1. 3.3 Properties of Rational Numbers
Objective: 6.EE.3,6.EE.4 Apply the properties of operations to make equivalent expressions. Identify when two expressions are equivalent.

2. The Commutative Property
You can add and multiply real numbers in any order.
Examples:
2 + 7 = 7 + 2
3 ● 9 = 9 ● 3
Algebraically:
a + b = b + a
ab = ba

3. The Commutative Property
Commute: to move to an from
Think of commuting to and from school. Just like you moving from one place to the other, numbers can too!

4. State whether each situation below is commutative
or not commutative.
1) Waking up in the morning and going to school.
not commutative
2) Brushing your teeth and combing your hair.
commutative
3) Putting on your socks and putting on your
shoes.
not commutative
4) Eating cereal and drinking orange juice.
commutative

5. The Associative Property
You can regroup real numbers when you add and multiply.
Examples:
(6 + 8) + 2 = 6 + (8 + 2)
(7 ● 4) ● 5 = 7 ● (4 ● 5)
Algebraically:
(a + b) + c = a + (b + c)
(ab)c = a(bc)

6. The Associative Property
Associate: to keep company, as a friend
Think of associating with your friends: you hang out with them and stick together. Numbers in parentheses are grouped, or friends!

7. Commutative vs. Associative
Identify each property shown below.
1) = 4 + 7
Comm. Prop. Of Add. 2)
Assoc. Prop. Of Mult. 3)
Comm. Prop. Of Mult.
4) (4 + 2) + 3 = (2 + 4) + 3
Comm. Prop. Of Add.

8. Comm. Prop. of Add. Comm. Prop. of Mult. Assoc. Prop. of Add.
Identify the property shown below.
1) (2 + 10) + 3 = (10 + 2) + 3
Comm. Prop. of Add. 2)
Comm. Prop. of Mult.
3) (6 + 8) + 9 = 6 + (8 + 9)
Assoc. Prop. of Add. 4)
Assoc. Prop. of Mult.

9. Operations that are NOT Commutative or Associative
Subtraction
Division