The document discusses three properties of addition: 1) The associative property - The grouping of addends does not change the sum 2) The commutative property - The order of addends does not change the sum 3) The identity property - Adding 0 to a number does not change the number It provides examples of applying each property to demonstrate that the sum is unchanged regardless of grouping or order of addends.

1. 2-1 Addition Properties
Math Notes
Algebra and Functions 1.2

2. Three Properties

3. Three Properties
Associative Property

4. Three Properties
Associative Property
Commutative Property

5. Three Properties
Associative Property
Commutative Property
Identity Property

6. Associative Property

7. Associative Property
The way in which addends are grouped does
not change the sum.

8. Associative Property
The way in which addends are grouped does
not change the sum.
When you see ( ) parentheses, do the
work within the ( ) first.

9. Associative Property
The way in which addends are grouped does
not change the sum.
When you see ( ) parentheses, do the
work within the ( ) first.
(2 + 3) + 4 =

10. Associative Property
The way in which addends are grouped does
not change the sum.
When you see ( ) parentheses, do the
work within the ( ) first.
(2 + 3) + 4 = 5+4=

11. Associative Property
The way in which addends are grouped does
not change the sum.
When you see ( ) parentheses, do the
work within the ( ) first.
(2 + 3) + 4 = 5+4= 9

12. Associative Property
The way in which addends are grouped does
not change the sum.
When you see ( ) parentheses, do the
work within the ( ) first.
(2 + 3) + 4 = 5+4= 9
2 + (3 + 4) =

13. Associative Property
The way in which addends are grouped does
not change the sum.
When you see ( ) parentheses, do the
work within the ( ) first.
(2 + 3) + 4 = 5+4= 9
2 + (3 + 4) = 2+7=

14. Associative Property
The way in which addends are grouped does
not change the sum.
When you see ( ) parentheses, do the
work within the ( ) first.
(2 + 3) + 4 = 5+4= 9
2 + (3 + 4) = 2+7= 9

15. Commutative Property

16. Commutative Property
The order in which numbers are added does
not change the sum.

17. Commutative Property
The order in which numbers are added does
not change the sum.
18 + 9 =

18. Commutative Property
The order in which numbers are added does
not change the sum.
18 + 9 = 27

19. Commutative Property
The order in which numbers are added does
not change the sum.
9 + 18= 27

20. Commutative Property
The order in which numbers are added does
not change the sum.
9 + 18= 27
2 + 3=

21. Commutative Property
The order in which numbers are added does
not change the sum.
9 + 18= 27
2 + 3= 5

22. Commutative Property
The order in which numbers are added does
not change the sum.
9 + 18= 27
3 + 2= 5

23. Identity Property

24. Identity Property
When 0 is added to any number, the sum is
that number.

25. Identity Property
When 0 is added to any number, the sum is
that number.
18 + 0 = 18

26. Identity Property
When 0 is added to any number, the sum is
that number.
18 + 0 = 18
n+0=n

27. Name the property used.

28. Name the property used.
76 + 0 = 76

29. Name the property used.
76 + 0 = 76
76 + 17 = 17 + 76

30. Name the property used.
76 + 0 = 76
76 + 17 = 17 + 76
(6 + 4) + 8 = 6 + (4 + 8)

31. Name the property used.
Identity Property
See the zero?
76 + 0 = 76
76 + 17 = 17 + 76
(6 + 4) + 8 = 6 + (4 + 8)

32. Name the property used.
Identity Property
See the zero?
76 + 0 = 76 Commutative
See the numbers
76 + 17 = 17 + 76 switched?
(6 + 4) + 8 = 6 + (4 + 8)

33. Name the property used.
Identity Property
See the zero?
76 + 0 = 76 Commutative
See the numbers
76 + 17 = 17 + 76 switched?
(6 + 4) + 8 = 6 + (4 + 8)
Associative Property
6 + 4 is added first and 4 + 8 was added first
Sum did not change.