1. 08/29/2017 15+(-26)= 45-(-15)= -102+(-154)= -53+91=
Agenda
Ticket in the Door
Ticket in the Door
Review Ticket in the door
Current Lesson: Cornell Notes Applying Properties of rational Numbers
Ticket out the Door
15+(-26)=
45-(-15)=
-102+(-154)=
-53+91=
Format your paper for Cornell Notes

2. Two Kinds of Real Numbers
Rational Numbers
Irrational Numbers

3. What are Rational Numbers Review

4. Rational Numbers
A rational number is a real number that can be written as a ratio of two integers.
A rational number written in decimal form is terminating or repeating.
EXAMPLES OF RATIONAL NUMBERS 16
1/2
3.56 -8
1.3333…
-3/4

5. Properties
A property is something that is true for all situations.

6. Four Properties Distributive Commutative Associative
Identity properties of one and zero

7. We
commute
when we
go back
and forth
from work
to home.

8. Algebra terms commute
when they trade places

9. This is a statement of the
commutative property
for addition:

10. It also works for
multiplication:

11. Commutative Property of addition and multiplication
Order doesn’t matter
A x B = B x A
A + B = B + A

13. To associate with someone
means that we like to
be with them.

14. ( ) The tiger and the panther are associating with each other.
They are leaving the
lion out.
( )

15. In algebra:

16. The panther has decided to
befriend the lion.
The tiger is left out.
( )

17. In algebra:

18. This is a statement of the Associative Property:
The variables do not change
their order.

19. Associative Property of multiplication and Addition
Associative Property  (a · b) · c = a · (b · c)
Example: (6 · 4) · 3 = 6 · (4 · 3)
Associative Property  (a + b) + c = a + (b + c)
Example: (6 + 4) + 3 = 6 + (4 + 3)

20. The Associative Property also works for multiplication:

21. Distributive Property
A(B + C) = AB + AC
4(3 + 5) = 4x3 + 4x5

22. . . .and one for Not one for addition The distributive property only
has one form.
Not one for
addition
. . .and one for
multiplication
. . .because both operations are
used in one property.

23. 4(2x+3) =8x +12 This is an example of the distributive property. 2x +3

24. Here is the distributive property using variables:
y z x xy xz

25. The
identity
property
makes me
think
about my
identity.

26. The identity property for addition asks, “What can I add to myself
to get myself back again?

27. The above is the identity property
for addition.
is the identity element
for addition.

28. The identity property for multiplication asks,
“What can I multiply to myself
to get myself back again?

29. The above is the identity property
for multiplication.
is the identity element
for multiplication.

30. Identity Properties
If you add 0 to any number, the number stays the same.
A + 0 = A or = 5
If you multiply any number times 1, the number stays the same.
A x 1 = A or 5 x 1 = 5

31. Example 1: Identifying Properties of Addition and Multiplication
Name the property that is illustrated in each equation.
A. (–4)  9 = 9  (–4) B.
(–4)  9 = 9  (–4)
The order of the numbers changed.
Commutative Property of Multiplication
The factors are grouped differently.
Associative Property of Addition

32. Example 2: Using the Commutative and Associate Properties
Simplify each expression. Justify each step.
Commutative Property of Addition =
Associative Property of Addition
= (29 + 1) + 37 =
Add.
= 67

33. Exit Slip! Name the property that is illustrated in each equation.
1. (–3 + 1) + 2 = –3 + (1 + 2)
2. 6  y  7 = 6 ● 7 ● y
Simplify the expression. Justify each step. 3.
Write each product using the Distributive Property. Then simplify
4. 4(98)
5. 7(32)
Associative Property of Add.
Commutative Property of Multiplication 22
392
224