# Adding Fractions with Unlike Denominators Lesson

**Adding Fractions with unlike denominators** involves having to find a common denominator and then adding the fractions together. In order to add fractions, the denominators have to be the same, called a common denominator. Once the fractions have a common denominator, then we simply add the numerators and place the value over the common denominator. Let’s review an example of adding fractions with like denominators.

In order to add fractions we use the following steps:

1) Check to see if the denominators are the same, if so move on to the next step. Otherwise, find the least common denominator.

2) Add the numerators, and write the sum over the common denominator.

3) Simplify the fraction if necessary.

When the denominators are different we must find the least common denominator, to do that we must find the smallest number that is a multiple of both denominators. For example, if the denominators are 4 and 7, we would list out the multiples of both numbers:

**Multiples of 4** are 4, 8, 12, 16, 20, 24, 28, 32, and so on.

**Multiples of 7** are 7, 14, 21, 28, 35, and so on.

If you notice, the smallest number that is in both lists of multiples is 28, therefore 28 is the least common multiple, and would be the least common denominator.

So, if we were adding the fractions 1/4 and 2/7, the least common denominator would be 28 as shown above.

Then we would need to multiply 1/4 x 7/7 and 2/7 x 4/4 in order to obtain two fractions with like denominators, which would be 7/28 and 8/28. Now we can add the numerators, and write the sum over the common denominator, which would be 15/28.

So to review the steps used for **adding fractions with unlike denominators** is:

1) Find the least common denominator (by listing the multiples of both denominators).

2) Multiply each fraction by the required fractions in order to convert them to equivalent fractions with like denominators.

3) Add the numerators, and write the sum over the least common denominator.

4) Simplify the fraction, if necessary.

For example, let’s add the fractions ⅗ and ⅔.

Step 1, is to list out the multiples of each denominator:

**Multiples of 5** are 5, 10, 15, 20, 25, and so on.

**Multiples of 3** are 3, 6, 9, 12, 15, 18, 21, and so on.

We notice that their least common multiple is 15, which will become our least common denominator. Therefore, we will multiply ⅗ by 3/3 and ⅔ by 5/5.

Therefore, we will add:

**Examples**

**Example 1:** Add and 4/9 and 5/6.

Solution:

Start by finding the least common denominator:

**Multiples of 9** are 9, 18, 27, 36, 45, and so on.

**Multiples of 6** are 6, 12, 18, 24, 30, and so on.

Notice, that the least common multiple is 18, therefore this is the least common denominator. So we will convert each fraction to equivalent fractions with like denominators.

Next, we will add the numerators and write them over the least common denominator.

**Solution:**

Start by finding the least common denominator:

**Multiples of 5** are 5, 10, 15, 20, 25, 30, 35, 40, 45, and so on.

**Multiples of 8** are 8, 16, 24, 32, 40, 48, and so on.

Notice, that the least common multiple is 40, therefore this is the least common denominator. So we will convert each fraction to equivalent fractions with like denominators.

Next, we will add the numerators and write them over the least common denominator.

**Solution:**

Start by finding the least common denominator:

**Multiples of 12** are 12 ,24, 36, 48, and so on.

**Multiples of 6** are 6, 12, 18, 24, and so on.

Notice, that the least common multiple is 12, therefore this is the least common denominator. So we will convert each fraction to equivalent fractions with like denominators. Notice that our first fraction already has a denominator of 12, therefore, we do not need to convert this one.

Next, we will add the numerators and write them over the least common denominator.

Now, 9/12 is not in its simplest form, we can reduce this fraction by dividing both the top and bottom by 3.

Therefore, the final answer is 3/4.

**FAQs on Adding Fractions with Unlike Denominators**

**1) What are unlike denominators?**

Unlike denominators are denominators that are different in two or more fractions.

**2) Why is it important to have a common denominator when adding fractions?**

A common denominator is necessary for adding or subtracting fractions because it allows you to combine the fractions without changing their values.

**3) How do you find a common denominator for fractions with different denominators?**

Find the least common denominator (LCD) by identifying the least common multiple (LCM) of the denominators. The LCD is the smallest number that each denominator can divide into evenly.

**4) Can you add fractions with unlike denominators without finding a common denominator?**

No, finding a common denominator is essential to perform the operation correctly.

**5) What is the process for adding fractions with unlike denominators?**

Find a common denominator, convert each fraction to an equivalent fraction with that common denominator, and then add the numerators while keeping the denominator constant.

**6) Do you simplify the result after adding fractions with unlike denominators?**

Yes, it’s a good practice to simplify the result by reducing the fraction to its simplest form, if possible.

**7) Can you subtract fractions with unlike denominators using the same method?**

Yes,subtracting fractions with unlike denominators follows a similar process. Find a common denominator, convert each fraction, and then subtract the numerators while keeping the denominator constant.

**8) Are there any shortcuts for adding fractions with unlike denominators?**

While finding a common denominator is a standard method, some may find it helpful to use the “cross-multiplication” method for addition. It involves multiplying each fraction by the other’s denominator and then adding the results.

**9) Can you add more than two fractions with unlike denominators?**

Yes, you can add more than two fractions with unlike denominators. Follow the same process: find a common denominator, convert each fraction, and then add all the numerators while keeping the denominator constant