Post on 08-Mar-2018
transcript
1
1‐2: PROPERTIES OF REAL NUMBERS
Mr. GalloAlgebra 2
Real Number Review
2
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 dof $15.50 to a local charity, which subset of real numbers best describes the amount of money raised?
3
Graphing Real Numbers
What is the graph of the numbers : 5 , 2,2.62
2 640‐2‐4‐6
Ordering Real Numbers
How do compare?
17 &3.8
4
Properties of Real Numbers
Properties of Real NumbersProperties of Real Numbers
Let a, b and c represent real numbers
Property Addition Multiplication
Closure
Commutative
Associative
Identity
Inverse
Distributive
5
Examples: Which property does the equation illustrate?
A.
B.
C.
2 31
3 2
3 4 5 4 3 5
3 2 3 3 2g h g g h g
1
1-3: Algebraic ExpressionsMr. GalloAlgebra2
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?
2
Modeling a SituationYou 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?
3
Writing and Evaluating an ExpressionTicket 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
◦
◦
◦
4
Properties for Simplifying Algebraic ExpressionsLet 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?
5
1-4: Solving Equations
Mr. GalloAlgebra 2
Review of Properties
Properties of EqualityAssume a, b and c represent real numbers.
Property Definition Example
Reflexive
Symmetric
Transitive
Substitution
6
Review of Properties cont.
Properties of EqualityAssume 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)
7
Example 2: Solve the following equation
2 1 16y 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 . What is t in terms of A? 1000 1 0.05A t
1
M R . G A L L O
A L G E B R A 2
1-5: Solving Inequalities
Equations
What is an inequality?
What is the solution to an inequality?
How do I know when to use an inequality?
2
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
4x
4x
4x
4x
2 640‐2‐4‐6
2 640‐2‐4‐6
2 640‐2‐4‐6
2 640‐2‐4‐6
3
Review of Properties
Properties of InequalitiesAssume a, b, c and d represent real numbers.
Property Definition Example
Transitive
Addition
Subtraction
Review of Properties cont.
Properties of InequalitiesAssume a, b, c and d represent real numbers.
Property Definition Example
Multiplication
Division
4
Solving & Graphing Inequalities
1)
2)
3)
4)
5)
Example 1: Solve and graph the following inequality
4 7 20x
2
2 9 5 3x
‐8
5
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
6
9 5 4x x 3 3 3 2x x
Compound Inequalities
7
Solving an “and” Inequality
What is the solution of and ? Graph the solution.32
a 3 5 8a
2 640‐2‐4‐6
Solving an “or” Inequality
What is the solution of or ? Graph the solution.
5 2 21m 4 1 21m
0 42-2‐4‐6‐8
1
Mr. GalloAlgebra 2
0 5-5
What is the Absolute Value of a real number?◦
Characteristics:◦
◦
2
2 640‐2‐4‐6
What is the solution of Graph the solution
What is the solution of:2 5 9x
13 6 2 5
3x
3
What are the solutions for ? 5x
2 640‐2‐4‐6
2-1
4 3 5x
4 3 5x
‐2 10
4
2 640‐2‐4‐6
What are the solutions for ? 5x
2 6 10x
2 6 10x
0 42-2‐4‐6‐8
5
Solutions of Absolute Values
Symbols Definition Graph
x a
x ax a
x ax a