5-1 Properties of Addition

The rules you have been following for addition are called properties of addition.  The properties are always true when using the operation of addition.

1.  The commutative property of addition

The addends can be arranged and added in any order without changing the sum.

6 + 2 = 8 and 2 + 6 = 8, therefore 6 + 2 = 2 + 6

2.  The associative property of addition

The addends can be grouped in any way without changing the sum.

(3 + 5) + 2 = 10   and   3 + (5 + 2) = 10, so

(3 + 5) + 2 = 3 + (5 + 2)

Fill in the addends below to better understand the commutative and associative properties of addition.

( + 6) + 2 = 9 + (6 + 2)	3 + (9 + 2) = ( 3 + 9) +
(7 + ) + 4 = 7 + (5 + 4)	+ (5 + 6) = (2 + 5) + 6
(1 + 5) + = 1 + (5 + 9)	( + 2) + 9 = 3 + (2 + 9)
(8 + 2) + = 8 + (2 + 4)	+ (4 + 6) = (4 + 4) + 6
(2 + ) + 3 = 2 + (7 + 3)	6 + (4 + ) = (6 + 4) = 9
(2 + 4) + 3 = + (4 + 3)	9 + (3 + 1) =( + 3) + 1
( + 2) + 5 = 7 + (2 + 5)	8 +( + 5) = (8 + 2) + 5
+ (5 + 4) = (7 + 5) + 4	+ (9 + 2) = (6 + 9) + 2
(7 + 3) + = 7 + (3 + 6)	( + 4) + 8 = 5 + (4 + 8)
10 + (2 + 2) = ( + 2) + 2	+ (6 + 5) = (4 + 6) + 5
7 +( + 2) = (7 + 7) + 2	+ (1 + 9) = (6 + 1) + 9
(8 + 9) + 7 = + (9 + 7)	3 + (8 + 3) = ( + 8) + 3
(6 + 4) + 2 = 6 + ( + 2)	+ (9 + 0) = (7 + 9) + 0
1 + ( + 2) = (1 + 1) + 2	+ (9 + 8) = (4 + 9) + 8
2 + ( 8 + 7) = ( 2 + 8) +	3 + (6 + 7) = (3 + 6) +