Transcript Properties

Today’s Objective: To understand and
use properties to write and solve
expressions and equations.
Why is it important? Using properties
makes it easier to work complicated
problems.
Properties
A property is something that is true for all
situations.
Four Properties
1. Distributive
2. Commutative
3. Associative
4. Identity properties of one and zero
Look at this problem:
2(4 + 3)
Through your knowledge of order of operations, you know what to do
first to evaluate this expression.
2(7)
14
Now, look what happens when I do something different with the
problem.
*
*
2(4 + 3) = 8 + 6 = 14
No difference.
This is an example of the
distributive property.
Now why would one ever use the distributive property to solve 2(4 + 3)?
The answer is generally,
“You wouldn’t! Just use the order of operations.”
One place this is going to become very important is when we have an
expression in the parenthesis which can not be simplified, like:
2(4 + x)
You need to be able to recognize and use the distributive property
throughout all of Algebra.
This is one property you need to know by name, forwards, and
backwards!
EX1β
EXAMPLE: Use the distributive property to find each product.
a. 7 * 98
b. 8(6.5)
First break down
(decompose) the number
98:
How can we decompose
6.5? Hint: How do we read
the decimal?
Then distribute.
Then distribute.
Finally, add.
Finally, add.
7(90 + 8)
630 + 56
686
8(6 + 0.5)
48 + 4
52
The distributive property can make large calculations easier for using mental math.
Distributive Property
A(B + C) = AB + AC
4(3 + 5) = 4(3) + 4(5)
Commutative Property
of addition and multiplication
Order doesn’t matter
AxB=BxA
A+B=B+A
Associative Property of
multiplication and Addition
Associative Property of 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)
Identity Properties
If you add 0 to any number, the number stays
the same.
A + 0 = A or 5 + 0 = 5
If you multiply any number times 1, the
number stays the same.
A x 1 = A or 5 x 1 = 5