Copyright © Cengage Learning. All rights reserved. Real Numbers and Their Basic Properties 1

Copyright © Cengage Learning. All rights reserved. Section 1.6 Algebraic Expressions

3 1.Translate an English phrase into an algebraic expression. 2.Evaluate an algebraic expression when given values for its variables. 3.Identify the number of terms in an algebraic expression and identify the numerical coefficient of each term. Objectives

4 Translate an English phrase into an algebraic expression 1.

5 Algebraic Expressions Variables and numbers can be combined with the operations of arithmetic to produce algebraic expressions. For example, if x and y are variables, the algebraic expression x + y represents the sum of x and y, and the algebraic expression x – y represents their difference.

6 Algebraic Expressions There are many other ways to express addition or subtraction with algebraic expressions.

7 Your Turn Let x represent a certain number. Write an expression that represents a. the number that is 5 more than x b. the number 12 decreased by x. Solution: a. The number “5 more than x” is the number found by adding 5 to x. It is represented by x + 5. b. The number “12 decreased by x” is the number found by subtracting x from 12. It is represented by 12 – x.

8 Algebraic Expressions There are several ways to indicate the product of two numbers with algebraic expressions

9 Algebraic Expressions There are also several ways to indicate the quotient of two numbers with algebraic expressions.

10 Evaluate an algebraic expression when given values for its variables 2.

11 Evaluating Algebraic Expression Algebraic Expression: (combination of variables and operators that represents a single value) x + y – 10 2x + 4 Evaluating an Algebraic Expression (replacing variables with numeric values, resulting in a single value) Let x = 3; y = 4. x + y – 10 = – 10 = -4 Let x = 5. 2x + 4 = 2(5) + 4 = 14

12 Your Turn If x = 8 and y = 10, evaluate: a. x + y b. y – x c. 3xy d.

13 Your Turn We substitute 8 for x and 10 for y in each expression and simplify. a. x + y = = 18 b. y – x = 10 – 8 = 2 c. 3xy = (3)(8)(10) = (24)(10) = 240 Do the multiplications from left to right.

14 Your Turn d. Comment When substituting a number for a variable in an expression, it is a good idea to write the number within parentheses. This will avoid mistaking 5(8) for 58. Simplify the numerator and the denominator separately. Simplify the fraction. cont’d

15 Identify the number of terms in an algebraic expression and identify the numerical coefficient of each term 3.

16 Terms and Coefficients in Algebraic Expression Given: 7x + (⅓)y – xyz Terms: Combination of variables and constants which are added in an expressions e.g., 7x, (⅓)y, and –xyz are terms Factors of a term: Constants and variables which are multiplied in a term e.g., in 1 st term, 7 and x; in 2 nd term, ⅓ and y in 3 rd term, -x, y, and z Coefficient of a term: Constant factor e.g., in 1 st term, 7; in 2 nd term, ⅓; in 3 rd term, -1

17 Example d. The expression 3x 2 – 2x has two terms. The coefficient of the first term is 3. Since 3x 2 – 2x can be written as 3x 2 + (–2x), the coefficient of the second term is –2. cont’d