Applying Properties of Real Numbers Sec. 1.2 Sol: A.11, A.12, A.1

Rational VS. Irrational numbers Rational Numbers Can be written as quotients (fractions) of integers. Ex: Can be written as decimals that terminate or repeat. Ex: 0.75 or Irrational Numbers Cannot be written as quotients of integers. Cannot be written as decimals that terminate or repeat. Ex:

Real number line Real number lines are graphed as points on a line and increase from left to right. Ex: Graph the real numbers on a number line. (work on Board) Try This: Graph the numbers

Venn DiagramKey: R- Real numbers I – Irrational numbers W – Whole numbers Q- rational numbers Z – integers N – Natural numbers Q I Z Z W N

Natural Numbers: { 1, 2, 3, 4, 5,…} Whole Numbers: {0, 1, 2, 3, 4, 5,…} Integers: {…, -3, -2, -1, 0, 1, 2, 3, …}

Properties of addition and multiplication. Let a,b, and c be real numbers Property Closure Commuitative Associative Addition a + b is a real number a + b = b + a (a +b) + c = a + (b + c) Multiplication ab is a real number ab = ba (ab)c = a(bc)

Properties of addition and multiplication. Let a,b, and c be real numbers Property Identity Inverse Addition a + 0 = a, 0 + a = a “No changing the Value” a + (-a) = 0 Multiplication a(1) = a, (1) a = a a(1/a)=1, a≠0 Distributive property: a(b+c) = ab + ac “Give it away”

Ex: Identify the property used 1.5 +(9 + 12)=(5 + 9) (1) = 250 Try These: 1. (2 × 3)× 9=2 ×(3 × 9) = (5 + 25) = 4(5) + 4(25) 4.1(500) = 500

Defining Subtraction and Division Subtraction: Adding the opposite (Additive inverse ex: b→ - b) Ex: a – b = a + (-b) Division: Multiplying by the reciprical. (Multiplicative inverse)

Ex: Use properties and definition of Properties to show that (10÷c)c=10 where c ≠0 (10÷c)c = = = 10 Given Def. of division Assoc. prop. Of mult. Inverse prop. Of Mult. Identity prop. Of Mult.

Try these: 1.b(4 ÷ b)=0 2.3x + (6 + 4x) = 7x + 6