Properties

6.19

• Identify properties for addition

and multiplication

• Multiplicative property of zero

• Inverse property for multiplication

COMMUTATIVE PROPERTY

Commutative Property

a + b = b + a

(a)(b) = (b)(a)

Order doesn’t matter

Commutative Property

Order doesn’t matter

2 + 3 = 3 + 214 + 5 = 5 + 14

2(4) = 4(2)2 x 27 = 27 x 2

Does the Commutative Property work with Subtraction?

5 – 3 – 1

2 – 1

1

3 – 1 – 5

2 – 5

- 3

≠

Does the Commutative Property work with Division?

4 ÷ 2 ÷ 2 2 ÷ 2 1

2 ÷ 2 ÷ 4 1 ÷ 4 1/4

≠

Check for understanding….

Name the property:

a. 5 + 6 + 7 = 6 + 5 +

7

Commutative

Property of Addition

Name the property:

b. 3(2)(5) = 5(3)(2)

Commutative

Property of

Multiplication

ASSOCIATIVE PROPERTY

Try:(1 + 3) + 14 4 + 14 18

Now Try:1 + (3 + 14)1 + 17 18

=

When you are multiplying, change the grouping. See what happens. You will get the same answer.

Try:

(2 x 3) x 4 6 x 4 24

Now Try:

2 x( 3 x 4)2 x 1224

=

Does the Associative Property work with Subtraction?

(14 – 3) – 2 11 - 2 9

14 – (3 – 2)14 - 1 13≠

Does the Associative Property work with Division?

≠

Check for understanding…..3 + (5 + 19) = (3+ 5) + 19

Associative Property of Addition

(2 x 4) x 16 = 2 x (4 x 16)

Associative Property of Multiplication

10 + 11 + 12 = 11 + 10 + 12

Commutative Property of Addition

20 x 14 x 8 = 14 x 8 x 20

Commutative Property of

Multiplication

ADDITIVE IDENTITY PROPERTY

5 + 0 = 5

4 + 0 = 4

30 + 0 = 30

0.5 + 0 =

____0.5

If you add zero to any

number,the number

keeps its identity –

It stays the same!

MULTIPLICATIVE IDENTITY PROPERTY

15 x 1 = 15

34 x 1 = 34

9 x 1 = 9

101 x 1 =

101

If you

multiply a

number by 1,

the number

keeps its

identity --- It

stays the

SAME!

Check for understanding….

What integer

is the

multiplicative

identity?

1

What integer is

the additive

identity?

0

MULTIPLICATIVE INVERSE PROPERTY

Zero does NOT have a multiplicative inverse

because you can NEVER have zero in the denominator of a

fraction!

Do all real numbers have a multiplicative inverse?

NO, Zero does NOT have a multiplicative inverse because you can NEVER have zero in the denominator of a fraction!

MULTIPLICATIVE PROPERTY OF ZERO

The product of any

number and zero is

zero!

a x 0 = 0

5 x 0 = 0