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

Copyright Scott Storla 2014

Properties


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.



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.


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.


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


1 1 4 3

1 1 4 3

The associative property of multiplication.


4 5 6

6 4 5

y y

y y


The commutative property of addition.

3 5 2 1

2 1 3 5

x x

x x


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.



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)


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


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.


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


2 2

0


The additive inverse.

31

8

3

8

The multiplicative identity.

1 2

2

x

x

The multiplicative inverse.


15 2

5

1 2

x

x


2

2

6 7

6 0 7

x x

x x


The additive inverse. (4x + –4x + 7)

The additive identity.

0 0

1 0 0



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



____________________________________

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


___________________________________

____________________________________

(4 7) 4

4 (7 4 )

4 ( 4 7)

(4 4 ) 7

0 7

7

y y

y y

y y

y y


The associative property of addition

____________________________________

____________________________________

The commutative property of addition

The associative property of addition

____________________________________The additive inverse

The additive identity


____________________________________

____________________________________

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



____________________________________

____________________________________

The distributive property

Added

___________________________________

____________________________________


Wrote adding an opposite as subtraction

Wrote subtraction as adding an opposite


____________________________________

____________________________________

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


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


Properties

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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