Teaching Notes 6.9: Adding and Subtracting Algebraic
Fractions with Unlike Denominators
Adding and subtracting algebraic fractions requires students to be able to find the least common
denominator, write equivalent fractions, and, in the case of subtraction, use the distributive
property. Students might make errors in any of these operations.- Review the steps for adding and subtractingfractions with unlike denominators by present-
ing this example to your students:
7
12
+
4
30
.
- Explain that students must factor the denominators to find the least common denomina-
tor (LCD). 12= 3 · 22 ,30= 5 · 2 ·3 The LCD is 5· 22 · 3 =60. - Point out that students must now write equivalent fractions, add, and simplify, if possi-
ble.
7
12
·
5
5
+
4
30
·
2
2
=
35
60
+
8
60
=
43
60
- Note that the same steps are followed for subtraction.
- Emphasize that these same steps apply to addition and subtraction of algebraic fractions.
- Review the information and example on the worksheet with your students. Go through the
steps of the example in detail and provide additional examples if necessary. You may find it
helpful to review 6.8: ‘‘Writing Equivalent Algebraic Fractions.’’
EXTRA HELP:
When subtracting, be sure to use the distributive property to distribute the negative sign to each
term of the second fraction.ANSWER KEY:
(1)
17 x
36(2)
− 1
x(x+1)(3)
2 x+ 3
x^2(4)
4(x−6)
(x+3)(x−3)(5)
7 x
18
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(Challenge)Shawn is incorrect. The common denominator is (x+1)^2. He probably forgot to
write an equivalent fraction. The correct answer is
3 x+ 8
(x+1)^2.
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240 THE ALGEBRA TEACHER’S GUIDE