Transcript Commutative Properties

Warm up #2 Ch 1: SIMPLIFY if possible
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2
3
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5
Try These
5y
5
8a
3ab
9 abc
3ab
6 xy
8y
15 y
54
Warm-Up #2 Ch 1: SIMPLIFY if possible
1
2
3
4
5
Answers
5y
y
5
8a 8
3ab 3b
9 abc
3ab 3c
6 xy 3 x
8y
4
15 y 5 y
54 18
•We will write equivalent expression using the
properties
Vocabulary:
 Equivalent Expression:
Expressions that have equal values for the same
replacement values of their variables
Commutative Properties
Multiplication
3 • 8 = 8 • 3
We can change
the order when
multiplying
without
affecting the
product.
Addition
7 + 3 = 3 + 7
We can change
the order when
adding without
affecting the
sum.
Commutative Properties
Subtraction
 7 - 3 = 3 – 7 ??
Commutative
Property does
NOT apply to
subtraction.
Division
 3 ÷ 8 = 8 ÷ 3 ??
Commutative
Property does
NOT apply to
division.
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!
Commutative
Property
Addition
Multiplication
+
=
+
Write an equivalent expression
using the commutative prop
1. 7 + 11
2. 3 +x
3. 5y
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
Multiplication
Addition
9 • 1 = 9
 7+0=7

When
any
 When zero is
number
is
added to any
multiplied by 1,
number, the sum the product is
is the same
the same
number.
number.
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
(Parenthesis) around different pairs of
numbers
(a + b) + c = a + (b + c)
(5 + 2) + 3 = 5 + (2 + 3)
The Associative Property
(Parenthesis) around different pairs of
numbers
(a • b) • c = a • (b • c)
(2 • 3) • 5 = 2 • (3 • 5)
Associative: To associate
(
+
+(
)+
+
)
http://youtu.be/iSuteidOkD4
Assignment:
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