Teaching Notes 6.6: Adding and Subtracting Algebraic
Fractions with Like Denominators
Adding and subtracting algebraic fractions often results in either of two problems. Students may
add or subtract the terms in the numerator incorrectly or they may apply the cancellation rule
incorrectly.- Demonstrate addition of fractions with the following example:
3
20
+
1
20
=
4
20
=
4
5 × 4
=
1
5
.
Note that students factored 20 either mentally or on paper to simplify the fraction.- Demonstrate subtraction of fractions with the following example:
3
8
−
(
−
1
8
)
=
3
8
+
1
8
=
4
8
=
4
2 × 4
=
1
2
. Note that students must rewrite subtraction as addition of the opposite
term and then proceed to add and simplify.
3. Emphasize that the process of adding and subtracting algebraic fractions is similar to the
examples, except that students will add or subtract numbers and variables. They may also
have to factor polynomials to simplify the fraction. You may wish to review 6.5: ‘‘Simplifying
Algebraic Fractions.’’
4. Review the information and examples on the worksheet with your students. Depending on
their abilities, you may find it necessary to go through the steps of the examples in detail. Be
sure that your students understand how to simplify using cancellation.
EXTRA HELP:
Rewrite subtraction by adding the opposite of every term in the numerator of the second fraction.ANSWER KEY:
(1)x− 1 (2)1
2
(3)
1
x+ 4(4)
x+ 4
x− 2(5)
x+ 3
x+ 5(6)
x− 5
x− 1
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(Challenge)Julian’s error is in subtraction. The correct answer is
x^2 − 7 x− 6
x^2 +x− 2
, which cannot
be simplified.
------------------------------------------------------------------------------------------234 THE ALGEBRA TEACHER’S GUIDE