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# Lesson03 - THE UNIVERSITY OF AKRON Mathematics and Computer Science Lesson 3 Basic Algebra Part I Directory Table of Contents Begin Lesson 3 mptii

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~ w mptii menu THE UNIVERSITY OF AKRON Mathematics and Computer Science Lesson 3: Basic Algebra, Part I Directory Table of Contents Begin Lesson 3 A n l g e b r a R v i w Iam DP S N Z Q R C a 3 a 4 = a 7 ( ab ) 10 = a 10 b 10 ( ab (3 ab 4))=2 ab 4 ( ab ) 3 ( a 1 + b 1 )=( ab ) 2 ( a + b ) ( a b ) 3 = a 3 3 a 2 b +3 ab 2 b 3 2 x 2 3 x 2=(2 x + 1)( x 2) 1 2 x +13=0 = x = 26 G= { ( x, y ) | y = f ( x ) } f ( x )= mx + b y = sin x T L s o Copyright c ° 1995–2000 D. P. Story Last Revision Date: 2/2/2000

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Lesson 3: Basic Algebra, Part I Table of Contents 3. Basic Algebra, Part I You are manipulating Numbers 3.1. The Basics The Arithmetical Operations Terms vs Factors Paren- theses, Brackets, and Braces How to Negate Correctly How to Invert Correctly 3.2. How to Add/Subtract Algebraic Expressions Adding/Subtracing Grouped Expressions
3. Basic Algebra, Part I Algebra is the language of mathematics, engineering and the sciences. We use algebra to express our thoughts, ideas, and to communicate with others who understand the language of algebra. Algebra is a language in which we can precisely pose ourselves ques- tions; Algebra is a set of tools for answering those questions. You are manipulating Numbers When we manipulate algebraic quantities, we are, in fact, manipu- lating numbers . This point must be ever kept in mind. The rules for manipulating algebraic quantities reﬂect the properties of the number system . This is an important point. Therefore, when you manipulate symbolic quantities in a questionable way, you must ask yourself the question, “Is what I have just done valid when I replace the symbols by numbers?” This should be your guiding principle.

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Section 3: Basic Algebra, Part I A Fundamental Guiding Principle of Algebra : “Is the algebraic manipulation that I just performed valid when I replace the symbols by numbers?” 3.1. The Basics In this section we take a brief survey of the arithmetical operations and some of the properties of these operations that are exploited to perform algebraic manipulations. The Arithmetical Operations Let the letters a , b , and c represent (real) numbers. As you well know we can add, subtract, multiply, and divide these numbers. In algebra, these operations are carried out symbolically : 1. Addition. The sum of a and b is a + b . The number a is called a term of the expression a + b . (Of course, b is a term too.)
Section 3: Basic Algebra, Part I 2. Subtraction. The diference oF a and b is a b . The number a is called a term oF a b . (OF course, b is a term too.) 3. Mulitplication. Product oF a and b is ab or a · b , or sometimes, a × b . The numbers a and b are called factors oF the product ab . 4. Division. The quotient oF a by b is a b ,or a/b , or less Frequently (in algebra), a ÷ b . Division is only de±ned when the denominator b ± = 0. The number a is the numerator , and b is the denominator .

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## This note was uploaded on 09/24/2009 for the course CHEM 333 taught by Professor Baird during the Spring '09 term at UC Davis.

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Lesson03 - THE UNIVERSITY OF AKRON Mathematics and Computer Science Lesson 3 Basic Algebra Part I Directory Table of Contents Begin Lesson 3 mptii

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