

1 1aa There are no Inverse Properties for Subtraction and Division.

What number can you multiply a number by to get 1 (the multiplicative identity)?

Justifying with Algebraic PropertiesFor the work below, justify each step by naming the property that was used or other valid reasoning.

Statement Reason-5 + 2x + 82x + 8 + (-5)2x + 3 + 5 + (-5)2x + 3 + 02x + 3

GivenCommutative Property of

Addition

8 = 3 + 5Inverse Property of Addition

Identity Property of Addition

Is it Correct?Examine the work below. Is the work valid? If so, justify your conclusion by naming the algebraic properties. If not, explain which statement (or statements) is incorrect.

9 3 5

9 3 5

6 3 3 5

6 0 5

6 5

y

y

y

y

y

The work is invalid. The circled step

incorrectly applied the Associative

Property. There is no Associative

Property of subtraction. Only

addition and multiplication.