Algebra 2 Chapter 1.2 Properties of Real Numbers Target Goals: 1.Use the properties of real numbers to evaluate expressions

Real Number System SetLetter/ Symbol DefinitionExamples Natural (aka: counting) NBasic counting numbers{1, 2, 3, …} WholesWNaturals + 0{0, 1, 2, 3, …} IntegersZPositive and negative whole numbers {…, -3, -2, -1, 0, 1, 2, 3, …} RationalsQFractions of two integers Decimal form is repeating or terminating ½, -¾, 0.125, 1/3 = 0.333… IrrationalsIDecimal form doesn’t terminate and doesn’t repeat π,π,

Name the set(s) of numbers to which each number belongs. Ex )-185Z, Q, R Ex )Z, Q, R Ex )I, R Ex )Q, R

Properties of Real Numbers For any real numbers a, b, and c, the following are true: PropertyAdditionMultiplication Commutativea + b = b + a a * b = b * a Associative (a + b) + c = a + (b + c) (ab)c = a(bc) Identitya + 0 = a = 0 + a a * 1 = a = 1 * a Inversea + (-a) = 0 = -a + a Closurea + b is a real number a * b is a real number Distributivea (b + c) = ab + ac and (b + c) a = ba + bc

Name the property illustrated by each of the following: Ex 1)2(x + 3) = 2x + 6 Distributive Property Ex 2)(-8 + 8) + 15 = Additive Inverse

Find the additive inverse and multiplicative inverse for each of the following: Ex 3)-7 A.I. = M.I. = Ex 4)1.25 A.I. =M.I. = Ex 5)-2 ½ A.I. = M.I. =

Ex 6) Application Jimmy went to a post office and bought eight 42¢ stamps and eight 27¢ postcard stamps. What was the total amount of money Jimmy spent on stamps?

Ex 7)Application: Kayla makes $8 per hour working at a grocery store. The number of hours Kayla worked each day in one week are 3, 2.5, 2, 1, and 4. How much money did Kayla earn this week?

Simplify each of the following: Ex 8)3(4x – 2y) – 2(3x + y) Ex 9)4(3a – b) + 2(b + 3a)

Target Goals 1.Use the properties of real numbers to evaluate expressions