Teaching Notes 2.3: Rewriting Mixed Numbers
as Improper Fractions
When rewriting mixed numbers as improper fractions in the lower grades, most students were
taught to multiply the denominator by the whole number, add the numerator, and then place the
answer over the denominator. This rule applies only to positive mixed numbers, however, and can
be the source of errors if applied to negative mixed numbers.- Explain why the rule your students learned in the lower grades is valid for rewriting a posi-
tive mixed number as an improper fraction. Use the following example: One large pizza is cut
into 8 slices. If a student orders 2
1
8
pizzas for his friends and himself, he has 16 slices (two
pies), plus 1 more slice for a total of 17 slices. Therefore, 21
8
=
17
8
.
- Explain that the method above does not apply to rewriting negative mixed numbers.
Note that a negative number is the opposite of a positive number. To change a negative
mixed number to an improper fraction, students must express the negative mixed
number as a positive improper fraction and then write its opposite. For example,
− 21
8
=−
(
2
1
8
=
8 × 2 + 1
8
)
=−
17
8
.
- Review the information and examples on the worksheet with your students.
EXTRA HELP:
Before expressing the mixed number as an improper fraction, be sure it is in simplest form.ANSWER KEY:
(1)23
4
(2)−
53
8
(3)
38
15
(4)−
47
6
(5)
43
12
(6)−
39
4
(7)
27
16
(8)−
49
10
(9)
24
5
(10)−
52
5
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(Challenge)Yes, they are equivalent but each number could be rewritten. 31
3
=
10
3
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52 THE ALGEBRA TEACHER’S GUIDE