Elementary Algebra

1
Elementary Algebra

• A review of concepts and computational skills
• Chapters 1-2

2
Real Numbers

• Natural 1, 2, 3,4.
• Whole 0, 1, 2, 3, 4..
• Integers-- -2, -1, 0 1, 2.
• Rational can be written as p/q ½, -3, 4.3
• Irrational cannot be written as p/q
  non-repeating, non-terminating decimals

3
The Real Number Line

• Ordering numbers
• Graphing numbers on a number line
• Interval Notation ( ), , (
• Unbounded intervals

4
Absolute Values

• Think of absolute value as distance from zero on
  the number line
• a a if a gt 0 and a -a if a lt 0

5
Fractions

• Equivalent fractions
• Finding common denominators
• Adding, subtracting fractions- first find a
  common denominator
• Multiplying, dividing
• Adding mixed numbers
• Decimals and percents

6
Adding and Subtracting Reals

• In general, adding means moving right on the
  number line, subtracting means moving left
• Adding a negative numbersame as subtracting
• Adding 2 positive numbers
• Adding 2 negative numbers
• Adding a positive and a negative

7
Multiplying and Dividing Reals

• Multiply or divide 2 positive numbers
• Multiply or divide 2 negative numbers
• Multiply or divide 1 positive, 1 negative number
• Divide by zero

8
Exponential Expressions

• An exponent tells you to multiply repeatedly
• a3a x a x a
• Exponent also called power

9
Order of Operations

• Please Excuse My Dear Aunt Sally
• P- parentheses grouping
• E- Exponents
• M- Multiply
• D- Divide
• A- Add
• S- Subtract

10
Algebraic Expressions and Equations

• Expressions can evaluate or simplify only!
• Equations can solve for an unknown or variable
• Language Sum, Difference, Product, Quotient

11
Properties of Equalities

• Commutative
• Associative
• Distributive
• Additive Inverse
• Multiplicative Inverse

12
More Properties of Equality

• Addition/Subtraction
• Multiplication/Division
• Using these properties to solve linear equations
  one step and multi step

13
Strategies for Solving Equations

• Use distributive property to get rid of
  parentheses
• Simplify both sides of equation
• Use addition/subtraction to get like terms on
  opposite sides
• Use multiplication/division to isolate variable
• Check your solution in original equation

14
More equations

• Equations involving fractions
• Equations involving decimals
• Identitiesinfinitely many solutions
• Conditional Equations- finite solutions
• Inconsistent Equations- no real solutions

15
Formulas

• Just like solving linear equations for a
  particular variable given values for others
• Distance
• Temperature conversions
• Interest
• Geometric formulas

16
Translating Verbal Expressions into Algebraic
Expressions

• Addition Sum, add to, more than, increased by
• Subtraction less than, difference, decreased by
• Multiplication Product, twice, triple, half,
  percent
• Division ratio, quotient, half

17
Inequalities

• altb means a lies to the left of b on the number
  line
• agtb means a lies to the right of b on the number
  line
• Solution will be a set rather than 1 value
• Graphing solution sets on the number line
• Solve inequalities like equations express answer
  as a set of numbers