Review of Basic Algebra Contemporary Business Mathematics with Canadian Applications Ninth Edition S. A. Hummelbrunner/K. Suzanne Coombs PowerPoint: D. Johnston, Revised by P. Au Chapter 2 Review of Basic Algebra Copyright © 2012 Pearson Canada Inc.

Objectives After completing chapter two, the student will be able to: Simplify algebraic expressions. Evaluate expressions with positive, negative, and exponent zero. Use a calculator to evaluate expressions with fractional exponents. Write exponential expressions in logarithmic form. (continued) Copyright © 2012 Pearson Canada Inc.

Objectives (continued) Use a calculator to determine the value of natural logarithms. Solve algebraic equations using addition, subtraction, multiplication, division and formula rearrangement. Solve word problems by creating equations. Copyright © 2012 Pearson Canada Inc.

Formula Simplification You can combine like terms. 3x + 2x + 7x = 12x 6x - 4y -2 x +8y = 4x + 4y 7xy - 3xy - xy = 3xy 4c - 5d -3c +4d = c - d 3x2 + 2.5x2 = 5.5x2 Copyright © 2012 Pearson Canada Inc.

Formula Simplification If brackets are preceded by a + sign, do not change the sign of the terms inside the brackets. (7a - 2b) + (4a -5b) = 11a -7b If brackets are preceded by a - sign, change the sign of each term inside the brackets. (4c - 5d) - (2c -3d) = 2c -2d Copyright © 2012 Pearson Canada Inc.

Copyright © 2012 Pearson Canada Inc. Formula Evaluation Copyright © 2012 Pearson Canada Inc.

Copyright © 2012 Pearson Canada Inc. Exponents Power an Base a Exponent n The factor a is multiplied by itself n times. POWER = BASE TO THE EXPONENT Copyright © 2012 Pearson Canada Inc.

Copyright © 2012 Pearson Canada Inc. Using Exponents 63 = 6 x 6 x 6 (-2)4 = (-2)(-2)(-2)(-2) (1+i)5 = (1+i)(1+i)(1+i)(1+i)(1+i) (1/4)2 = (.25)(.25) Copyright © 2012 Pearson Canada Inc.

Operations with Powers Copyright © 2012 Pearson Canada Inc.

Negative and Zero Exponents a -n = 1/an 2 -4 = 1/24 = 1/16 (1+i) -3 = 1/(1+i)3 (1.05)0 = 1 (-4) -2 = 1/(-4)2 = 1/16 (¾) -3 = 1/(¾)3 = 2.37 Copyright © 2012 Pearson Canada Inc.

Copyright © 2012 Pearson Canada Inc. Fractional Exponents Copyright © 2012 Pearson Canada Inc.

Copyright © 2012 Pearson Canada Inc. Fractional Exponents Copyright © 2012 Pearson Canada Inc.

Examples of Fractional Exponents Copyright © 2012 Pearson Canada Inc.

Exponents and Logarithms Copyright © 2012 Pearson Canada Inc.

Properties of Logarithms Copyright © 2012 Pearson Canada Inc.

Copyright © 2012 Pearson Canada Inc. Equations An equation is an expression of equality between two algebraic expressions. 3x = 36 2x + 4 = 60 5x - .4 = 2.5 Copyright © 2012 Pearson Canada Inc.

Solving Equations Using Addition X - 3 = 9 Add 3 to both sides. X - 3 + 3 = 9 + 3 X = 12 Copyright © 2012 Pearson Canada Inc.

Solving Equations Using Subtraction X + 3 = 8 Subtract 3 from both sides. X + 3 - 3 = 8 - 3 X = 5 Copyright © 2012 Pearson Canada Inc.

Solving Equations Using Multiplication Copyright © 2012 Pearson Canada Inc.

Solving Equations Using Division Copyright © 2012 Pearson Canada Inc.

Using Two or More Operations to Solve an Equation Copyright © 2012 Pearson Canada Inc.

Copyright © 2012 Pearson Canada Inc. Solving Word Problems Step 1 - Describe in words the unknown X. Step 2 - Translate information in the word problem in terms of the unknown X. Step 3 - Set up an algebraic equation matching the expression from step #2 to a specific number. Step 4 - Solve equation, state conclusion, and check result . Copyright © 2012 Pearson Canada Inc.

Copyright © 2012 Pearson Canada Inc. Solving a Word Problem Copyright © 2012 Pearson Canada Inc.

Copyright © 2012 Pearson Canada Inc. Summary Copyright © 2012 Pearson Canada Inc.