To add fractions with unlike denominators, you first need to find a common denominator. This allows you to add the numerators together.
Steps to Add Fractions with Unlike Denominators
Here's a breakdown of the process:
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Find a Common Denominator: The most common approach is to find the least common multiple (LCM) of the denominators. This LCM becomes the common denominator.
- Example: To add 1/2 and 1/3, the denominators are 2 and 3. The least common multiple of 2 and 3 is 6.
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Rewrite the Fractions: Convert each fraction into an equivalent fraction with the common denominator.
- Example:
- 1/2 becomes 3/6 (because 1/2 * 3/3 = 3/6)
- 1/3 becomes 2/6 (because 1/3 * 2/2 = 2/6)
- Example:
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Add the Numerators: Once the fractions have the same denominator, you can add the numerators. The denominator remains the same.
- Example: 3/6 + 2/6 = (3+2)/6 = 5/6
Example Table
| Fraction 1 | Fraction 2 | Unlike Denominators | Least Common Multiple (LCM) | Fraction 1 (Rewritten) | Fraction 2 (Rewritten) | Sum |
|---|---|---|---|---|---|---|
| 1/2 | 1/3 | 2, 3 | 6 | 3/6 | 2/6 | 5/6 |
| 1/4 | 2/5 | 4, 5 | 20 | 5/20 | 8/20 | 13/20 |
| 3/8 | 1/6 | 8, 6 | 24 | 9/24 | 4/24 | 13/24 |
In summary, to add fractions like 1/2 and 1/3, you find a common denominator (like 6), rewrite the fractions as 3/6 and 2/6 respectively, and then add the numerators, resulting in 5/6.
