Last updated on July 4th, 2025
Unlike fractions are those which have different denominators. Adding fractions with different denominators involves converting them into like fractions, i.e., fractions with the same denominator. This method is used to add different fractions of discounts or savings. In this topic, we will learn how to add fractions with different denominators.
When two fractions have different denominators, they are often referred to as unlike fractions. Fractions like 2/7 and 8/9 are examples. To find their sum, we first need to determine their Least Common Multiple (LCM). The next step is to multiply the numerator and denominator of both fractions by the correct factors to make them like denominators.
To add fractions with unlike denominators, follow the steps given below:
Step 1: We first determine the Least Common Multiple (LCM) of the denominators of the given fractions.
Step 2: Then, make the denominators the same by multiplying the numerator and denominator by the appropriate factors.
Step 3: Find the sum of these fractions by adding their numerators.
Step 4: Express the sum in its simplest form.
As we have learned the different steps involved in adding unlike fractions, let’s understand them with the help of an example:
Adding 2 Fractions with Different Denominators
To add 2 fractions with different denominators, we use the same steps as discussed:
Add 3/4 + 5/8
Solution:
1. We first find the LCM of 4 and 8:
2. Now, we make the denominators equal by converting them to 8:
3. Determine what, when multiplied by 4, gives 8:
4. Multiply by 2 with both the numerator and denominator resulting 6/8.
5. Now add the numerators, since the denominators are the same.
3/4 + 5/8 = 6/8 + 5/8 = (6 + 5)/8 = 11/8.
Adding 3 Fractions with Different Denominators
Similarly, we add three fractions with different denominators:
Add 2/3 + 4/7 + 5/7
Solution:
1.The LCM of 3 and 7 is 21
2. Now, we will multiply the fractions by appropriate factors that give 42 as the denominator:
3. Add the numerators:
4. Convert to a mixed fraction:
Adding Mixed Fractions with Unlike Denominators
Before adding mixed fractions, we must convert them into improper fractions and follow similar steps. Let’s look at the steps involved using an example:
Add 3 2/5 and 2 3/4
Convert into improper fractions:
3 2/5 = (3 × 5 + 2) /5 = 17/5
2 3/4 = (2 × 4 + 3)/4 = 11/4
LCM of 4 and 5 is 20
Now, convert the fractions to have the same denominator, 20
17/5 = (17 × 4) / (5 × 4) = 68/20
11/4 = (11 × 5)/ (4 × 5) = 55/20
Add the numerators:
(68 + 55)/ 20 = 123/20
Convert to a mixed fraction:
123/20 = 6 3/20
Solving unlike fractions helps students develop problem-solving skills. Let’s look at a few real-life applications with unlike denominators:
Students often make errors when solving fractions with unlike denominators. Here are a few common mistakes and the ways to avoid them:
Find the sum of 2/7 and 4/5
The sum is 38/ 35, which equals 1 335.
To find the sum, we first determine their LCM.
Since the LCM of 7 and 5 is 35,
We convert 2/7 to make the denominator 35:
2/7 = (2 × 5) / (7 × 5) = 10 / 35
Convert 4/5 to make the denominator 35:
4/5 = (4 × 7) / (5 × 7) = 28/35
Now, add the numerators:
10/35 + 28/35 = (10 + 28)/35 = 38/35
As a final step, convert the fraction to a mixed number:
38/ 35 = 1 335
Add 5/12 + 3/8
19/24
We first find the LCM of the denominators 12 and 8, which is 24.
Then convert the fractions to have a denominator of 24:
5/12 = (5 × 2)/ (12 × 2) = 10/24
3/8 = (3 × 3)/ (8 × 3) = 9/24
Now, add the numerators:
10/24 + 9/24 = 19/24
Lena studies 5/9 of an hour in the morning and 7/12 of an hour in the evening. How many hours does she study in total?
1 5/36 hours.
Find the LCM of denominators 9 and 12, which is 36.
Then convert the fractions to have a denominator of 36:
5/9 = (5 × 4)/ (9 × 4) = 20/36
7/12 = (7 × 3)/(12 × 3) = 21/36
Now, add the numerators:
20/36 + 21/36 = 41/36
Convert to a mixed fraction:
41/36 = 1 5/36
Therefore, Lena studies 1 5/36 hours in total.
John ran 3/5 of a mile in the morning and 4/7 of a mile in the evening. How much did he run in total?
John ran 1635 miles in total.
To find the total distance, we need to find the sum of the fractions 3/5 and 4/7.
The LCM of 5 and 7 = 35
Convert fractions to make their denominators the same:
Convert 3/5:
3/5 = (3 × 7)/ (5 × 7) = 21/35
4/7 = (4 × 5)/ (7 × 5) = 20/35
Add the numerators:
21/35 + 20/35 = 41/35
Convert to a mixed fraction:
41/35 = 1635
Therefore, John ran 1635 miles in total.
A water tank contains 4/9 of its capacity filled with water. A pipe adds another 2/5 of the tank's capacity. What fraction of the tank is filled now?
The tank is now 38/45 full.
We find the total fraction of the tank that is filled by adding 4/9 and 2/5.
LCM of the denominators 9 and 5 is 45
Convert fractions to make their denominators 45:
Convert 4/9: (4 × 5)/ (9 × 5) = 20/45
Convert 2/5: (2 × 9)/ (5 × 9) = 18/45
Now, add the fractions:
20/45 + 18/45 = 38/45
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
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