Warm Up Place the following numbers in ascending order, then circle the integers. ½, -2, -12/3, ¾, 0.3, 0, 5/5 Hint: Use your calculator to turn the fractions into decimals; this will help you put them in the right order.

The Real Number System Essential Question: How do we use the real number properties to rewrite algebraic expressions?

The Real Number System The rational and irrational numbers together make the real number system There are six real number properties that are true for all of the real numbers

The Real Number Properties Identity Commutative Associative Distributive Additive Inverse Multiplicative Inverse (reciprocal)

Identity There are two kinds of identities Additive: 0 Multiplicative: 1 The identity, keeps a number the same 3 + 0 = 3 (additive identity) 4 x 1 = 4 (multiplicative identity)

Commutative Property The word “commute” means to travel back and forth Works for addition and multiplication Addition: A + B = B + A Multiplication: AB = BA

Practice: Rewrite the following expressions using the commutative property 3 ∙ 5 = -3 + 2x = 3 + x 5 ∙ 3 2x + (-3) = 2x - 3

Associative Property The word “associate” means to group Works for addition and multiplication Addition: (A + B) + C = A + (B + C) Multiplication: A(BC) = (AB)C

Practice: Rewrite the following expressions using the associative property X + (3 + 2y) = 3 ∙ (5 ∙ 12) = 4 + (2x + 2y) = (x + 3) + 2y (3 ∙ 5) ∙ 12 (4 + 2x) + 2y

Practice: Name the Property Used 4 + x = x + 4 3x ∙ 1 = 3x (2 + 1) + 3 = 2 + (1 + 3) Y + 0 = Y

Distributive Property Works across addition and subtraction Addition: A (B + C) = AB + AC Subtraction: A(B – C) = AB - AC

Practice: Rewrite the following expressions using the distributive property