Mr. Gallo Algebra 2 1 2: PROPERTIES OF REAL NUMBERS Real Number Review 1
Subsets of the Real Numbers Classifying Variables Example 1: What set of numbers would best describe the number of participants in a race? Example 2: What if each participant made a donation d of $15.50 to a local charity, which subset of real numbers best describes the amount of money raised? 2
Graphing Real Numbers What is the graph of the numbers 5, 2,2.6 : 2 6 4 2 0 2 4 6 Ordering Real Numbers How do 17 & 3.8 compare? 3
Properties of Real Numbers Properties of Real Numbers Properties of Real Numbers Let a, b and c represent real numbers Property Addition Multiplication Closure Commutative Associative Identity Inverse Distributive 4
Examples: Which property does the equation illustrate? A. 2 3 1 3 2 B. 345435 C. 3 g h 2g 3g3h 2g 5
1-3: Algebraic Expressions Mr. Gallo Algebra2 Modeling Words with an Algebraic Expression What algebraic expression models the word phrase seven fewer than a number t? What algebraic expression models the word phrase two times the sum of a and b? 1
Modeling a Situation You are on a bicycle trip. You traveled 52 miles the first day. Since then, your average rate has been 12 miles per hour. What algebraic expression models the distance you traveled so far? Evaluating Algebraic Expressions What is the value of the expression for the given values of the variables? 2
Writing and Evaluating an Expression Ticket prices for admission to a museum are $8 for adults, $5 for children and $6 for seniors. a. What algebraic expression models the total number of dollars collected in ticket sales? b. If 20 adult tickets, 16 children s tickets and 10 senior tickets are sold one morning, how much money is collected in all? Vocabulary 3
Properties for Simplifying Algebraic Expressions Let a, b and c represent real numbers: Definition of Subtraction Definition of Division Distributive Property for Subtraction Multiplication by 0 Multiplication by -1 Opposite of a Sum Opposite of a Difference Opposite of a Product Opposite of an Opposite Simplifying Algebraic Expressions Combine like terms. What is a simpler form of each expression? 4
1-4: Solving Equations Mr. Gallo Algebra 2 Review of Properties Properties of Equality Assume a, b and c represent real numbers. Property Definition Example Reflexive Symmetric Transitive Substitution 5
Review of Properties cont. Properties of Equality Assume a, b and c represent real numbers. Property Definition Example Addition Subtraction Multiplication Division Solving equations with more than one operation (variables on both sides) 1) 2) 3) 4) 5) 6
Example 2: Solve the following equation 2 y1 16 y Ex. 5: If $1000 is in a bank account earning 5% simple interest, the dollar value of the account A in t years is given by A 100010.05t. What is t in terms of A? 7
1-5: Solving Inequalities MR. GALLO ALGEBRA 2 What is an inequality? Equations What is the solution to an inequality? How do I know when to use an inequality? 1
Writing an Inequality from a Sentence 1. The quotient of a number and 3 is no more than 15 2. The product of 7 and a number is more than 50 Writing and Graphing Inequalities Inequality Word Sentence Graph x 4 6 4 2 0 2 4 6 x 4 6 4 2 0 2 4 6 x 4 6 4 2 0 2 4 6 x 4 6 4 2 0 2 4 6 2
Review of Properties Properties of Inequalities Assume a, b, c and d represent real numbers. Property Definition Example Transitive Addition Subtraction Review of Properties cont. Properties of Inequalities Assume a, b, c and d represent real numbers. Property Definition Example Multiplication Division 3
Solving & Graphing Inequalities 1) 2) 3) 4) 5) Example 1: Solve and graph the following inequality 4 x 7 20 2 x 9 53 2 8 4
Using an Inequality Plumber A charges $75 for a service charge and $40 per hour. Plumber B charges $50 per hour but no service charge. How many hours must a plumbing job last for Plumber A to cost less than Plumber B? Example 2: Complete Got It? #3 on p.35 in your book 5
x x 3 3 3 2 9 x5x4 Compound Inequalities 6
Solving an and Inequality a 3 a 5 8 What is the solution of 3 and? Graph the solution. 2 6 4 2 0 2 4 6 Solving an or Inequality 4m 121 What is the solution of 5 2m 21 or? Graph the solution. 8 6 4-2 0 2 4 7
Mr. Gallo Algebra 2 What is the Absolute Value of a real number? Characteristics: -5 0 5 1
What is the solution of Graph the solution 2x 5 9 What is the solution of: 1 3 6 2 5 3 x 6 4 2 0 2 4 6 2
What are the solutions for x 5? 6 4 2 0 2 4 6 4x 3 5 4x 3 5 2-1 0 1 2 3
What are the solutions for x 5? 6 4 2 0 2 4 6 2x 6 10 2x 6 10 8 6 4-2 0 2 4 4
Solutions of Absolute Values Symbols Definition Graph x a x x x x a a a a 5