Adding Fractions With Unlike Denominators
2026-02-28 17:52 Diff
https://brightchamps.com/en-us/math/numbers/adding-fractions-with-unlike-denominators

Let’s understand these steps 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:
 

Step 1: We first find the LCM of 4 and 8:

  •  LCM = 8

Step 2: Now, we make the denominators equal by converting them to 8:

  • Since 5/8 already has 8 as the denominator, we will only convert the denominator of 3/4.
     

Step 3:  Determine what, when multiplied by 4, gives 8.

Step 4: Multiply by 2 with both the numerator and denominator, resulting 6/8.


Step 5:  Now add the numerators, since the denominators are the same. 

  • 3/4 + 5/8 = 6/8 + 5/8 = (6 + 5) / 8 = 11/8.

We can express it as a mixed fraction of \(1^3/_8\).

Adding 3 Fractions with Different Denominators


Similarly, we add three fractions with different denominators:


Add 2/3 + 4/7 + 5/7


Solution: 

Step1: The LCM of 3 and 7 is 21


Step 2: Now, we will multiply the fractions by appropriate factors that give 21 as the denominator:

  • 2/3 → (2 × 7)/ (3 × 7) = 14/21
  • 4/7 → (4 × 3) / (7 × 3) = 12/21
  • 5/7 → (5 × 3) / (7 × 3) = 15/21

Step 3: Add the numerators:

  • (14 + 12 + 15) / 21 = 41/21


Step 4: Convert to a mixed fraction:

  • 41/21 = \(1^{20}/_{21}\)

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 \(2^{3}/_{4}\)

Step 1: 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

Step 2: 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

Step 3: Add the numerators:


(68 + 55)/ 20 = 123/20

Step 4: Convert to a mixed fraction:


123/20 = \(6^{3}/_{20}\)