Use our free Adding Three Fractions with Different Denominators Calculator to quickly find the sum of any three fractions. This powerful tool provides the answer in standard, simplified, and mixed number formats, making complex fraction addition simple and accurate. Perfect for homework, exam preparation, or professional calculations.
Formula:
To add three fractions with different denominators (let's say a/b, c/d, and e/f), the general approach is:
Step 1: Find a Common Denominator. Multiply the denominators together (b × d × f) to get a common multiple. This will be the new denominator for all three fractions.
Step 2: Convert Each Fraction. Rewrite each fraction with the common denominator:
- a/b becomes (a × d × f) / (b × d × f)
- c/d becomes (c × b × f) / (d × b × f)
- e/f becomes (e × b × d) / (f × b × d)
Step 3: Add the New Numerators. Sum the numerators of the converted fractions:
Sum = (a × d × f) + (c × b × f) + (e × b × d)
Step 4: Form the Resulting Fraction. The sum will be: ((a × d × f) + (c × b × f) + (e × b × d)) / (b × d × f)
Step 5: Simplify. Reduce the resulting fraction to its simplest form and convert to a mixed number if it's an improper fraction.
Where:
- a, c, e are the numerators (top numbers) of the three fractions.
- b, d, f are the denominators (bottom numbers) of the three fractions.