Properties of Real Numbers Mr. Halling and Mrs. King Algebra FDR High School
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
The Commutative Property What does it mean to commute?
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 5 + 2 = 7 so 2 + 5 = 5 + 2 2 x 5 = 10 and 5 x 2 = 10 so 2 x 5 = 5 x 2 In simple terms: Order doesn’t matter when adding or multiplying
The Associative Property With whom do you associate?
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
The Distributive Property What does it mean to distribute?
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!
What is the inverse of something? Inverse Properties What is the inverse of something?
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!
What is a person’s identity? Identity Properties What is a person’s identity?
Identity Properties If a is a real number: a + 0 = a a x 1 = a Examples: 89 + 0 = 89 18 x 1 = 18 In simple terms: Adding 0 and Multiplying by 1 Don’t Change Anything!!
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