Commutative and Associative Properties Commutative Property Think of

Commutative and Associative Properties

Commutative Property • Think of it as the “commute” ative property. • Let’s say it is 7 miles from your house to school. • When you return home, it will still be 7 miles. • Regardless of the direction you are going, the distance is the same. • This is true for addition and multiplication. • Changing the order, or direction, does not affect the sum (addition) or the product (multiplication).

Examples: • 5 + 7 = 12 • 5 x 7 = 35 • 7– 5=2 • 7 ÷ 5 = 7/5 7 + 5 = 12 7 x 5 = 35 5 – 7 = -2 5 ÷ 7 = 5/7 • As you can see the commutative property is only true for addition and multiplication. • It is false for subtraction and division.

Associative Property • Think about the people you are grouped with, or associate with. • Parenthesis are very important in this property. • They are used for grouping. • Being that parenthesis are first in the order of operations, they indicate what you should do first.

Examples: (3 + 5) + 7 = 3 + (5 + 7) 8 + 7 = 3 + 12 15 = 15 • Here, the 3 is hanging out with the 5. • Then it changes and 5 is hanging out with the 7. (4 x 5) x 6 = 4 x (5 x 6) 20 x 6 = 4 x 30 120 = 120 • Here the 4 and 5 are hanging out. • Then 5 and 6 are hanging out.

More Examples: (10 – 7) – 4 = 10 – (7 – 4) (8 ÷ 4) ÷ 2 = 8 ÷ (4 ÷ 2) 3 – 4 = 10 – 3 2÷ 2=8÷ 2 -1 = 7 1=4

Notice how the associative property only works for addition and multiplication.