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Adding Fractions With Unlike Denominators
Adding fractions with unlike denominators means we need to add fractions that have different denominators. In this case, we convert the given fractions to like fractions to get common denominators so that it becomes easier to add them. This is done by finding the Least Common Multiple (LCM) of the given denominators. We convert each fraction in such a way so that we have a common denominator, and then we add the numerators to get the sum.
In this article, we will learn how to add fractions with different denominators stepwise. We will also discuss the addition of mixed fractions with unlike denominators along with a few solved examples for a better understanding of the concept.
What is Adding Fractions with Unlike Denominators?
When the denominators are not the same, the fractions are known as unlike fractions. For example, 3/5 and 6/7 are called unlike fractions because they have different denominators. To add two or more given fractions, whose denominators are unlike or different, we need to find the Least Common Multiple (LCM) of the denominators. After finding the LCM, we multiply the given fractions with such a number so that their denominators remain common. After making the denominators equal, we can simply add the numerators.
Steps For Adding Fractions with Unlike Denominators
The following steps show the procedure for adding fractions with unlike denominators.
 Step 1: First, we find out the Least Common Multiple (LCM) of the given denominators.
 Step 2: Then, we write down each fraction in a form such that the LCM becomes the common denominator. For this, we multiply the numerator and denominator with a common number with the help of the LCM.
 Step 3: After this step, we add the numerators of these like fractions (which have common denominators now).
 Step 4: Finally, we reduce the resultant fraction to its lowest terms, if needed.
These steps can be understood with the help of the example given in the following section.
How to Add Fractions with Unlike Denominators?
Now, let us learn how to add fractions with unlike denominators by following the steps given above.
Example: Add 5/6 + 7/3
Solution:
 Step 1: Since the fractions have different denominators, we find the LCM of 6 and 3. The LCM of 6 and 3 is 6.
 Step 2: Now, convert the given fractions to equivalent fractions such that the LCM becomes their common denominator. As we can see 5/6 already has the LCM as its denominator, so we will only change the fraction 7/3 and make it an equivalent fraction, which will be 14/6.
 Step 3: After this, we can add the numerators of both the fractions since the denominators are the same.
 Step 4: 5/6 + 14/6 = (5 + 14)/6 = 19/6. This can be converted to a mixed fraction and written as \(3\dfrac{1}{6}\)
Adding 3 Fractions with Different Denominators
For adding three or more fractions with unlike denominators we apply the same steps as given above. Let us learn how to add 3 fractions with different denominators with the help of the following example.
Example: Add 1/2 + 3/5 + 7/3
 Step 1: First, we will find the LCM of 2, 5, and 3, which is 30.
 Step 2: Now, we will make each fraction an equivalent fraction in such a way that the LCM 30 becomes the denominator of each fraction.
 Step 3: The equivalent fractions with denominator 30 are 15/30, 18/30, and 70/30.
 Step 4: Add all the numerators (15 + 18 + 70)/30 = 103/30. This can be converted to a mixed fraction and written as \(3\dfrac{13}{30}\)
Adding Mixed Numbers with Unlike Denominators
If we need to add mixed numbers with unlike denominators, we convert the mixed fraction to an improper fraction. After this, we can add the fractions by following the steps given above. Let us understand this with the help of the following example.
Example: Add \(5\dfrac{1}{7}\) and \(4\dfrac{1}{5}\)
First, convert the mixed number into an improper fraction.
\(5\dfrac{1}{7}\) = 36/7
\(4\dfrac{1}{5}\) = 21/5
Now add 36/7 and 21/5
LCM of 7 and 5 is 35
Equivalent fractions
36/7 = 180/35
21/5 = 147/35
Now add the numerators,
(180 + 147)/35 = 327/35 = \(9\dfrac{12}{35}\)
Important Notes on Adding Fractions with Unlike Denominators
 For adding fractions with unlike denominators, we take the LCM of the different denominators and convert them to like fractions and then add the numerators.
 For adding mixed fractions with unlike denominators, we convert them into improper fractions and then add.
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Adding Fractions with Unlike Denominators Examples

Example 1: Add 8/9 + 1/3 + 7/6
Solution: For adding fractions with unlike denominators, first, we will find out the LCM of numbers 9, 3 and 6
LCM = 18
Now, we will convert each fraction into equivalent fractions by taking the denominator as the LCM
8/9 = 16/18
1/3 = 6/18
7/6 = 21/18
Now, we can add the numerators.
(16 + 6 + 21)/18 = 43/18. This can be converted to a mixed fraction \(2\dfrac{7}{18}\)

Example 2: Add 5/8 + 1/5
Solution: To add fractions with unlike denominators, first, we will find out the LCM of numbers 8 and 5
LCM = 40
Then, we will convert each fraction into equivalent fractions by taking the denominator as the LCM 40
5/8 = 25/40
1/5 = 8/40
Now, we can add the numerators.
(25 + 8)/40 = 33/40
So, the sum of 5/8 + 1/5 is 33/40

Example 3: Add mixed fractions \(3\dfrac{1}{4}\) and \(2\dfrac{2}{3}\)
Solution: To add the given mixed fractions, we first convert them into improper fractions.
\(3\dfrac{1}{4}\) = 13/4 and \(2\dfrac{2}{3}\) = 8/3
Now, since the denominators are unlike, we take the LCM of 3 and 4. LCM (3, 4) = 12. Now, convert the fractions into like fractions.
13/4 = 39/12 and 8/3 = 32/12. Now add the two fractions.
39/12 + 32/12 = 71/12 = \(5\dfrac{11}{12}\)
Answer: \(3\dfrac{1}{4}\) + \(2\dfrac{2}{3}\) = \(5\dfrac{11}{12}\)
FAQs on Adding Fractions with Unlike Denominators
How to Add Fractions with Different Denominators?
Adding fractions with unlike denominators means that two fractions that have different denominators need to be added. In this case, we convert the given fractions to like fractions to get common denominators so that it becomes easier to add them. This is done by finding the Least Common Multiple (LCM) of the given denominators. We need to convert each fraction in such a way so that we have a common denominator and after that, we add the numerators to get the sum.
What are the Examples of Adding Fractions with Unlike Denominators?
An example of adding fractions with unlike denominators is given as follows. Let us add 1/3 + 6/5.
 We can see that the denominators are not the same, hence, we need to make the denominators equal, after which we can add the fractions.
 In this example, 1/3 + 6/5, we will first find the LCM of the denominators 3 and 5 which is 15.
 Then, we will multiply both the fractions with such a number so that the denominators remain the same.
 This results in (5 + 18)/15 = 23/15.
 Now, let us convert the improper fraction to a mixed number: 23/15 = \(1\dfrac{8}{15}\)
What is the Strategy for Adding Fractions with Unlike Denominators?
The strategy for adding fractions with unlike denominators is to find the LCM of the given denominators and make each fraction as an equivalent fraction with the LCM as the denominator.
What are the Steps For Adding Fractions with Unlike Denominators?
The steps for adding fractions with unlike denominators are given below. Let us understand this with an example and add 1/5 + 1/10
 Step 1: First, we will find the LCM of 5 and 10 which is 10.
 Step 2: Now, make each fraction an equivalent fraction in such a way so that the LCM (10) becomes the denominator of each fraction.
 Step 3: The equivalent fractions with denominator 10 will be 2/10 and 1/10
 Step 4: Add the numerator part (2 + 1)/10 = 3/10
Can we Add Fractions with Unlike Denominators Without Using LCM?
No, we cannot add fractions with unlike denominators without using the LCM.
What is the Rule for Adding Fractions with Unlike Denominators?
The basic rule for adding fractions with unlike denominators is to find the LCM of the different denominators and convert the given unlike fractions into like fractions. This can be done by changing their denominators equal to the LCM. Once the denominators become the same, the numerators can be added.
How to Add 3 Fractions with Different Denominators?
In order to add 3 fractions with different denominators, we use the same rules that are used for adding 2 fractions with different denominators. For example, let us add 1/6 + 1/3 + 1/2
We need to find the LCM of 6, 3, and 2 which is 6. Now, we will convert each fraction into an equivalent fraction using LCM as the denominator.
1/6 = 1/6
1/3 = 2/6
1/2 = 3/6
Now, add the numerators of these fractions which is: 1/6 + 2/6 + 3/6 = (1 + 2 + 3)/6 = 6/6. This fraction can be further reduced to 1 after simplifying.
How to Add and Subtract Fractions with Different Denominators?
In order to add and subtract fractions with different denominators, we use the same rules. We need to find the LCM of the different denominators and convert the given unlike fractions into like fractions. After this step, we add or subtract the numerators according to the question.
How to Add Fractions with Whole Numbers and Different Denominators?
In order to add fractions with whole numbers and different denominators, we should write the whole number in its fraction form, that is, write 1 as its denominator and then add it using the same rules for the addition of fractions. For example, let us add 6 + 3/4 + 1/2.
 In this case, 6 is the whole number and we can write it as 6/1.
 So, let us rewrite the fractions as 6/1 + 3/4 + 1/2.
 Then, we will find the LCM of the denominators so that they are converted to like fractions. The LCM of 1, 4, and 2 will be 4.
 Now, the fractions can be written as 6/1 + 3/4 + 1/2 = (24 + 3 + 2)/4 = 29/4. This can be converted to mixed fraction as \(7\dfrac{1}{4}\)
How to Add Improper Fractions with Different Denominators?
In order to add improper fractions with different denominators, we use the same rules that are used for the addition of fractions. For example, let us add these improper fractions with different denominators: 7/2 + 8/3.
 We will first find the LCM of the denominators. The LCM of 2 and 3 is 6.
 Then, we will convert the given fractions into equivalent fractions. So, 7/2 will become 21/6, and 8/3 will become 16/6.
 Now, we can add them because their denominators are the same. This means (21 + 16)/6 = 37/6 = \(6\dfrac{1}{6}\)
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