Transcript Commutative Properties

•We will write equivalent expressions using the
properties
Vocabulary:
 Equivalent Expression:
Expressions that have equal values for the same
replacement values of their variables
Commutative Properties
Multiplication
Addition
Rule: a  b  b  a Rule:
Ex:
2  3  3 2
Ex:
a b  ba
2 3  3 2
To commute means to move
 The news talks about the
daily commute on the
freeway.
 Think about how the
cars move this will help
you to remember
commutative property is
when the numbers
move!
Write an equivalent expression
using the commutative prop
1. 7 + 11  11  7
2. 3 +x  x  3
3. 5y  y  5
It can help you to do more simple
calculations
For Example:
180  64  20 
200
264
Mental Math
1
 9  16 
2
8
72
Identity Properties
Addition
Rule: a + 0 = a
Multiplication
Rule: a 1  a
Ex: 7 + 0 = 7
Ex: 7 1  7
Identity is who you are
 Same with numbers. We
want to be able to do an
operation (such as +0 or
mult by 1) and get the
same thing back, its
identity
(Using the Identity Property of Multiplication)
2
Write an equivalent expression for by
3
5
multiplyin g by "1". Use for 1.
5
2 5 10
 
3 5 15
Do you
reduce
this???
Answer is: NO!!!!
 Usually we reduce everything!
 We reduce when the directions say to:
1. Simplify
2. Evaluate
3. Solve
4. Calculate (add, sub, mult, divide)
 When the directions say to write an equivalent
expression we do not reduce
x
Write an equivalent expression for by
2
y
multiplyin g by "1". Use for 1.
y
x y xy
 
2 y 2y
The Associative Property
Of Addition
(Parenthesis) around different pairs of
numbers
Rule: (a + b) + c = a + (b + c)
Ex: (5 + 2) + 3 = 5 + (2 + 3)
The Associative Property
Of Multiplication
(Parenthesis) around different pairs of
numbers
Rule: (a • b) • c = a • (b • c)
Ex: (2 • 3) • 5 = 2 • (3 • 5)
Associative: To associate
(
+
+(
)+
+
)
Use the Commutative and
Associative Property to write three
equivalent expressions
( a  b)  2
Commutative
Associative
(b+a) +2
a+ (b+2)
2+ (a+b)
Assignment:
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