The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Teaching Notes 2.12: Evaluating Rational Expressions

Evaluating expressions when variables represent rational numbers involves the application of the

order of operations. Students must follow the order of operations correctly and they must be able

to add, subtract, multiply, and divide rational numbers correctly. Mistakes may occur anywhere

within the procedure.

1. Explain that to evaluate an expression, students must substitute the correct values for vari-
   ables and then follow the rules for the order of operations.


2. Depending on the abilities of your students, you may find it helpful to review the process for
   adding, subtracting, multiplying, and dividing rational numbers.


3. Review the steps of the order of operations and the example on the worksheet with your
   students. Remind them of basic notation:
   
   
   • −ameans the opposite ofa,soifa=−^3
     4
     ,−a=
   
   
   
   

3

4

.

• abmeansa×b.


• a
  b

meansa÷b.

EXTRA HELP:

Be sure that you substitute the correct values for every variable in an expression.

ANSWER KEY:

(1) 2 (2) 1

1

8

(3)−

2

3

(4)

1

18

(5) 1 (6)−

4

9

(7)

1

2

(8)

2

3

(9)−

7

12

(10)

4

9

(11)−

1

64

(12) 6

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(Challenge)a=

1

5

anda=−

1

5

because

(

1

5

) 2

=

1

25

and

(

−

1

5

) 2

=

1

25

.

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70 THE ALGEBRA TEACHER’S GUIDE