1. Properties of Real Numbers
Objective: Identify and use properties of real numbers.

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 and 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. Identity Property of Addition
The sum of 0 and any number is the number
Example with numbers: = 4
Algebraic example:
a + 0 = a

9. Identity Property of Multiplication
The product of 1 and any number is the number
Example with numbers: 8 x 1 = 8
Algebraic example:
a x 1 = a

10. The Distributive Property
Multiply the outside value with the quantity in the parentheses.
Examples:
3(4 + 8) = 3(4) + 3(8)
3(12)=
36 = 36
Algebraically:
a(b + c) = ab + ac
a(b – c ) = ab – ac

11. The Distributive Property
Distribute: to spread out, to share
Think of mail. The postal worker must distribute all letters to the houses. One person, many houses: One number to all numbers in the parentheses!

12. The Distributive Property
Use the Distribute Property to rewrite and/or solve.
9(52)
2) 12(98)
3) 7(34)

13. Simplify using the distributive property.1) 4) 2) 5) 3) 6)

14. Simplify using the distributive property.1) 4) 2) 5) 3) 6)

15. Which Property is Represented?
1 + (6 + 7) = (1 + 6) + 7
1 x 10 = 10
3 x 5 = 5 x 3
6 + 0 = 6
4 x (4 x 2) = (4 x 4) x 2
x + y = y + x