Transcript Properties I

Properties of Operations
Properties of Operations
This lesson gives a “mathematical property”
name to the things you already know how to
do.
Our objective? Classify mathematical properties
as they are used to show equivalent
expressions.
We are naming things you already do!
Vocabulary
Commutative Property: Order does not change the
value of an addition or multiplication expression.
Associative Property: Grouping does not change the
value of an addition or multiplication expression.
Identity Properties: Multiplying by 1 or adding 0 does
not change the value of a number.
Identity Property of Addition n + o = n
Identity Property of Multiplication n(1) = n
Zero Property of Multiplication: Any number
multiplied by 0 is 0.
Examples: These charts are in your notes. Study them!!!
COMMUTATIVE PROPERTY (Ordering)
Words
Numbers
You can add numbers
in any order
a+ b = b + a
8 + 18 = 18 + 8
You can multiply
numbers in any order
a(b) = b(a)
5(12) = 12(5)
ASSOCIATIVE PROPERTY (Grouping)
Words
When you are only
adding you can
group numbers in
any order
When you are only
multiplying, you
can group numbers
in any order
Numbers
a + (b + c) = (a + b) + c
2 + (8 + 10) = (2 + 8) + 10
a ∙(b ∙c) = (a∙ b) ∙c
2 ∙ (4 ∙ 5) = (2 ∙ 4) ∙ 5
Identity Properties
When a number retains its “identity,” the value
remains the same.
Identity Property of Addition a + 0 = a
24 + 0 = 24 You can add 0 to any number, and
its value stays the same.
******************************************
Identity Property of Multiplication n(1) = n
a x 1 = a 36 x 1 = 36
You can multiply any value by 1 and
its value stays the same.
So . . . . . .
0 can be called the “additive identity.”
1 can be called (I love this one . . . . .)
the “multiplicative identity”
One more….
The Zero Property of Multiplication says . . . .
5x0=0
nx0=0
Any number x 0 = 0
Seeing What Has Changed….
1. 19 + (42 + 8) = ( 19 + 42) + 8
Did the order change?
No, but the grouping is
different.
Associative Property of +
Did the order change?
2. 12 + 8 = 8 + 12
Yes.
Commutative Property of Addition
3. 42 x 8 x 3 = 42 x 8 x 1
x 3
Wait! All the numbers are there, and the = says they have the same value.
Identity Property of Multiplication
????????????????
Seeing What Has Changed….
4. 32 x 85 = 85 x 32
Did the order change?
Yes
Commutative Property of Multiplication
Think about the Identity Properties. Why does
the ID property of addition use a 0, but the ID
property of mult. uses a 1? Why don’t they
use the same number?
More than one may be used!!!!!!!
Independent Practice
a.
5 x (14 x 32) = (5 x 14) x 32
____
Associative Prop. of X
5
b. 5 + 23 + 4 = 23 + 4 + ______
Commutative Prop. of +
c. 25 + 0 + 3 = 25 + 3
d.
Identity Prop. of +
4
(7 + 12) + 4 = (7 + ____)
+ 12
Associative Prop. of + and Commutative Prop. of +
7
e. 5 x 7 x 3 x 8 = 5 x 3 x 8 x ___
Commutative Prop. of x
f.
4
(43 x 1) x 4 = _____
x 43
Commutative Prop. and Identity Prop. of x
4
g. (6 + 3) + 4 = 6 + (3 + ___)
Associative Prop. of +
10 = 8 x (9 x 10)
h. (8 x 9) x _____
Associative Prop. of X
6 =6 x 7
i. 7 x ____
Commutative Prop. of X
j.
48 + 15
15 + 48 = _____
Commutative Property of +
b
k. (a + b) + c = (__+a)
+c
Commutative Property of +
Partner Challenge!
• Name that property:
1.
2.
3.
4.
5.
6.
7.
(Use the letter choices in your notes)
5x1=5 E
6xn=nx6 B
8+0=8 F
(3∙ 2) ∙ 5 = 3 ∙ (2 ∙ 5) D
12 + 4 = 4 + 12 A
2 + (5 + n) = (2 + 5) + n C
(5-5) + 3 = 3 (tricky!) F
8. (3-2) x 5 = 5 E
9.
+
=
+
A
10. (a+b) + c = (b+a) + c (be careful!) A
What Have We Learned?
• There are rules to describe the way you
combine numbers. These rules are called
“properties.”
• Change of Order is described by the
Commutative Properties
• Change of Grouping is described by the
Associative Properties
• Identity Properties leave a value unchanged
Look for properties in all processes!