Teaching Notes 2.8: Adding Rational Numbers
Adding rational numbers requires mastery of several skills: finding the least common
denominator, writing equivalent fractions, applying the rules for adding integers, and simplifying
the result. Depending on the problem, students may also have to change a mixed number to an
improper fraction or change an improper fraction to a mixed number. Negative numbers can make
the process even more confusing.- Explain that a rational number is a number that can be expressed as a quotient of integers.
Numbers such as
1
4
,−
5
2
, and 8 are examples of rational numbers.- Explain that adding positive and negative rational numbers involves many of the same steps
that are necessary for adding positive fractions. Depending on the abilities of your students,
you may find it helpful to review the steps for finding a common denominator, writing equiv-
alent fractions, adding the numerators, and simplifying the results. - Review the steps for adding rational numbers and the example on the worksheet with your
students. Emphasize that to add negative rational numbers, students must also do the
following:- Write all mixed numbers as improper fractions.
- Write the denominators of the fractions as positive numbers.
- Add the numerators, following the rules for adding integers.
EXTRA HELP:
Pay close attention to negative signs as you add rational numbers. It is a good idea to write negative
signs before the numerators.ANSWER KEY:
(1)−19
20
(2)
27
56
(3) 2
5
24
(4)− 2
5
14
(5)− 4
11
20
(6)−
1
8
(7) 1
17
28
(8)− 6
19
30
(9)−
15
56
(10)− 1
7
10
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(Challenge)Answers may vary. 1 and−1
2
is one solution.
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