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

Teaching Notes 2.10: Multiplying and Dividing

Rational Numbers

When students multiply and divide positive rational numbers, they do not need to be concerned

whether the sign of the answer is positive or negative. It is positive. However, when multiplying

or dividing negative rational numbers, they must determine the sign of their answer. For some

students, determining the correct sign can be a problem.

1. Explain that the procedure for multiplying and dividing negative rational numbers is similar
   to multiplying and dividing positive rational numbers. However, the answers may be positive
   or negative.


2. Review the procedure for multiplying and dividing rational numbers and the examples on
   the worksheet with your students. Note that they must pay particular attention to negative
   signs. Emphasize that when dividing, they must multiply by the reciprocal of the number
   after the division sign. Be sure that your students understand the steps for multiplying inte-
   gers and remind them that zero times a number is zero and that a number divided by zero is
   undefined.

EXTRA HELP:

Double-check the sign of your answer to make sure that it is correct.

ANSWER KEY:

(1)

5

9

(2) 7

1

2

(3)− 3

25

32

(4)−

8

11

(5)Undefined

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(Challenge)It is incorrect. For example, Sarah would rewrite

3

4

÷

(

−

1

2

)

as

3

4

×

(

−

1

2

)

=−

3

8

.

She would then find the reciprocal of her answer, which would be−

8

3

=− 2

2

3

. The correct

answer is

3

4

÷

(

−

1

2

)

=

3

4

×

(

−

2

1

)

=−

6

4

=− 1

1

2

.

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66 THE ALGEBRA TEACHER’S GUIDE