Adding and Subtracting Rational Numbers
Adding and Subtracting
Rational Numbers
After studying this lesson, you will be able to:
- Add and subtract rational numbers
- Simplify expressions containing rational numbers
Rational Numbers are the numbers which can be
expressed in the form 
where a and b are integers and b is not
equal to zero. The rules for adding and subtracting rational
numbers are the same as those for integers:
Addition Rule: (be sure to learn this rule)
If the two rational numbers have the same sign, add them. The
answer will take the sign of these numbers
If the two rational numbers have different signs, subtract
them. The answer will take the sign of the larger number.
Subtraction Rule: (be sure to learn this
rule)
Change the subtraction sign to a plus sign AND change the sign
of the next number to its opposite. Then, follow the addition
rules stated above.
This is called "adding the opposite".
Example 1
Solution
Since these numbers have different signs, we subtract.
Remember, you must have a common denominator before adding or
subtracting fractions. The common denominator is 12. Convert the
fractions to twelfths.
Again, since the signs are different we
subtract.
The answer takes the sign of the larger number. Therefore, the
answer is 
.
Example 2
1.45 - (-2.32)
Solution
Since this is a subtraction problem, we add the opposite then
follow addition rules. After adding the opposite the problem
looks like 1.45 + (2.32). The signs are the same, so we add and
take that sign. Therefore, the answer is 3.77
Example 3
3.14 - (-2.17) + 4.32 - 8.6
Solution
Add the rational numbers two at a time. Since the first two
involve subtraction, we add the opposite 3.14 + (2.17) to get
5.31. Next add 5.31 + 4.32 (same signs so we add). This gives us
9.63. Next we have 9.63 - 8.6. After adding the opposite we have
9.63 + (-8.6). Since these are different signs, we subtract and
take the sign of the larger to get 1.03
Example 4
Evaluate y 0.3 if y = -0.5 Evaluate means to find an answer,
so we substitute 0.5 for the y and then we simplify. After
substituting we have (-0.5) - 0.3 Since this is subtraction, we
add the opposite to get (-0.5) + (-0.3) Since the signs are now
the same, we add and take that sign to get -0.8
