Subtracting Fractions with Unlike Denominators
Subtracting Fractions with Unlike Denominators is a method of subtraction of fractions with different denominators. We can subtract fractions with different denominators by changing the fractions to like fractions. To convert the unlike fractions to like fractions, we take the LCM of the denominators and find equivalent fractions with the same denominators. Subtracting fractions with unlike denominators is a complex process, so to make the calculations easy, we make the denominators the same.
In this article, we will discuss the concept of subtracting fractions with unlike denominators. We will understand its meaning and the steps to subtract fractions with different denominators. We will also explore the concept of subtracting mixed numbers with unlike denominators and solve a few examples for a better understanding of the concept.
What is Subtracting Fractions with Unlike Denominators?
Before learning to subtract fractions with unlike denominators, let us recall the meaning of like and unlike fractions. Like fractions have the same denominator whereas the unlike fractions have different denominators. For example, fractions 4/9 and 2/5 are unlike fractions as they have different denominators. On the other hand, fractions 2/5 and 4/5 are like fractions as they have the same denominators. For subtracting fractions with unlike denominators, we convert the unlike fractions into like fractions. To convert them to like fractions, we will find the LCM of the different denominators and multiply the fractions with a suitable number to find their equivalent fractions. Let us understand the steps to subtracting fractions with different denominators.
Steps For Subtracting Fractions with Unlike Denominators
To subtract fractions with unlike denominators, we follow certain steps to find the difference. Below given are steps for subtracting fractions with different denominators:
 Step 1: Find the LCM of the different denominators of the fractions.
 Step 2: Multiply and divide the fractions with a suitable number to obtain the denominator as the LCM obtained in Step 1.
 Step 3: Now, we have obtained the like fractions which are equivalent to the original fractions.
 Step 4: Subtract the numerators of like fractions obtained.
 Step 5: Simplify the fraction obtained after subtraction to its lowest form, if possible.
Let us now solve a few examples using the above steps to understand the process of subtracting fractions with unlike denominators.
Examples of Subtracting Fractions with Unlike Denominators
Now that we have understood the steps for subtracting fractions with unlike denominators, let us solve an example to understand the concept better.
Example: Subtract the fractions 2/3 and 4/5.
Solution: Let us solve the problem by following the steps of subtracting fractions with unlike denominators discussed in the previous section:
Step 1: Find the LCM of 3 and 5
LCM (3, 5) = 15
Step 2: Multiply and divide the fractions 2/3 and 4/5 by a suitable number to change their denominator to 15.
2/3 = (2 × 5) / (3 × 5) = 10/15
4/5 = (4 × 3) / (5 × 3) = 12/15
Step 3: 10/15 and 12/15 are the like fractions equivalent to the original fractions.
Step 4: Subtract the like fractions.
10/15  12/15 = (1012)/15
= 2/15
Step 5: 2/15 cannot further be reduced.
Answer: 2/3  4/5 = 2/15
Subtracting Mixed Numbers with Unlike Denominators
So far we understood the concept of subtracting fractions with unlike denominators. Let us now learn to subtract mixed fractions with unlike denominators. To find the difference of mixed numbers with different denominators, we first simplify the mixed fractions into improper fractions and then follow the same steps that we discussed before. Let us consider an example and subtract mixed numbers with unlike denominators.
Example: Subtract 3 2/3 from 4 1/2.
Solution: First, we will change the mixed number to an improper fraction and then subtract.
4 1/2 = 9/2 and 3 2/3 = 11/3
Now, we have to subtract 11/3 from 9/2. Since the denominators are different, we will find the LCM of 2 and 3.
LCM (2, 3) = 6
Multiply and divide the fractions 11/3 and 9/2 by a suitable number to change their denominator to 6.
11/3 = (11 × 2) / (3 × 2) = 22/6
9/2 = (9 × 3) / (2 × 3) = 27/6
Subtracting 22/6 from 27/6, we have
27/6  22/6 = 5/6
⇒ 9/2  11/3 = 5/6
⇒ 4 1/2  3 2/3 = 5/6
Since 5/6 cannot further be reduced, the difference of mixed numbers with unlike denominators 3 2/3 and 4 1/2 is equal to 5/6.
Important Notes on Subtracting Fractions with Unlike Denominators
 We can subtract fractions with unlike denominators by changing the fractions to like fractions.
 For subtracting mixed numbers with different denominators, we first simplify the mixed fractions into improper fractions.
 For subtracting fractions with unlike denominators, we convert the unlike fractions into like fractions by finding the LCM of the denominators.
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Subtracting Fractions with Unlike Denominators Examples

Example 1: Find the difference: 7/4  4/5  1/2
Solution: We need to subtract fractions with unlike denominators. First, we will find the LCM of denominators 2, 4, and 5.
LCM(2, 4, 5) = 20
So, we have
7/4 = (7 × 5) / (4 × 5) = 35/20
4/5 = (4 × 4) / (5 × 4) = 16/20
1/2 = (1 × 10) / (2 × 10) = 10/20
Next, 7/4  4/5  1/2
= 35/20  16/20  10/20
= (35  16  10)/20
= 9/20, which cannot further be reduced.
Answer: 7/4  4/5  1/2 = 9/20

Example 2: Subtract 4/7 from 8/3.
Solution: 4/7 and 8/3 are unlike fractions as they have different denominators. So, first we find the LCM of 3 and 7.
LCM (3, 7) = 21
8/3 = (8 × 7) / (3 × 7) = 56/21
4/7 = (4 × 3) / (7 × 3) = 12/21
So, we have
8/3  (4/7)
= 56/21  (12/21)
= 56/21 + 12/21
= (56 + 12)/21
= 35/21
= 5/3
Answer: 8/3  (4/7) = 5/3

Example 3: Subtract fractions with unlike denominators: 6/13 from 7/4.
Solution: To subtract 6/13 from 7/4, find the LCM of 13 and 4.
LCM(13, 4) = 52
7/4 = (7 × 13) / (4 × 13) = 91/52
6/13 = (6 × 4) / (13 × 4) = 24/52
6/13 from 7/4
= 7/4  6/13
= 91/52  24/52
= 67/52
Answer: Subtraction of 6/13 from 7/4 is equal to 67/52.
FAQs on Subtracting Fractions with Unlike Denominators
What is Subtracting Fractions with Unlike Denominators?
Subtracting Fractions with Unlike Denominators is a method of subtraction of fractions with different denominators.
How to Subtract Fractions with Different Denominators?
We can subtract fractions with different denominators by subtracting the equivalent fractions of the given fractions.
What are the Steps for Subtracting Fractions with Unlike Denominators?
Below given are steps for subtracting fractions with different denominators:
 Step 1: Find the LCM of the different denominators of the fractions.
 Step 2: Multiply and divide the fractions with a suitable number to obtain the denominator as the LCM obtained in Step 1.
 Step 3: Now, we have obtained the like fractions which are equivalent to the original fractions.
 Step 4: Subtract the numerators of like fractions obtained.
 Step 5: Simplify the fraction obtained after subtraction to its lowest form, if possible.
What is the Rule for Subtracting Fractions with Unlike Denominators?
The basic rule for subtracting fractions with unlike denominators is to find make the denominators the same finding the LCM of the unlike denominators.
Give an Example of Subtracting Fractions with Unlike Denominators.
An example of subtracting fractions with unlike denominators is:
Solve of 3/4  1/5.
LCM (4, 5) = 20
3/4  1/5 = 15/20  4/20
= 11/20
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