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