1. Properties of Real Numbers
Pre-Algebra
Mrs. Yow

2. “Rules of the Road”

3. “Rules of the Math Road”
Identity Property of
Addition and Multiplication
Commutative Property of Addition and Multiplication
Associative Property of
Addition and Multiplication
Distributive Property of
Multiplication over
Addition or Subtraction
Zero Property of Multiplication
aka Multiplicative Prop. Of zero
Inverse Operations of
Addition and Subtraction
Inverse Operations of
Multiplication and Division

4. Commutative Property Notice there is no “N” in the word!
Root word is COMMUTE – definition - regular travel between one’s place of work and one’s home.
This indicates movement – just like in our commutative property!

5. Commutative Property a • b = b • a ab = ba
The order of addition and multiplication can reverse and the value will not change.
Examples: a + b = b + a
a • b = b • a
ab = ba
Write two concrete examples with answer on your notes page (Use actual numbers in your example)

6. Associative Property
Root Word: Associate – definition – to connect or to join together with – as in GROUP
Just like in our Associative Property!
The Regrouping Property

7. Associative Property a • (b • c) = (a • b) • c or a(bc) = (ab)c
Associative property – Numbers that are being added or multiplied can be regrouped and the value will not change.
Examples: a + (b + c) = (a + b) + c or
a • (b • c) = (a • b) • c or
a(bc) = (ab)c

8. Identity Property
Root Word: Identity: definition – the state or face of remaining the same
Sound familiar?

9. Identity Property
Identity property – The number 0 can be added to any other number and the value will not change. The number 1 can be multiplied by any other number, and the value will not change. An operation is performed on a number which results in identically the same number. The number 1 is referred to as the identity element for multiplication. The number 0 is referred to as the identity element for addition.
Examples: a + 0 = a
a • 1 = a

10. Distributive Property
Root Word: Distribute: Definition: - to dispense
Like when I “distribute” BlowPops……everybody gets one…..
Let’s look at the Distributive Property……

11. Distributive Property
Distributive property – A number written outside of the parentheses is multiplied by everything inside of the parentheses. The operation in the parentheses must be addition or subtraction. The outside operation must always be multiplication.
Examples: a(b + c) = ab + ac or
ab + ac = a(b + c)

12. Zero Property of Multiplication
JUST WHAT IT SOUNDS LIKE…….
YOU HAVE KNOWN THIS ONE SINCE 1ST GRADE!!
Zero property of multiplication – any number, variable, or expression that is multiplied by zero is equal to zero.
Examples: 0(3x + 2y) = 0,
(3 • 0)(2 + 4) = 0 • 6 = 0

13. Zero Property of Multiplication
AKA
Multiplicative Property of Zero
Fun word to say but hard word to spell

14. Inverse Operation of Add/Sub
Do we really need to talk about this one any more?
Inverse operations of addition/subtraction – The application of the inverse property of addition or subtraction results in the number that is the identity element for addition. The identity element for addition is the number 0. The two numbers are additive inverses or opposites.
Examples: 2 – 2 = 0, -3x + 3x = 0

15. Inverse Operations of Mult/Div
This one either??
Inverse operations of multiplication/division – The application of the inverse property of multiplication or division results in the number that is the identity element for multiplication. The identity element for multiplication is the number 1. The two numbers are multiplicative inverses or reciprocals.
Examples: 2 • = 1, x • = 1, = 1