Transcript Properties of Real Numbers

Properties
of Real Numbers
(Section 2.6)
6 Properties:
• Commutative Property
• Associative Property
• Distributive Property
• Identity
• Inverse
• Zero
Commutative
Property
We
commute
when we
go back
and forth
from work
to home.
Algebra terms commute
when they trade places
xy
y x
This is a statement of
1) commutative property
for addition:
x y  y x
This is the statement for
2) Communtative of
Multiplication:
xy  yx
To associate with
someone means that
we like to be with
them.
The tiger and the panther
are associating with each
other.
They are leaving the
lion out.
(
)
( x  y)  z
The panther has decided to
befriend the lion.
The tiger is left out.
(
)
In algebra:
x  (y  z )
This is a statement of the
3) Associative Property of
Addition:
( x  y)  z  x  ( y  z )
This is the statement for
4) Associative Property
of multiplication:
( xy)z  x( yz )
Sometimes executives ask
for help in distributing
papers.
We add here:
4(2x+3)
We multiply
here:
This is an example
of
5) Distributive
4(2x+3) =8x+12
4
2x
+3
8x
12
The Identity
Property makes
me think about
my identity.
1) Identity property for addition
asks, “What can I add to myself
to get myself back again?
0x
x_
0x
x_
The above is the identity property
for addition.
0
is the identity element
for addition.
7) Identity property for
Multiplication
asks, “What can I multiply to myself
to get myself back again?
1 x
x(_)
1 x
x(_)
The above is the identity property
for multiplication.
1
is the identity element
for multiplication.
8) Additive property of Inverse
asks, “What do you add to a number to
get zero?”
X + (-X)= 0
9) Multiplicative property for Inverse
is, a number which when multiplied by
X yields 1.
-The reciprocal
X + 1/X = 1
10) Multiplicative Property of Zero
The product of any number and zero is
zero.
a x 0= 0