Properties of Addition and MultiplicationBy Stephanie Lohr

Commutative Property

• Commutative Property of Addition--changing the order in which you add does not change the sum.

5 38 3 5 8

a b b a

9 7 7 9

So, 5 33 5

2.1 6 6 2.1

More Examples:

Commutative Property

• Commutative Property of Multiplication--changing the order in which you multiply numbers doesn’t change the product.

ab ba

122 24 212 24

86 6 87.53 37.5

So, 122 212More Examples:

Associative Property

• Associative Property of Addition--changing the way the numbers are grouped does not change the sum.

(a b) c a (b c)

(31) 6 103 (1 6)10

(2.5 4) 8 2.5 4 8

Add parenthesis to show Associative Property

6 2 9 6 (2 9)

23.5 8 7 23.5 8 7So,(31) 6 3 (1 6)

Associative Property

• Associative Property of Multiplication--changing the way the numbers are grouped does not

change the product.

(ab)c a(bc)

(63)118

6(31)18

So,(63)16(31)

Add parenthesis to showAssociative Property

(792)2379223

5.1635.1(63)

7.3210 7.3210

Identity Property

• Identity Property of Addition--if you add zero to a number, you get the same number!

a 0 a

8 0 8

5 0 5

7.342 0 7.342

0 is called the identity of addition!!

Identity Property

• Identity Property of Multiplication--if you multiply a number by 1, you get the same number!

616 91 9

a1a

2.345612.3456

1 is called the identity of multiplication!!

Zero Property (of Multiplication)

• Any number multiplied by 0 equals 0!

a0 0

90 0

8,823,4270 0

1,000,0000 0

Inverse Property

• Inverse Property of Multiplication--a number multiplied by its reciprocal equals 1.

21

21

1

55 1

3 13

1

Inverse Property

• Additive Inverse Property--a number plus its opposite equals 0.a ( a)0

9 ( 9) 0

9.3 9.3 0

5 ( 5) 0

Distributive Property

• A number outside parenthesis gets multiplied by every number inside parenthesis.

5(4 2)20 1030

4(8 2)10(9 5)(109) (105)

(48) (42)

(54) (52)

Identify the Property

54 453 0 340 0(9 3.2) 5 9 (3.2 5)

9.819.8

Commutative Prop. Of Multiplication

Identity Prop. Of Addition

Zero Property

Associative Prop. Of Addition

Identity Prop. Of Multiplication