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Intermediate Algebra by Gustafson and Frisk

Intermediate Algebra by Gustafson and Frisk. Chapter 1 A Review of Basic Algebra. Section 1.1: The Real Number System. SETS: collections of objects. Integers Positive Numbers Negative Numbers Even Numbers Odd Numbers. Natural Numbers Whole Numbers Rational Numbers Irrational Numbers

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Intermediate Algebra by Gustafson and Frisk

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  1. Intermediate Algebraby Gustafson and Frisk Chapter 1 A Review of Basic Algebra

  2. Section 1.1: The Real Number System SETS: collections of objects. Integers Positive Numbers Negative Numbers Even Numbers Odd Numbers • Natural Numbers • Whole Numbers • Rational Numbers • Irrational Numbers • Real Numbers • Use { } {x | x > 5}is read “the set of all x such that x is greater than 5”

  3. Section 1.1: The Real Number System GRAPHS: plot on the number line. Individual numbers are dots -3 -2 -1 0 1 2 3 4

  4. Section 1.1: The Real Number System GRAPHS: plot on the number line. Intervals including end points [ [ ] -3 -3 -2 -2 -1 -1 0 0 1 1 2 2 3 3 4 4

  5. Section 1.1: The Real Number System GRAPHS: plot on the number line. Intervals not including end points ( ( ) -3 -3 -2 -2 -1 -1 0 0 1 1 2 2 3 3 4 4

  6. Section 1.2: Arithmetic & Properties of Real Numbers OPERATIONS: • Addition • Subtraction (the same as adding a number with the opposite sign) • Multiplication • Division (the same as multiplying by the reciprocal)

  7. Section 1.2: Arithmetic & Properties of Real Numbers ADDITION: • Addends that have the same signs • Add absolute values • Keep the sign of the addends • Addends that have opposite signs • Subtract absolute values • Keep the sign of the addend with the largest absolute value

  8. Section 1.2: Arithmetic & Properties of Real Numbers MULTIPLICATION: • Multiply absolute values • If the factors have the same signs, the product is positive • If the factors have opposite signs, the product is negative

  9. Section 1.2: Arithmetic & Properties of Real Numbers STATISTICS: measures of central tendency • Mean • Median • Mode

  10. Section 1.2: Arithmetic & Properties of Real Numbers Properties: • Associative – addition, multiplication • Commutative – addition, multiplication • Distributive – multiplication is distributed over additiona (b + c) = ab + ac

  11. Section 1.2: Arithmetic & Properties of Real Numbers Identities: • Addition – zero • Multiplication – one Inverses: • Addition – opposites • Multiplication – reciprocals

  12. Section 1.3: Definition of Exponents EXPONENTS: repeated multiplication • In the expression: ana is the base and n is the exponent • Exponents are NOT factors • Means to multiply “a” n times

  13. Section 1.3: Definition of Exponents ORDER OF OPERATIONS: If an algebraic expression has more than one operation, the following order applies: Clear up any grouping. Evaluate exponents. Do multiplication and division from left to right. Do addition and subtraction from left to right.

  14. Section 1.5: Solving Equations Algebraic Expression vs. Equation • Expressions: a combination of numbers and operations • Equation: a statement that two expressions are equal

  15. Section 1.5: Solving Equations EXPRESSIONS: • Terms • Like terms • When multiplying, the terms do not need to be alike • Can only add like terms!

  16. Section 1.5: Solving Equations TO SOLVE AN EQUATION IN ONE VARIABLE: • If you see fractions, multiply both sides by the LCD. This will eliminate the fractions. • Simplify the algebraic expressions on each side of the equal sign (eliminate parentheses and combine like terms). • Use the addition property of equality to isolate the variable terms from the constant termson opposite sides of the equal sign. • Use the multiplication property to make the coefficient of the variable equal to one. • Check your results by evaluating.

  17. Section 1.5: Solving Equations TYPES OF EQUATIONS: • CONDITIONAL: if x equals this, then y equals that. • IDENTITY: always true no matter what numbers you use. • CONTRADICTION: never true no matter what numbers you use. • FORMULAS: conditional equations that model a relationship between the variables.

  18. Section 1.6 & 1.7: Solving Problems, Applications TYPES OF PROBLEMS: • Geometry • Percent • Physics (forces) • Uniform motion • Mixtures • Good ‘ole common sense analysis

  19. Chapter 1: Basic Algebra Review SUMMARY: • KNOW YOUR VOCABULARY! You can’t follow directions if you don’t know what the words in the instructions mean. • Memorize the processes and the properties. • I will provide formulas for your reference. • Ask questions if you are unsure. • Always check your work to make sure that you answered the question, and that your answer is reasonable.

  20. This powerpoint was kindly donated to www.worldofteaching.com http://www.worldofteaching.com Is home to well over a thousand powerpoints submitted by teachers. This a free site. Please visit and I hope it will help in your teaching

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