Fraction Calculator

Add, subtract, multiply, or divide two fractions with step-by-step solutions and simplified results.

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Enter Two Fractions

Operation

First Fraction

Second Fraction

Simplified Result

—

Decimal

—

Exact value

Mixed Number

—

Whole + fraction

GCD Used

—

To simplify

Unsimplified

—

Before reduction

Step-by-Step Solution

Add, subtract, multiply, or divide two fractions and see the simplified result, its decimal equivalent, and the full step-by-step working.

How It Works

How Fraction Calculator Works

To add or subtract two fractions, the calculator first finds the least common denominator (LCD) — the lowest common multiple of the two denominators — then scales each numerator to match that shared denominator before combining them.

Multiplication is more direct: numerators multiply together and denominators multiply together. Division is handled by multiplying the first fraction by the reciprocal (flipped version) of the second, which is mathematically equivalent to dividing.

Whatever the operation, the raw result is reduced to lowest terms by dividing both numerator and denominator by their greatest common divisor (GCD), and is also shown as a decimal and as a mixed number for easy comparison.

Worked Example

See It In Action

Adding the default fractions 1/2 + 1/3: the LCD of 2 and 3 is 6, so 1/2 becomes 3/6 and 1/3 becomes 2/6. Adding gives 3/6 + 2/6 = 5/6. Since GCD(5, 6) = 1, the fraction is already in simplest form, equal to 0.833333 as a decimal.

Real-World Use Cases

Who Uses Fraction Calculator and Why

Scaling a recipe up or down when ingredient amounts are given as fractions (like doubling 2/3 cup).
Combining measurements in a woodworking or sewing project where cut lengths are marked in fractions of an inch.
Checking algebra or arithmetic homework that requires showing the least common denominator step.
Converting an awkward improper fraction result into a mixed number for a cleaner final answer.

Common Mistakes

Mistakes to Avoid

Adding numerators and denominators straight across (like 1/2 + 1/3 = 2/5) instead of first converting both fractions to a shared denominator.
Entering 0 as a denominator, which the calculator flags as an error since division by zero is undefined.
Forgetting that multiplication and division of fractions don't need a common denominator at all — only addition and subtraction do.

Pro Tips

Tips for Best Results

Use the decimal equivalent shown alongside the fraction result as a quick sanity check that your answer is in the right ballpark.
If your result is an improper fraction larger than one whole, check the Mixed Number card for the more readable equivalent.

Troubleshooting

Fixing Common Problems

The calculator shows an error instead of a result. — Check that you haven't entered 0 as either denominator — a fraction with a zero denominator has no defined value.

Glossary

Terms Explained

Least common denominator (LCD): The smallest number both fractions' denominators divide into evenly, used to make two fractions directly comparable before adding or subtracting.

Greatest common divisor (GCD): The largest number that divides both the numerator and denominator evenly, used to reduce a fraction to its simplest form.

FAQ

Frequently Asked Questions

Why do fractions need a common denominator to be added?

Fractions represent parts of a whole divided into different-sized pieces. Converting both fractions to the same denominator makes the "pieces" the same size, so the numerators can be added or subtracted directly and meaningfully.

How is a fraction simplified to lowest terms?

The calculator divides both the numerator and denominator by their greatest common divisor (GCD). For example, 6/8 has a GCD of 2, so dividing both by 2 gives the simplified fraction 3/4.

What happens if I enter 0 as a denominator?

The calculator shows an error, since a fraction with a denominator of zero is mathematically undefined — division by zero has no defined value.

Can I convert the result into a mixed number?

Yes — the "Mixed Number" result card automatically converts any result larger than one whole into a whole number plus a remaining fraction, such as showing 7/6 as 1 1/6.