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.

4. Simplify to get answer.

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.

1.      a + b

          4 + 2

   =          6

1.  Copy the expression

2.  Then substitute numbers

3.  Add the two numbers and get answer.

 

 

 

 

 

2.      a – b

          4 – 2

     =      2

 

1.  Copy the expression

2.  Then substitute numbers

3. Subtract the two numbers and get answer

 

 

 

 

3.     ab

       4 • 2

   =       8

1.  Copy the expression

2.  Then substitute numbers

3.  Multiply the two numbers and get answer.  Remember when two numbers are side by side we multiply.

 

 

 

 

 

4.      a

         b

        
         4

         2

 

   =      2

 

 

1.  Copy the expression

 

 

2.  Then substitute numbers

 

 

3.  Divide the two numbers and get answer. 

 

 

 

 

5.      5ab

          5 • 4 • 2

           20 • 2

   =        40

1.  Copy the expression

2.  Then substitute numbers

3.  Multiply 5 x 4 and get 20, then multiply that with 2 and get answer. 

 

 

 

 

 

 

6.      a + 6b

         4 + 6 • 2

          4 + 12

  =          16

1.  Copy the expression

2.  Then substitute numbers

3.  Notice you have two operations—you have to multiply 6 x 2 and then add 4.  In cases like this, ALWAYS multiply first then add.

So multiply the 6 x 2 and get 12 and then add the 4 and then get your answer.

 

 

 

 

 

 

7.     2ab -3b + 2

         2 • 4 • 2 – 3 • 2 + 2

         16 – 6 + 2

           10  + 2

      =       12

1.  Copy the expression

2.  Then substitute numbers

3.  Notice you have several operations to do for this problem.  Remember, if you have to do multiplication and addition or subtraction—do the multiplication first.  So multiply the 2 x 4 x 2 and get 16.  BE CAREFUL.  Multiply the 3 x 2 which is 6.  So now you have 16 – 6 + 2.  Now you can subtract 16 – 6 and then add 2 to get your answer.

 

 

 

 

 

8.      4a – 3b

         3ab – 4

 

         4 • 4 – 3 • 2

         3 • 4 • 2 – 4

 

          16 – 6

          24 – 4

 

            10

            20

 

        =   1

             2

1.  Copy the expression

2.  Then substitute numbers

3.  Begin to work on the numerator (top) and multiply the 4 x 4 and 3 x 2.  Then work on the denominator (bottom) 3 x 4 x 2.

 

4.  Then subtract when needed.

 

 

 

5.  If the fraction can be reduced, reduce or simplify it.  In this case, we can simply the fraction by dividing 10 into the numerator and denominator.

 

6.  Final answer.

 

 

 

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

 

                                                           

 

CHECK ANSWERS

 

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