CHAPTER 1                            LESSON 1

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EVALUATING SIMPLE EXPRESSIONS

CHAPTER INTRODUCTION

Most students in mathematics have substituted numerical values for letters in a formula to determine a required value. This process is called evaluating a formula.

In the formula A = lw, (Area = length x width) A=10 when l = 5 and w = 2.

However, when I = 4 and w = 3, A is equal to 12. The value of the expression lw depends upon the values of the variables / and w. In general, the value of any algebraic expression depends upon the values of the variables it contains. If these values change, the value of the expression usually changes.

Since this process of substituting given values in a given expression is used throughout the study of algebra, it is of utmost importance that algebra students acquire skill in its use. Evaluation will be used in conjunction with formulas, dependence, graphs of equations and formulas, checking equations, and checking answers of examples done by algebraic processes.

In this unit we study the evaluation of elementary expressions, expressions with parentheses, expressions with exponents, and formulas. It should be noted that parentheses are used to group two or more numbers so that they may be treated as a single quantity. Exponents are used to indicate the power of a given number. The power of a number is the product obtained when a number is multiplied by itself one or more times. The exponent "2" indicates the given number is used twice as a factor in multiplication, the exponent "3" indicates the number is used three times as a factor in multiplication, the exponent "4," 4 times, the exponent "5," 5 times, etc.

LESSON:      Simple Expressions

Aim: To find the value of simple algebraic expressions.

Procedure

1. Copy given expression.

2. Substitute numbers for variables.

3. Find the value of each term (part of expression separated by the + or - sign). Note examples 6, 7 and 8.

5. If the expression is a fraction simplify, evaluate both numerator and denominator separately and then change to simplest form to get answer. See example solution 8.                                 ;

EXAMPLES

Find the value of the following expressions if a = 4 and b = 2. This lesson’s assignment:

Work on Set 1 and 2.  Be ready for a quiz on Lesson 2.

Find the value of the following algebraic expressions:

Set 1

If a = 8 and b = 2

 1.        a + b 2.       a - b 3.       ab 4.        a            b 5.       3a 6.       2ab 7.       a + 3b 8.       a + 3 9.       4a + 5b 10.    5a – 2b 11.    4ab + 3b 12.     6a – 2ab 13.    3a + 5b + 3 14.    3a + 4ab + 2b 15.     a           2 16.    12b            a 17.     a + b            a – b 18.     4a + 4b                5 19.     3a + 8b              a + b 20.     4ab – 3b            2a + 13

Set 2

If x = 6 and y = 3

 1.        x + y 2.       x - y 3.       xy 4.        x            y 5.       4y 6.       5xy 7.       x + 4y 8.       x + 4 9.       3x + 2y 10.    4x – 5y 11.    2xy + 3x 12.     5xy – 2y 13.    4x – 3y + 7 14.    3x + 5xy - y 15.     y           3 16.    7x            y 17.     x - y           x + y 18.     3x – 2y                6 19.     2x – 3y             x + 3y 20.     5xy – 2y             4x - xy