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

Teaching Notes 6.10: Multiplying and Dividing Algebraic

Fractions

To multiply and divide algebraic fractions correctly, students must be competent at factoring,

simplifying, and, in the case of division, using the reciprocal. The need to use multiple skills

often results in errors in computation and careless mistakes.

1. Explain that algebraic fractions are multiplied and divided according to the same rules as
   ordinary fractions.


2. Present the following multiplication example.^8
   15

5

12

2

21

33

9

· ==^8

15

5

12

· Note the process of

cancelling, which requires students to divide the numerators and denominators by common

factors before actually multiplying.

3. Present the following division example.^8
   15

5

12

32

4

5

25

÷ ==^8

15 5

·^12 Note that the divisor

must be changed to its reciprocal and the division rewritten to multiplication before can-

celling can be attempted.

4. Review the information and example on the worksheet with your students. Emphasize that
   when the numerator and denominator are algebraic expressions, which include polynomials,
   factoring should be written out to avoid careless errors. Remind your students to use the
   reciprocal when dividing. Emphasize that they should leave their answers in factored form.

EXTRA HELP:

Always rewrite division as multiplication, using the reciprocal of the fraction immediately following

the division sign.

ANSWER KEY:

(1)2(x+4) (2)

1

x+ 3

(3)

x(x+4)

10(x+1)

(4)

x^2

2(2x+3)

(5)

2 x+ 1

(x−2)(x−1)

(6)

(x−4)(x−3)

(x−2)^2

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(Challenge)Sienna did not use the reciprocal. The correct answer is

(x−2)^2

(x+4)(x−4)

.

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242 THE ALGEBRA TEACHER’S GUIDE