Math

Fraction Calculator — Free 2026

Add, subtract, multiply, and divide fractions instantly. Get the simplified result, mixed number, and decimal equivalent in one click.

Fraction A — Numerator Please enter a valid integer.

Fraction A — Denominator Please enter a valid non-zero integer.

Operation

Fraction B — Numerator Please enter a valid integer.

Fraction B — Denominator Please enter a valid non-zero integer.

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Result

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Simplified

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Mixed Number

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Decimal

How It Works

Enter Fraction A
Choose an operation
Enter Fraction B
Read your results

Understanding Fractions and How to Calculate Them

Fractions represent parts of a whole. Written as one number over another — like 3/4 — the top number (numerator) tells you how many parts you have, while the bottom number (denominator) tells you how many equal parts the whole is divided into. Fractions appear everywhere in daily life, from cooking recipes and construction measurements to financial calculations and probability. Despite being introduced early in school, fraction arithmetic remains one of the areas where people most commonly reach for a calculator, especially when the denominators differ.

Adding and Subtracting Fractions

When fractions share the same denominator, adding or subtracting them is simple: keep the denominator and add or subtract the numerators. For example, 2/7 + 3/7 = 5/7. When the denominators differ, you need a common denominator. The most reliable method is cross-multiplication: for a/b + c/d, compute (a*d + c*b) / (b*d). This always works, though the result may need simplifying. For instance, 3/4 + 1/2 becomes (3*2 + 1*4) / (4*2) = 10/8, which simplifies to 5/4, or 1 1/4 as a mixed number.

Subtraction follows the same pattern with a minus sign instead. The key mistake to avoid is subtracting denominators — a common error that produces incorrect results. Always find a common denominator first, then subtract only the numerators.

Multiplying and Dividing Fractions

Multiplication is the simplest fraction operation: multiply the numerators together and multiply the denominators together. So 3/4 * 1/2 = 3/8. No common denominator is needed. Division requires one extra step — flip the second fraction (take its reciprocal) and multiply. Dividing 3/4 by 1/2 becomes 3/4 * 2/1 = 6/4 = 3/2. This "keep, change, flip" rule is perhaps the most memorable fraction shortcut taught in schools.

Simplifying and Converting Fractions

A fraction is in simplest form when the numerator and denominator share no common factor other than 1. To simplify, find the greatest common divisor (GCD) of both numbers and divide each by it. For example, 10/8 has a GCD of 2, so it simplifies to 5/4. This calculator handles simplification automatically using the Euclidean algorithm, which efficiently finds the GCD of any two integers.

An improper fraction — where the numerator exceeds the denominator — can also be expressed as a mixed number. Divide the numerator by the denominator: the quotient becomes the whole number, and the remainder becomes the new numerator. So 5/4 = 1 whole with 1 remaining, giving 1 1/4. Mixed numbers are often more intuitive in everyday contexts, like saying "one and a quarter cups" rather than "five-quarters cups."

For related calculations, try our percentage calculator to convert fractions to percentages, or use the ROI calculator when working with fractional returns on investments.

Common Fraction Mistakes to Avoid

The most frequent error is adding numerators and denominators separately (e.g., claiming 1/2 + 1/3 = 2/5). This is incorrect — you must find a common denominator first. Another common mistake is forgetting to simplify the final result, or incorrectly cancelling terms during multiplication. When dividing, people sometimes flip the wrong fraction. Remember: always flip the second fraction (the divisor), never the first. This calculator eliminates these errors by performing each step automatically and showing you the simplified result, mixed number, and decimal all at once.

Frequently Asked Questions

How do you add fractions with different denominators?

To add fractions with different denominators, find a common denominator by multiplying the two denominators together (or finding the LCD). Cross-multiply each numerator by the other fraction's denominator, add the results, and place the sum over the common denominator. For example, 3/4 + 1/2 = (3x2 + 1x4) / (4x2) = 10/8 = 5/4.

How do you multiply fractions?

Multiplying fractions is straightforward: multiply the numerators together and multiply the denominators together. For example, 3/4 x 1/2 = (3x1) / (4x2) = 3/8. Then simplify by dividing both numerator and denominator by their greatest common divisor if possible.

How do you divide fractions?

To divide fractions, multiply the first fraction by the reciprocal (flipped version) of the second fraction. For example, 3/4 divided by 1/2 = 3/4 x 2/1 = 6/4 = 3/2. This "keep, change, flip" method works for all fraction division problems.

What is a mixed number and how do I convert one?

A mixed number combines a whole number with a proper fraction, like 1 1/4. To convert an improper fraction (where the numerator is larger than the denominator) to a mixed number, divide the numerator by the denominator. The quotient is the whole number part, and the remainder over the original denominator is the fraction part. For example, 5/4 = 1 remainder 1, so 5/4 = 1 1/4.

Can this calculator handle negative fractions?

Yes. You can enter negative numbers for any numerator or denominator. The calculator will correctly handle the signs throughout the operation and display the result with the negative sign on the numerator, following standard mathematical convention.