Section 1-1 Day 1 – Real number Sets

Whole Numbers Integers Rational Numbers Real Numbers Irrational Numbers 0, 1, 2, 3,......, -3, -2, -1, 0, 1, 2, 3,... Whole numbers with their Opposites Any number that can be written as a fraction, terminating, or repeating decimal ½ /2 Cannot be written as a fraction, terminating, or repeating decimal.

Example 1 Name the set(s) to which each number belongs. a) 1 Whole Integer Rational Real Rational Real irrational Whole Integer Rational Real HW: 1-5

Example 2 Graph the real numbers - √5 and 7/2. Use a calculator to approximate the values: -√5 =7/2 = Graph using a number line: HW: 6-10

Example 3 Order the following from least to greatest. Use a calculator to approximate the values: √3 =-2/3 =-5/4 = ,1, 2 HW: 11, 12

Homework Section 1-1 Day 1 Real Number Sets worksheet

Section 1-1 Day 2 – Algebraic Properties

Properties of Addition and Multiplication PropertyAdditionMultiplication Commutativea + b = b + aab = ba Associative (a + b) + c = a + (b + c) (ab)c = a(bc) Identitya + 0 = aa 1 = a Inversea + (-a) = 0a 1 = 1 a Distributive a(b + c) = ab + ac

Definitions Subtraction: Adding the opposite (Additive Inverse) Division: Multiplying by the reciprocal (Multiplicative Inverse)

Example 1 Identify the property that the statement illustrates: a) 5 + (9 + 12) = (5 + 9) + 12 Associative property of addition Identity property of multiplication b) = 250 HW: 11-16

Example 2 Use properties and definitions of operations to show that the statement is true. Justify each step Given Definition of Division Commutative Prop of Multiplication Associative Prop of Multiplication Multiplication HW: 18-22E

Example 3 Tell whether the statement is always, sometimes, or never true for real numbers a, b, and c. Explain your answer. Substitute numbers in for a, b, c a = 1, b = 2, c = 3 HW: 50,51,54 It doesn’t work Always, BUT can we make it work?

Homework Section 1-1 Day 2 Pages , even, 50, 51, 54

Section 1-1 Day 3 – Units and Measurement

Vocabulary Unit: a standard of measurement, ie feet, inches, days, or seconds Unit Analysis: used to check that calculations make sense. Conversions: changing from one unit of measurement to another

Example 1 Use unit analysis with operations: a) You work 8 hours and earn $60. What is your earning rate? $60 = 8 hrs 18 gal $2.65 = gal $7.50 per hour b) You buy 18 gallons of gas at $2.65 per gallon. What is your total cost? $47.70 HW: 26-30e

Example 2 Perform the indicated conversion a) 350 feet to yards b) 2.2 kilograms to grams HW: 32-38e

Example 3 Convert the rate into the given units 20 mi/h to feet per second HW: 42,44,48

Homework Section 1-1 Day 3 Pages even, 48

Example 3 - Continued c) You drive 90 kilometers per hour. What is your speed in meters per second? 90 km 1 hr 1 min 1000 m = 1 hr 60 min 60 sec 1 km 25 m/sec