Adding Fractions Calculator

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.

Results

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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Fraction Values Compared

Frequently Asked Questions

How do you add fractions with unlike denominators?

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).

What is the formula for adding two fractions?

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.

How do you add fractions with the same denominator?

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.

Can this calculator handle negative fractions?

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.

What is a mixed number and how is it shown?

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.

What is the Least Common Denominator (LCD)?

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.

Can I add more than two fractions?

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.

How do I simplify a fraction to its lowest terms?

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.

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