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

Teaching Notes 2.9: Subtracting Rational Numbers

When students subtract rational numbers, they must remember to rewrite the subtraction

problem as an addition problem and then follow the rules for adding rational numbers. The

several steps involved in this process can result in frequent mistakes.

1. Explain that a rational number is a number that can be expressed as a quotient of integers.
   Numberssuchas3,−7,− 2

1

4

,5

2

3

,and

7

9

are examples of rational numbers.

2. Explain that when subtracting a rational number from another rational number, students
   must rewrite the problem by adding the opposite of the number after the subtraction sign.
   They must keep the sign of the first number the same. Then they must follow the rules for
   adding rational numbers. Depending on the abilities of your students, you may wish to rein-
   force these rules with subtraction of integers. Once your students become familiar with the
   process, they can move onto subtraction with more complicated rational numbers.


3. Review the steps for subtracting rational numbers and the example on the worksheet.
   Depending on the abilities of your students, you may find it helpful to also review the steps
   for finding a common denominator, writing equivalent fractions, adding the numerator, and
   simplifying the result.

EXTRA HELP:

Be sure to rewrite the problem correctly before you begin to solve the problem.

ANSWER KEY:

(1)−

17

20

(2)

23

24

(3) 2

19

20

(4)− 4

1

5

(5)−

1

2

(6)−

1

8

(7) 5

17

28

(8)− 2

11

20

(9)− 2

13

20

(10) 1

59

78

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(Challenge)Answers may vary. One correct problem is− 2

1

3

− 5

1

2

. − 2

1

3

+

(

− 5

1

2

)

=− 7

5

6

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64 THE ALGEBRA TEACHER’S GUIDE