Fraction Calculator

What are fractions?

A fraction represents a part of a whole, written as a numerator (top number) over a denominator (bottom number). The numerator tells how many parts you have, and the denominator tells how many equal parts the whole is divided into. Fractions are fundamental to mathematics and appear throughout daily life — in cooking recipes, measurements, financial calculations, and probability.

Proper fractions have a numerator smaller than the denominator (like 3/4). Improper fractions have a numerator larger than the denominator (like 7/4). Mixed numbers combine a whole number with a fraction (like 1 and 3/4). This calculator handles all three forms and converts between them automatically.

How to add fractions

To add fractions with different denominators, first find a common denominator — the simplest approach is to multiply the two denominators together. Then adjust each numerator by multiplying it by the other fraction's denominator. Add the adjusted numerators and place the sum over the common denominator. Finally, simplify by dividing both numerator and denominator by their greatest common divisor (GCD).

How to multiply fractions

Multiplication is simpler: multiply the numerators together and the denominators together. For example, 2/3 multiplied by 4/5 equals 8/15. Division works by multiplying by the reciprocal — to divide by a fraction, flip it and multiply. So 2/3 divided by 4/5 equals 2/3 multiplied by 5/4, which equals 10/12, simplified to 5/6.

How to use this tool

Enter two fractions using the numerator and denominator fields, select the operation (add, subtract, multiply, or divide), and the result appears instantly. The calculator automatically simplifies the result to its lowest terms and shows the step-by-step solution so you can learn the process.

Simplifying fractions

A fraction is in simplest form when the numerator and denominator share no common factors other than 1. To simplify, find the greatest common divisor (GCD) of both numbers and divide each by it. For example, 12/18 simplifies to 2/3 because the GCD of 12 and 18 is 6.

Practical tips

In cooking, fractions are everywhere — doubling a recipe that calls for 3/4 cup means calculating 3/4 multiplied by 2, which gives 3/2 or 1 and 1/2 cups. In construction, measurements are often in fractions of inches. Understanding how to add and subtract fractions quickly makes these everyday tasks much easier.

Frequently asked questions

What is the difference between a fraction and a decimal?

They are two ways to represent the same value. The fraction 3/4 equals the decimal 0.75. Some fractions produce terminating decimals (3/4 = 0.75), while others produce repeating decimals (1/3 = 0.333...). Fractions are exact, while decimal representations may require rounding.

Can I use negative numbers in fractions?

Yes. A negative fraction can have the minus sign on the numerator, the denominator, or in front of the fraction — all three representations are equivalent. By convention, the negative sign is usually placed on the numerator or in front of the fraction.