Adding and Subtracting Fractions With Different Denominators
Learning Outcomes
Add and subtract fractions with different denominators
Add and subtract fractions with different denominators that contain variables
Identify and use fraction operations
Once we have converted two fractions to equivalent forms with common denominators, we can add or subtract them by adding or subtracting the numerators.
Add or subtract fractions with different denominators
Find the LCD.
Convert each fraction to an equivalent form with the LCD as the denominator.
Remember, always check to see if the answer can be simplified. Since [latex]5[/latex] and [latex]6[/latex] have no common factors, the fraction [latex]\Large\frac{5}{6}[/latex] cannot be reduced.
Try It
Watch the following video to see more examples and explanation about how to add two fractions with unlike denominators.
Because [latex]31[/latex] is a prime number, it has no factors in common with [latex]36[/latex]. The answer is simplified.
Try It
You can also add more than two fractions as long as you first find a common denominator for all of them. An example of a sum of three fractions is shown below. In this example, you will use the prime factorization method to find the LCM.
Think About It
Add [latex]\Large\frac{3}{4}+\Large\frac{1}{6}+\Large\frac{5}{8}[/latex]. Simplify the answer and write as a mixed number.
What makes this example different than the previous ones? Use the box below to write down a few thoughts about how you would add three fractions with different denominators together.
Show Solution
Since the denominators are not alike, find the least common denominator by finding the least common multiple (LCM) of 4, 6, and 8.
When you subtract fractions, you must think about whether they have a common denominator, just like with adding fractions. Below are some examples of subtracting fractions whose denominators are not alike.
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