Knowing the properties of addition can help you evaluate, or find the value of numerical and algebraic expressions.

Commutative Property

The order in which numbers are added does not affect their sum.

3 + 8 = 8 + 3

The Commutative Property allows you to add two or more numbers in any order.

You can also use the Commutative Property with algebraic expressions. For any addends a and b ,

a + b = b + a

Associative Property

The way in which numbers are grouped does not affect their sum.

(2 + 6) + 4 = 2 + (6 + 4)

The Associative Property allows you to group three or more numbers in any way to add them.

You can also use the Associative Property with algebraic expressions. For any addends a, b , and c ,

(a + b) + c = a + (b + c)

Identity Property

The sum of any number and zero is that number.

5 + 0 = 5

You can also use the Identity Property with algebraic expressions. For any addend a ,

a + 0 = a

Evaluate. Identify the property or properties that you used.

1.) 16.42 + 0

2.) 8.4 + (3.5 + 5.7) = (8.4 + 3.5) + 5.7

3.) r + 0

4.) b + 38.4 = 38.4 + b

5.) 0.25 + (0.53 + 0.14) = (0.25 + 0.53) + 0.14

6.) m + (3m + 9.3) = (m + 3m) + 9.3

7.) (14 + 35) + 68 = 68 + (14+35)

8.) 97.2 + 0

9.) 38 + (14 + 34) = (38 + 14) + 34

10.) 14 + (14 + 8.3) = (14 + 8.3) + 14

Fill in the blanks with >, <, or = to make each statement true.

11.) 87 + c + 16 _____ 105 + c

12.) 15 + (5 + 3) + 0 ______ 23

13.) 13.7 + (7 + 10) ______ (13.7 + 7) + 10

14.) 125 + 32 ______ 124 + 35

1.) Identity Property

2.) Associative Property

3.)  Identity Property

4.) Commutative Property

5.) Associative Property

6.) Associative Property

7.) Commutative Property

8.) Identity Property

9.) Associative Property

10.)  Commutative Property

11.) 87+ c + 16 __<__ 105 + c

12.) 15+ (5 + 3) + 0 __=__ 23

13.) 13.7+ (7 + 10) __=__ (13.7 + 7) + 10

14.) 125+ 32 __<__ 124 + 35