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

Teaching Notes 6.8: Writing Equivalent Algebraic Fractions

Writing equivalent algebraic fractions is a prerequisite skill for adding and subtracting algebraic

fractions with different denominators. Students often make errors in finding the missing factor

and in multiplying.

1. Demonstrate the process for writing equivalent fractions by providing this example:

3

4

=

20

.

Students should identify 4 and 5 as factors of 20. (There are other factors, of course, but

4 × 5 =20.) To write an equivalent fraction, explain that students should multiply

3

4

by

5

5

with the result of

15

20

. Note that when they multiply by

5

5

they are actually multiplying by 1,

and multiplying any number by 1 does not affect the number’s value.

2. Explain that the same process is used to write equivalent algebraic fractions, except that the
   factors may be a polynomial, number, or variable, depending on the denominator.


3. Review the information and example on the worksheet with your students. If necessary,
   review the steps for factoring polynomials. Be sure that students understand the steps for
   multiplying.

EXTRA HELP:

Use the distributive property if you multiply a binomial by a number or a variable. Use FOIL to

multiply two binomials.

ANSWER KEY:

(1) 3 x+ 6 (2)x+ 3 (3) 5 x− 25 (4) 2 x+ 2 (5)x^3 +x^2 (6)x^2 + 7 x+ 12

------------------------------------------------------------------------------------------

(Challenge)Because

x+ 2

x+ 2

=1, the equivalent fraction must be equal to 1. The numerator

------------------------------------------------------------------------------------------must equalx^2 +^6 x+4.

238 THE ALGEBRA TEACHER’S GUIDE