How to Add and Subtract Fractions with Unlike Denominators

Add Fractions with Unlike Denominators

Adding and subtracting fractions with unlike denominators is a bit more involved than for fractions with like (matching) denominators. The reason for this is that we are not adding "apples with apples." If I eat one slice of a pizza that was cut into 8 slices, and my friend ate one slice from a same-sized pie that was cut into 10 slices, it is not as simple as saying that we ate two slices combined. That doesn't describe the actual portion eaten. This article shows you the steps to add and subtract fractions with unlike denominators.

Instructions

1. 

   The first step is to determine the LCM of the two denominators. This article explains the basics of that procedure. Please see the Resource section below for an article that goes into greater depth. Look at the problem shown at left: (3/5) + (1/10). The LCM of the two denominators is 10. The second fraction already has that denominator, so we can leave it alone. We must "convert" the first fraction to also have a denominator of 10.

2. 

   It's important to understand that we never change the actual values of fractions. To do this, we must multiply both the numerator and denominator by the same number. In this case, to have a denominator of 10, we must multiply top and bottom by 2, as shown. Note that what we are really doing is multiplying the fraction by 2/2, which is equal to 1, and multiplying a value by 1 doesn't change it. That is why this is allowed. We converted the fraction into an equivalent one.

3. 

   that are denominators are the same, we can add the fractions according to the rule for adding fractions with like denominators, shown at left. We just add the numerators, and leave the denominator alone. If necessary, we would reduce our answer to lowest terms.

4. 

   Let's try another example: (1/4) + (1/6). The LCM of the denominators is 12. We'll convert the first fraction to have a denominator of 12 by multiplying by 3/3. We'll convert the second fraction by multiplying by 2/2. It's OK that we used a different number for each fraction, since both 2/2 and 3/3 are equal to 1, and again, multiplying by 1 never changes anything. We now have two fractions with like denominators, so we just add the numerators and leave the denominators alone.

5. 

   That is all there is to it. Subtracting fractions follows the exact same rules, as shown. Students should make sure that they fully understand these steps because in algebra we will do the same thing, but with more abstract fractions involving variables.

Resources

• Math with Larry (Free Online Math Help)
• How to Add/Subtract Fractions with Like Denominators
• How to Find the Least Common Multiple (LCM) of Two Numbers