1 / 17

Elementary Algebra

Elementary Algebra. A review of concepts and computational skills Chapters 1-2. 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.

edith
Download Presentation

Elementary Algebra

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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 > 0 and |a| = -a if a < 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 number—same 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 • a3=a 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 • Identities—infinitely 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 • a<b means a lies to the left of b on the number line • a>b 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

More Related