Transcript Commutative Property of Addition

Algebraic Properties
Learning Goal:
The student will be able to
summarize properties and make
connections between real number
operations.
The Commutative Property
The ORDER in
which you add
or multiply two
numbers does
not affect the
result.
Commutative Property of
Addition
a+b=b+a
3+7=7+3
Commutative Property
of Multiplication
ab = ba
7●3 = 3●7
The Associative Property
When you add or
multiply any three real
numbers, the
GROUPING (or
association) of the
numbers does not
affect the result.
Note: when values “leave”
the parentheses but do NOT
affect the value
Associative Property of Addition
a + (b + c) = (a + b) + c
5 + (6 + 7) = (5 + 6) + 7
Associative Property
of Multiplication
a(bc) = (ab)c
2(3●4)= (2●3)4
The Additive Identity Property
1. If 0 is added to any real
number, the sum is equal to
the given number.
Identity Property of Addition
a+0=a
2. When you multiply any given 6 + 0 = 6
real number by 1, the
Identity Property
of Multiplication
product is equal to the given
number.
a●1=a
Note: Think of a mirror image.
2 ● 1= 2
Distributive Property
• When you distribute something, you
separate it into portions.
• The distributive property states that for any
numbers a, b, and c:
a(b + c) = (ab) + (ac)
a(b – c) = (ab) – (ac)
Example: -4(5 + 3) = (-4 x 5) + (-4 x 3)
-20 + -12 = -32
-(3 – 2) = (-1 x 3) –(-1 x 2)
-3 – (-2) = -1
The Inverse Property
The sum of a number
and its opposite is zero.
Inverse Property of Addition
a + -a = 0
2 + -2 = 0
The product of a
number and it’s
reciprocal is 1.
Inverse Property of Multiplication
a ● 1/a = 1
2●½=1
The Zero Property
Zero Property
When you multiply a
real number by 0, the
resulting product is
zero.
a●0=0
Try this….
1. x + 9 = 9 + x is an example of which property?
Commutative Property for Addition
2. x + ( y + 3 ) = x + ( 3 + y ) is an example of which
property?
Commutative Property for Addition
3. ( 5 y ) • ( 1 ) = 5 y is an example of
which property?
Identity Property for Multiplication
4. -22 + 22 = 0 is an example of which
property?
Inverse Property for Addition
Try this Cont.….
5. 5 • 1 = 5 is an example of which property?
Identity Property for Multiplication
6. ( x y ) z = x ( y z ) is an example of which property?
Associative Property for Multiplication
7. 10 • 0 = 0 is an example of which
property?
Zero Property for Multiplication
8.
property?
is an example of which
Inverse Property for Multiplication
The Closure Property
Closure Property of Addition
the sum of any two real
numbers is also a real
number and there is a
unique (only one)
solution
Closure Property of Multiplication
the product of any two
real numbers is a real
number and there is a
unique (only one)
solution
Example:
Example:
The sum of
any two even
numbers is
always even
If you multiply a whole
number by 2, your product is
always even
More about Closure…
Let's check out this
question. If you divide two
even numbers (from the set
of even numbers), is the
quotient even?
•12 / 6 = 2 Yes, 2 is even.
•24 / 2 = 12 Yes, 12 is even.
•100 / 4 = 25 NO, 25 is not even!
When you find even ONE example that does
not work, the set is not closed under that
operation. The even numbers are not closed
under division.