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Properties
A property is
something that is
true for all
situations.
Why Should you Learn about the
Properties of Multiplication?
It helps you solve problems
without working them out.
It helps with mental math.
It makes understanding
math easier.
Four Properties
1. Distributive
2. Commutative
3. Associative
4. Identity properties of one and zero
5. Zero Property
Commutative
Property
We
commute
when we
go back
and forth
from school
to home.
Algebra terms commute
when they trade places
xy
y x
Commutative Property
of addition and multiplication
Changing the order of the numbers in addition
or multiplication will not change the result.
 Commutative Property of Addition states:
a+b=b+a
For Example: 2 + 3 = 3 + 2
 Commutative Property of Multiplication
states: ab = ba
For Example: 4 • 5 = 5 • 4
Commutative
Property
Brainpop
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.
(
)
In algebra:
( 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
Associative Property:
( x  y)  z  x  ( y  z )
The variables do not change
their order.
Associative Property of
multiplication and Addition
Changing the grouping of the numbers in
addition or multiplication will not change the
result.
Associative Property or Multiplication  (a · b) · c = a · (b · c)
Example: (6 · 4) · 3 = 6 · (4 · 3)
Associative Property of Addition  (a + b) + c = a + (b + c)
Example: (6 + 4) + 3 = 6 + (4 + 3)
We have already used the
distributive property.
Sometimes I ask
for help in distributing
papers.
The distributive property only
has one form.
Not one for
.
.
.and
one
for
addition
multiplication
. . .because both operations are
used in one property.
Distributive Property
Multiplication distributes over addition.
a b  c   ab  ac
32  5   3  2  3  5
Zero Property
When any number is multiplied
with zero, the answer is zero.
98,756,432 X 0 = 0
The
identity
property
makes
me
think
about
my
identity.
The identity property for addition
asks,
“What can I add to myself
to get myself back again?
0x
x_
Identity Properties
Additive Identity Property: If you add 0 to
any number, the number stays the same.
a + 0 = a or 5 + 0 = 5
Multiplicative Identify Property: If you
multiply any number times 1, the number
stays the same.
ax1=a
or 5 x 1 = 5
Let’s play “Name that property!”
State the property or
properties that justify the
following.
3Commutative
+2=2
+
3
Property
State the property or
properties that justify the
following.
3(x – 10) = 3x
Distributive Property
– 30
State the property or
properties that justify the
following.
3
+
(4
+
5)
=
(3
Associative Property
+ 4) + 5
5.
6•4=4•6
Commutative Property
of Multiplication
State the property or
properties that justify the
following.
(5 + 2) + 9 = (2
Commutative Property
+ 5) + 9
2.
3+7=7+3
Commutative
Property of Addition
1.
(2 + 1) + 4 = 2 + (1 + 4)
Associative Property
of Addition
9.
3(2 + 5) = 3•2 + 3•5
Distributive Property
Test Yourself
Rewrite each equation with the correct answer, and
write the name of the property.
1. 9 X 3 = 3 X w
2. 3 X (4 X 2 ) = (n X 4) X 2
3. 56 X p = 11 X 56
Test Yourself Answers
1. 9 X 3 = 3 X 9 Commutative
2. 3 X (4 X 2) = (3 X 4) X 2 Associative
3. 56 X 11 = 11 X 56 Commutative
4. 4 X 8 = 8 X 4 Commutative
5. 5 X (7 X 2) = (5 X 7) X 2 Associative
6.
10.
11.
7.
12.
13.
14.
4 XX8)
509
(4X X
+ (4 X 9) Distributive
(2
X 5=
=2
(8 500)
X 5) Associative
195
5 = (200
5)300)
– (5 X+
5)(6
Distributive
6 XX310
= (6X X
X 10) Distributive
5 X 9 = 9 X 5 Commutative
5 X 205 = (5 X 200) + (5 X 5) Distributive
4 X (1 X 7) = (4 X 1) X 7 Associative