2.  Grades will be posted this evening at the v6math site.
Class time will not be spent answering grade questions.
 After you get your report card, if you have questions or
think there may be an error, I will discuss that with you
outside of class time.
 Grades are earned (good & bad), not given. Your grade is
a reflection of your effort and desire everyday, not just
test days. Grades are not a reflection of your intellect or
ability. (Lose the excuse)
 Notebooks graded on: Organization, Completeness, and
Neatness.
 Stop worrying about your grade; learn the material and
take care of your business (be responsible), your grade
will take care of itself.

4. Number Properties

5. Properties
Properties are the rules of the
game.
If these rules are changed, the
way we solve problems would
be totally different and make
no sense.

7. Commutative Property
Commutative Property of
Addition.
a+b=b+a
7+8=8+7
(-3)+ 4 = 4 + (-3)
The commutative property of
addition says what?
Order doesn’t matter.

8. Commutative Property
Commutative Property of
Multiplication
a•b=b•a
7•8=8•7
(-3)•4•5= 4 • 5 •(-3)
The commutative property of
multiplication says what?
Order doesn’t matter.

9. Associative Properties

10. Associative Property
Associative Property of Addition
(a + b) + c = a + (b + c)
(7 + 8) + 2 = 7+(8 + 2)
15 + 2 = 7 + 10
The associative property of
addition says what?
 That Grouping doesn’t
matter

11. Associative Property
Associative Property of
Multiplication.
 (a x b) x c = a x (b x c)
 (7 x 8) x 2 = 8 x (7 x 2)
 56 x 2 = 8 x 14
The associative property of
Multiplication says…
That Grouping doesn’t matter.

12. Identity Properties

13. Identity Properties
An identity for a particular
operation doesn’t change the
identity of the number when
the operation is done.
a + 0= a
7 + 0 =7
The Additive Identity is…
0
Zero plus a number is that
number.

14. Identity Properties
Multiplicative Identity
Multiplicative Identity is…
1
One times a number is that
number.

15. Inverse Properties

16. Inverse Properties
Additive Inverse - Opposite
Another number that added to the
original number is equal to the
additive identity, which is….
0
-3 + 3
5 + (-5)

17. Identify the Properties
Multiplicative Inverse:
The Reciprocal
Another number that when
multiplied by the original number
is equal to the Multiplicative
Identity, which is 1
½ •2 = 1 3 •?? = 1
-1/4 •?? = 1
If xy = 1, then x = ?

19. Original
Number
1/5
-1
-6/11
45
0
-8
Additive Inverse
Multiplicative
Inverse
Opposite &
Reciprocal

21. • Distributive property
– a(b + c) = ab + ac
– 3(5 + 7) 15 + 21 = 36
– example
– Multiplying a sum by
some number is the same
as multiplying each term
by that same number.