Enter up to three fractions — each with a numerator and denominator — and the Adding Fractions Calculator returns the simplified sum as both a reduced fraction and a mixed number. Works with unlike denominators by finding the least common denominator automatically.
Sum (Simplified Fraction)
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Result Numerator
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Result Denominator
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Mixed Number
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Least Common Denominator (LCD)
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Decimal Equivalent
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To add fractions with unlike denominators, first find the Least Common Denominator (LCD) of all fractions involved. Convert each fraction to an equivalent fraction with the LCD as the denominator, then add the numerators together. Finally, simplify the resulting fraction by dividing both numerator and denominator by their Greatest Common Factor (GCF).
The formula for adding two fractions a/b + c/d is: (a×d + c×b) / (b×d). This gives you a common denominator of b×d. The result can then be reduced to its simplest form by dividing the numerator and denominator by their GCF.
When fractions share the same denominator, simply add the numerators and keep the denominator unchanged. For example, 2/7 + 3/7 = 5/7. Then check if the result can be simplified further.
Yes. You can enter a negative numerator or negative denominator to represent a negative fraction. For example, entering numerator -1 and denominator 4 represents -1/4. The calculator will correctly handle the arithmetic and simplify the result.
A mixed number combines a whole number and a proper fraction — for example, 1 and 1/3 instead of 4/3. When the sum of your fractions is an improper fraction (numerator larger than denominator), the calculator converts it to a mixed number for easy reading.
The LCD is the smallest number that all denominators divide into evenly. It is the same as the Least Common Multiple (LCM) of the denominators. Using the LCD keeps numbers smaller and makes simplification easier compared to just multiplying denominators together.
Yes — this calculator supports adding up to three fractions at once. Enable the optional third fraction field and enter its numerator and denominator. The calculator finds the LCD of all three denominators and computes the fully simplified sum.
To reduce a fraction to lowest terms, find the Greatest Common Factor (GCF) of the numerator and denominator, then divide both by that number. For example, 14/24 simplifies to 7/12 because GCF(14, 24) = 2. This calculator does this step automatically.