CHAPTER 1 From Arithmetic to Algebra Source: Elementary & Intermediate Algebra, Fourth Edition Prepared and Edited by: Dr. Mohamad Hammoudi
Topics of Chapter 1 1.1: Transition to Algebra. 1.2: Evaluating Algebraic Expressions. 1.3: Adding and Subtracting Algebraic Expressions. 1.4:Sets. 2
1.1: Transition to Algebra Objectives: 1.1.1: Introduce the concept of variables 1.1.2: Identify algebraic expressions 1.1.3: Translate from English to algebra 3
1.1.1: Introduce the Concept of Variables In arithmetic , calculations are performed on numbers using the four basic operations of addition, subtraction, multiplication, and division. The addition is denoted by (+), the subtraction is denoted by (-), and multiplication is denoted by ( × ), and the division is denoted by ( ÷ ). In algebra , the same four basic operations are used. However, calculations are performed on variables . The variables are letters such as x, y, L and W which represent numerical values. The variables represent unknown numerical values . 4
1.1.1: Example of Variables Here we see two rectangles whose lengths and widths are labeled with numbers. If we need to represent the length and width of any rectangle, we can use the variables L for length and W for width . 5
1.1.2: Identify Algebraic Expressions Definition of Expression An expression is is a meaningful collection of numbers, variables, and symbols of operation. Examples: Identify which are expressions and which are not 2m + 3 x + . + 3 y =2x - 1 3a + 5b – 4c 6
Writing Expressions That Indicate Addition Definition of Addition x + y means the sum of x and y , or x plus y. The addition operation is commutative and associative . The order of the added terms and the order in which the operations are performed is not important . It is commutative because 2 + 3 = 3 + 2 = 5 It is associative because (2 + 3) + 4 = 2 + (3 + 4) = 9 Examples: Write using symbols The sum of a and 3. L plus W is written as. 5 more than m. x increased by 7. 7
Writing Expressions That Indicate Subtraction Definition of Subtraction x - y means the difference of x and y , or x minus y. The subtraction operation is neither commutative nor associative . The order of the subtracted terms and the order in which the operations are performed is important . It is not commutative because 5 - 3 ≠ 3 - 5 It is not associative because (3 - 5) - 7 ≠ 3 - (5 - 7) Examples: Write using symbols r minus s.