LESSON: Adding and Subtracting Fractions with Unlike Denominators

READ: Add Fractions With Different Denominators

Add Fractions With Different Denominators

Not all fractions have common or like denominators. When we have fractions with unlike denominators, we can still add them, but we will need to rename the fractions before we can add them. How do we add fractions with different denominators?

To add fractions that have different denominators, we have to rename the fractions so that they are alike. We rename them by changing the different denominators of the fractions to like denominators.

Example

$\frac{1}{2} + \frac{1}{4} = \underline{\;\;\;\;\;\;\;\;\;}$

In this example, we are trying to add halves and fourths. If something is divided into halves, it is divided into two pieces. If something is divided into fourths, it is divided into four pieces. We are trying to add fourths and halves. They are different quantities. You can see that although the bar is the same size, the parts are different sizes. We have to rewrite these fractions so that they have common denominators.

How do we rewrite fractions to have a common denominator?

The first step in doing this is to the find the least common multiple of both of the denominators. This LCM will become the lowest common denominator.

Let’s look at 2 and 4.

First, name the multiples of 2: 2, 4, 6, 8, 10 . . . .

Next, name the multiples of 4: 4, 8, 12, 16

The least common multiple of 2 and 4 is 4.

Our next step is to rewrite each fraction as an equivalent fraction that has four as a denominator.

$\frac{1}{2} = \frac{}{\;4\;}$ to name one-half in terms of fourths, we need to multiply the numerator and denominator by the same number. 2 $\times$ 2 $=$ 4, so we multiply the numerator by 2 also. 1 $\times$ 2 $=$ 2.

$\frac{1}{2} = \frac{2}{4}$

Our second fraction $\frac{1}{4}$ is already written in terms of fourths so we don’t need to change it at all.

Next, we can add the renamed fractions.

$\frac{2}{4} + \frac{1}{4} = \frac{3}{4}$

Our answer is $\frac{3}{4}$ . This answer is in simplest form, so our work is complete.

As long as you rename fractions with the lowest common denominator, you can add any number of fractions with unlike denominators.