1. Properties of Real Numbers
Mr. Halling and Mrs. King
Algebra
FDR High School

2. Do Now
Identify which of the following are equations and which are expressions.
1) 2x – 9y + 5
2) 2x + 12 = 16
3) 19y = 38x + 10

3. The Commutative Property
What does it mean to commute?

4. The Commutative Property
If a and b are both real numbers:
a + b = b + a
a x b = b x a
Some examples:
2 + 5 = 7 and = 7 so = 5 + 2
2 x 5 = and 5 x 2 = 10 so x 5 = 5 x 2
In simple terms: Order doesn’t matter when adding or multiplying

5. The Associative Property
With whom do you associate?

6. The Associative Property
If a, b, and c are all real numbers:
(a + b) + c = a + (b + c)
(a x b) x c = a x (b x c)
Example: (2 x 5) x 3 = 2 x (5 x 3)
10 x 3 = 2 x 15  30 = 30
In other words, even when we have three numbers, order still doesn’t matter

7. The Distributive Property
What does it mean to distribute?

8. The Distributive Property
If a, b, and c are real numbers:
a(b + c) = ab + ac
a(b – c) = ab – ac
Examples: 2(3 + 4) = (2 x 3) + (2 x 4) = 14
2(4 – 3) = (2 x 4) – (2 x 3) = 2
In simple terms: Sharing is caring!

9. What is the inverse of something?
Inverse Properties
What is the inverse of something?

10. Inverse Properties If a is a real number: a + (-a) = 0 a x (1/a) = 1
Examples: 8 + (-8) = 0
10 x (1/10) = 1
In simple terms: Opposites attract!

11. What is a person’s identity?
Identity Properties
What is a person’s identity?

12. Identity Properties If a is a real number: a + 0 = a a x 1 = a
Examples: = 89
18 x 1 = 18
In simple terms: Adding 0 and Multiplying by Don’t Change Anything!!

13. Exit Ticket 6(x + 3) = 6x + 18 22 + (3 + 4) = (22 + 3) + 4
Rip a piece of paper in half and share it with your partner. On your half of the paper, indicate what properties are illustrate below:
6(x + 3) = 6x + 18
22 + (3 + 4) = (22 + 3) + 4