Copyright Scott Storla 2014
Properties
Copyright Scott Storla 2014
A property allows us to use a general idea in specific situations.
For instance a property of fire is that it needs oxygen to burn.
We use this property when we blow on a struggling campfire or extinguish a frying pan fire with a cover.
Numbers and operations have properties too.
Copyright Scott Storla 2014
Copyright Scott Storla 2014
Property – The Commutative Property of Addition
English: The order of the terms doesn’t affect the sum.
Example: 3 4 4 3
Note: Subtraction is not commutative.
The Commutative properties are about order.
Property – The Commutative Property of Multiplication
English: The order of the factors doesn’t affect the product.
Example: 3 4 4 3
Note: Division is not commutative.
Copyright Scott Storla 2014
Property – The Associative Property of Addition
English: The grouping of the terms doesn’t affect the sum.
Example: 3 4 5 3 4 5
Note: Subtraction is not associative.
The Associative properties are about grouping.
Property – The Associative Property of Multiplication
English: The grouping of the factors doesn’t affect the product.
Example: 3 4 5 3 4 5
Note: Division is not associative.
Copyright Scott Storla 2014
2 3 2
2 2 3
Describe which property is being used to transform the upper expression to the lower expression. Don’t simplify the expression.
The commutative property of addition.
2 2 3
2 2 3
The associative property of addition.
8
8
t
t
The commutative property of multiplication.
4 1 3 1
1 1 4 3
The commutative property of multiplication.
1 1 4 3
1 1 4 3
The associative property of multiplication.
Copyright Scott Storla 2014
4 5 6
6 4 5
y y
y y
Describe which property is being used to transform the upper expression to the lower expression. Don’t simplify the expression.
The commutative property of addition.
3 5 2 1
2 1 3 5
x x
x x
The commutative property of multiplication.
2(1) 2( 1) 5( 1)
2(1) 2( 1) 5( 1)
The associative property of addition.
2 3
2 3
k
kThe associative property of multiplication.
Copyright Scott Storla 2014
Copyright Scott Storla 2014
The Distributive property of multiplication over addition
Property – The Distributive Property of Multiplication over Addition
English: A sum of terms, each with a common factor, can be rewritten as the product of the common factor and the sum of the remaining factors.
Example: 3(2) 3(5) 3(2 5) and 3(2) 3(5) (2 5)3
Property – The Distributive Property of Multiplication over Addition
English: A product which has a sum as one factor can be rewritten as the sum of products of the common factor and each original term.
Example: 3(2 5) 3(2) 3(5)
Copyright Scott Storla 2014
3 5
Use the distributive property to add or subtract like terms.
3 1 5 1
3 5 1
8 1
7 1 4 1
7 4 ( 1)
11( 1)
1 1 14 5 2
3 3 3
14 5 2
3
11
3
4 5 2y y y
4 5 2 y
y
1 y
5 2 12 2
7 2
7 2
2 2 21 9 3x x x
2( 1 9 3) x
211x
5 12 2
811
7 4
1
3
Copyright Scott Storla 2014
Property – The Additive Identity
English: 0 is the additive identity. Adding a term of 0 to an expression doesn’t change the value of the expression.
Example: 3 0 is equivalent to 3
The Identity properties
Property – The Multiplicative Identity
English: 1 is the multiplicative identity. Multiplying an expression by 1 doesn’t change the value of the expression.
Example: 1( )x is equivalent to x.
Copyright Scott Storla 2014
Property – The Additive Inverse
English: The expression which when added to the original gives a sum of 0.
Example: The additive inverse of 8 is 8 . The additive
inverse of 2x is 2x .
The Inverse properties
Property – The Multiplicative Inverse
English: The expression which when multiplied to the original expression gives a product of 1.
Example: The multiplicative inverse of 2 is 1/2.
The multiplicative inverse of y is 1
y . 0y
Copyright Scott Storla 2014
2 2
0
Describe which property is being used to transform the upper expression to the lower expression. Don’t simplify the expression.
The additive inverse.
31
8
3
8
The multiplicative identity.
1 2
2
x
x
The multiplicative inverse.
The multiplicative identity.
15 2
5
1 2
x
x
Copyright Scott Storla 2014
2
2
6 7
6 0 7
x x
x x
Describe which property is being used to transform the upper expression to the lower expression. Don’t simplify the expression.
The additive inverse. (4x + –4x + 7)
The additive identity.
0 0
1 0 0
The multiplicative identity.
The additive inverse.
The additive identity.
4 4 7
0 7
x x
0 7
7
1 0 0
1 1 1 0
2
2
6 0 7
6 9 9 7
x x
x x
The additive inverse.
Copyright Scott Storla 2014
____________________________________
Fill in the property which allows each step.
The associative property of multiplication
____________________________________
____________________________________
The multiplicative inverse
The multiplicative identity
2 1
1 2
2 1
1 2
1
x
x
x
x
Copyright Scott Storla 2014
___________________________________
____________________________________
(4 7) 4
4 (7 4 )
4 ( 4 7)
(4 4 ) 7
0 7
7
y y
y y
y y
y y
Fill in the property which allows each step.
The associative property of addition
____________________________________
____________________________________
The commutative property of addition
The associative property of addition
____________________________________The additive inverse
The additive identity
Copyright Scott Storla 2014
____________________________________
____________________________________
15 14 12 2
15 14 12 2
15 12 14 2
15 12 14 2
27 12
12 27
12 27
k j k j
k j k j
k k j j
k j
k j
j k
j k
Fill in the property which allows each step.
The commutative property of addition
____________________________________
____________________________________
The distributive property
Added
___________________________________
____________________________________
The commutative property of addition
Wrote adding an opposite as subtraction
Wrote subtraction as adding an opposite
Copyright Scott Storla 2014
____________________________________
____________________________________
2 5 11
2 5 5 11 5
2 5 5 16
2 0 16
2 16
1 12 16
2 2
12 8
2
1 8
8
x
x
x
x
x
x
x
x
x
Fill in the property which allows each step.
Additive property of equality
____________________________________
Added on the right side
Additive inverse
____________________________________
____________________________________
Additive identity
Multiplicative property of equality
____________________________________The associative property of multiplication
____________________________________The multiplicative inverse
____________________________________The multiplicative identity
Copyright Scott Storla 2014
Properties