Teaching Notes 2.2: Simplifying Fractions
A common mistake students make when simplifying fractions is to divide by a common factor but
not the greatest common factor (GCF). Unless students realize they did not use the GCF, the
resulting fraction is not expressed in simplified form.- Explain that to simplify a fraction students must divide the numerator and the denominator
by the GCF. If your students have trouble finding the GCF, see 1.11: ‘‘Finding the Greatest
Common Factor.’’ - Explain that a fraction is in simplest form if the GCF of the numerator and denominator is 1.
For example,
11
15
is in its simplest form because the GCF of 11 and 15 is 1. Emphasize that
students should check that the GCF of the numerator and denominator is 1 to determine if
the fraction is in simplest form. If the GCF is not 1, they should divide the numerator and
denominator by a common factor, continuing this process until the GCF is 1.- Explain that negative fractions are simplified in the same manner as positive fractions. Note
that the negative sign may be written before the numerator, before the fraction, or before
the denominator. For example,
− 3
5
,−
3
5
,and3
− 5
all express the same number.- Review the example on the worksheet with your students.
EXTRA HELP:
If the numerator and denominator of a fraction are even, the fraction is not simplified.ANSWER KEY:
(1)1
2
(2)−
5
7
(3)−
4
5
(4)
1
5
(5)
6
13
(6)
2
3
(7)
8
11
(8)−
5
16
(9)−
5
8
(10)
35
46
(11)−^3
7
(12)
4
5
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(Challenge)Answers may vary. For example, some students may argue that using 15 as the
GCF is indeed the easier way. Others may feel that dividing first by 5 and then by 3 is easier
because it is easier to recognize that 5 is a common factor of 105 and 120.105
120
=
21
24
It is theneasy to see that 3 is a common factor of 21 and 24.21
24
=
7
8
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50 THE ALGEBRA TEACHER’S GUIDE