6th Grade Math Textbook, Progress

8

Operations IV

Properties of Addition and Multiplication

The following properties of addition and multiplication

are true for any numbers a, b,and c.

Commutative Property of Addition

Changing the orderof the addends

does not change the sum.

a
bb
a

5 
 9  9 
 5

14  14

Commutative Property of Multiplication

Changing the orderof the factors

does not change the product.

abba

3  8  8  3

24  24

Think

“order”

Associative Property of Addition

Changing the groupingof the addends

does not change the sum.

(a
b)
ca
(b
c)

( 1 
 4 )
 7  1 
( 4 
 7 )

5 
 7  1 
 11

12  12

Associative Property of Multiplication

Changing the groupingof the factors

does not change the product.

(ab)ca(bc)

( 6  5 ) 2  6 ( 5  2 )

30  2  6  10

60  60

Think

“grouping”

Identity Property of Addition

The sum of zero and a number

is that number.

a
 0 a 0 
aa

89 
 0  89 0 
 89  89

Zero Property of Multiplication

The product of zero and a number is zero.

0 a 0 a 0  0

0  33  033  0  0

Identity Property of Multiplication

The product of one and a number

is that number.

1 aaa 1 a

1  8  88  1  8

Think

“same”

Think

“0 product”

Name the property of addition or multiplication used.

1. 18
   53  53
   18 2. (7
   8)
   2  7
   (8
   2) 3. 90
   0  90


2. 11  12  12  11 5. 2 (308)(230) 8 6. 1  25  25

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