Properties of Addition
Properties of Addition
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
Guided Practice (Ask your tutor for help.)
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
Answer Key
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