Name: _____________________________________________________________________ Date: ___________________
Student Accessible – studentaccessible.com – Maya Khalil
Properties of Addition and Multiplication
1. Commutative property of addition: Switching around the numbers you are
adding does not change the answer (sum) to an addition problem.
Example: 5 + 9 = 9 + 5
14 = 14
2. Commutative property of multiplication: Switching the order of the numbers
you are multiplying does not change the answer (product) to a multiplication
problem.
Example: 1 • 4 = 4 • 1
3. Associative property of addition: When adding three or more numbers, it does
not matter which two numbers you add first. Parentheses are used to show which
numbers are added first.
Example: (8 + 5) + 7 = 8 + (5 + 7)
13 + 7 = 8 + 12
20 = 20
4. Associative property of multiplication: When multiplying three or more
numbers, it does not matter which two numbers you multiply first.
Example: (1 • 4) • 2 = 1• (4 • 2)
40 • 2 = 1: • 8
80 = 80
5. Is subtraction commutative?____ give an example to explain your answer.
______________________________________________________________________
6. Is division commutative?____ give an example_____________________________
7. Ryan says that he uses the distributive property to simplify multiplication
problems. For example, when asked to multiply 4 • 23, Ryan rethinks the problem
as 4 • (20 + 3), then he performs:
4 • 20 + 4 • 3
80 + 12 = 92
Use the distributive property to solve the following problems:
8.
9.
10.
11.
12.
13.
8 • (10 + 5) = __________________________
7(6 + 9) = _____________________________
9(11 – 4) = ____________________________
-11(2 + 10) =___________________________
4(8 + (-5)) = ___________________________
7(x + 8) = _____________________________
Match each of the following equations with the correct property.
14.
15.
16.
17.
18.
19.
20.
21.
22.
(5 + 9) + 11 = 5 + (9 + 11) __
16(10 + 2) = 16 • 1: + 16 • 2 __
123 + 56 = 56 + 123 __
(24 • 9) • 6 = 24 • (9 • 6) __
18 • 7 = 7 • 18 __
xy = yx __
n(m + 7) = nm + 7n __
x + (y + z) = (x + y) + z __
9(5x – 3y) = 45x – 27y __
a. Distributive property
b. Commutative property (addition)
c. Commutative property (multipl.)
d. Associative property (addition)
e. Associative property (multipli.)