Fraction Calculator

What Is a Fraction?

A fraction is a way of writing a part of a whole. It has two numbers: the numerator (top) tells you how many parts you have, and the denominator (bottom) tells you how many equal parts the whole is divided into. In 3/4, the whole is split into 4 equal parts and you have 3 of them. A fraction calculator takes the fiddly arithmetic of fractions — finding common denominators, reducing to lowest terms, converting to mixed numbers — and does it instantly and without errors.

Fractions show up everywhere in daily life: cooking measurements, construction dimensions, discounts, and school mathematics. Because the rules for adding or dividing fractions are easy to mix up, even small hand calculations are a common source of mistakes.

How Fraction Math Works

Adding and subtracting fractions

You can only add or subtract fractions directly when they share the same denominator. The general rule is:

a/b + c/d = (a×d + c×b) / (b×d)

In words: multiply each numerator by the other fraction's denominator, add the results, and place the total over the product of the denominators. Subtraction works exactly the same way with a minus sign. For example, 1/4 + 1/6 = (6 + 4)/24 = 10/24 = 5/12.

Multiplying fractions

Multiplication is simpler — no common denominator is needed:

a/b × c/d = (a×c) / (b×d)

Just multiply straight across. Example: 2/3 × 3/5 = 6/15 = 2/5.

Dividing fractions

To divide, flip the second fraction (take its reciprocal) and multiply:

a/b ÷ c/d = (a×d) / (b×c)

Example: 1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6 = 2/3.

Simplifying fractions

A fraction is in simplest form when the numerator and denominator share no common factor other than 1. Divide both by their greatest common divisor (GCD). For 10/24, the GCD of 10 and 24 is 2, so 10/24 simplifies to 5/12.

How to Use This Calculator

1. Enter the two fractions (each numerator and denominator).
2. Choose the operation: add, subtract, multiply, or divide.
3. The result appears automatically — already simplified, and shown as a mixed number where appropriate.

Worked Example

Add 2/3 and 3/4:

1. Common denominator: 3 × 4 = 12.
2. Convert: 2/3 = 8/12 and 3/4 = 9/12.
3. Add the numerators: 8/12 + 9/12 = 17/12.
4. Simplify: 17 and 12 share no common factor, so the answer is 17/12, or 1 5/12 as a mixed number.

Tips

• Always reduce your final answer to lowest terms — teachers and exams expect it.
• When adding or subtracting, double-check that you converted to a common denominator first; adding numerators over different denominators is the most common fraction mistake.
• For division, remember "keep, change, flip": keep the first fraction, change ÷ to ×, flip the second fraction.
• A negative sign belongs with the numerator by convention: −3/4 is written with the minus in front, not in the denominator.