Adding Fractions (with common or uncommon denominators)

Adding Fractions with Common Denominators

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

Example :

The following video gives more examples of adding fractions with common denominators.

Adding Fractions With Uncommon Denominators

To add fractions with uncommom denominators, we need to change the fractions to equivalent farctions 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 denominators.

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