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. After converting each fraction in such a way so that we have a common denominator, we add the numerators to get the sum.
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. 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 converted 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
 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 as 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 \(3\dfrac{1}{6}\)
For adding three or more fractions with unlike denominators we apply the same steps.
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 so 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 the numerator part (15 + 18 + 70)/30 = 103/30. This can be converted to a mixed fraction and written as \(3\dfrac{13}{30}\)
Adding Mixed Fractions with Unlike Denominators
If we need to add mixed fractions 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.
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 = \(9\dfrac{12}{35}\)
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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
Practice Questions on Adding Fractions With Unlike Denominators
FAQs on Adding Fractions with Unlike Denominators
What is Adding Fractions with Unlike Denominators?
Adding fractions with unlike denominators means when 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. After converting each fraction in such a way so that we have a common denominator, we add the numerators to get the sum.
What are the Examples of Adding Fractions with Unlike Denominators?
The examples of adding fractions with unlike denominators are: 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 take 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. Let us 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 are 2/10 and 1/10
 Step 4: Add the numerator part (2 + 1)/10 = 3/10
What is Adding Fractions with Unlike Denominators Using LCM?
Adding fractions with unlike denominators using LCM means when we add fractions with different denominators, we need to find the LCM of the given denominators. Using this LCM, we convert the given fractions to like fractions, where the LCM becomes the common denominator of the new fractions. After this step, the numerators are added and the sum is obtained. For example, let us add 1/6 + 1/3
We need to find the LCM of 6 and 3 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
Now, add the numerators of these fractions which is: 1/6 + 2/6 = (1 + 2)/6 = 3/6. This fraction can be further reduced to 1/2 after simplifying.
Can we Add Fractions with Unlike Denominators Without Using LCM?
No, we cannot add fractions with unlike denominators without using the LCM.
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