Adding Fractions (like or unlike denominators)

The following examples shows how to add fractions with like denominators and unlike denominators. Scroll down the page for more examples and solutions.

Adding Fractions with Common or Like Denominators

When we add fractions that have the same, or common denominators, we add only the numerators. The denominators stay the same.

Example

 

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Adding Fractions With Uncommon or Unlike Denominators

To add fractions with uncommon denominators, we need to change the fractions to equivalent fractions with common denominators before we find the sum.

First, we would need to find the least common denominator (LCD), which is the LCM of the denominators.

Next, we write equivalent fractions using the least common denominator. Then, we proceed to add as before.

Example:

Evaluate

Solution:

Step 1: Find the LCD or LCM of 2 and 5

Multiples of 2: 2, 4, 6, 8, 10, 12

Multiples of 5: 5, 10, 15

The LCD or the Least Common Multiple of 2 and 5 is 10

Step 2: Write both fractions and as equivalent fractions with a common denominator of 10.

 

Step 3: Add the 2 equivalent fractions.

The following video shows more examples of adding fractions with uncommon or unlike denominators.

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