Page 245 - Basic College Mathematics with Early Integers

Objectives 3.5 ADDING AND SUBTRACTING UNLIKE FRACTIONS

Add or Subtract Unlike
Fractions.
Objective Adding and Subtracting Unlike Fractions
Write Fractions in Order.
In this section we add and subtract fractions with unlike denominators. To add or
Evaluate Expressions Given subtract these unlike fractions, we first write the fractions as equivalent fractions
Fractional Replacement Values. with a common denominator and then add or subtract the like fractions. Recall
from the previous section that the common denominator we use is called the least
Solve Problems by Adding or common denominator (LCD).
Subtracting Unlike Fractions. 3 1
To begin, let’s add the unlike fractions + .
4 6
The LCD of these fractions is 12. So we write each fraction as an equivalent
fraction with a denominator of 12, then add as usual.This addition process is shown
next and also illustrated by figures.

3 1
Add: The LCD is 12.
4 6
Figures Algebra
! Z
3 = 3 # 3 = 9 1 = 1 # 2 = 2
4 4 3 12 and 6 6 2 12
3 2
Remember, = 1 and = 1.
3 2
9 2 Now we can add just as we did in Section 3.4.
12 12

1
3 + = 9 + 2 = 11
4 6 12 12 12

9 2 11
12 12 12

11
Thus, the sum is .
12

Adding or Subtracting Unlike Fractions

Step 1: Find the least common denominator (LCD) of the fractions.
Step 2: Write each fraction as an equivalent fraction whose denominator is the
LCD.
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Step 3: Add or subtract the like fractions.
Step 4: Write the sum or difference in simplest form.

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