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

Teaching Notes 2.4: Comparing Rational Numbers

Comparing two rational numbers, especially two negative rational numbers, is a problem for some

students. Although they may understand that

2

3

>

1

3

, they may have trouble understanding that

−

1

3

>−

2

3

.

1. Explain the meaning of>and<, emphasizing that the symbol always points to the smaller
   number. (Or you might say that the symbol opens to the larger number.)


2. Caution your students to pay close attention to negative rational numbers. Point out that
   although

1

2

>

1

4

,−

1

2

<−

1

4

. Similarly, 0.50>0.25 but−0.50<−0.25.
3. Suggest that when comparing rational numbers students express each fraction or mixed
number as an equivalent fraction with a positive denominator. They should then compare
the numerators. Note that this reduces the chances that they will make a mistake because of
the sign of the fraction.
4. Review and discuss the number line, information, and the example on the worksheet with
your students. If necessary, review the steps for finding common denominators and writing
equivalent fractions.

EXTRA HELP:

A positive number is always larger than a negative number.

ANSWER KEY:

(1)> (2)> (3)< (4)< (5)> (6)<

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(Challenge)Yes. Explanations may vary. One response is−

1

4

=

− 5

20

and−

2

5

=

− 8

20

.Ifthe

numerators are compared,− 5 >−8, therefore−

1

4

>−

2

5

.

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54 THE ALGEBRA TEACHER’S GUIDE