Add, subtract, multiply, and divide fractions with step-by-step solutions and simplified results.
Step-by-step:
1/2 + 1/3
= (1×3 + 1×2) / (2×3)
= 5/6
Enter fractions like "1/2", negative fractions like "-3/4", mixed numbers like "2 1/3", whole numbers, or decimals such as "0.25". Choose the operation and the result is shown in lowest terms, as a mixed number, and as a decimal — with step-by-step working.
Addition: a/b + c/d = (a×d + c×b) / (b×d)
Subtraction: a/b − c/d = (a×d − c×b) / (b×d)
Multiplication: a/b × c/d = (a×c) / (b×d)
Division: a/b ÷ c/d = (a×d) / (b×c), where c ≠ 0
The result is reduced by dividing the numerator and denominator by their greatest common divisor (GCD).
Divide both numerator and denominator by their Greatest Common Divisor (GCD). This calculator simplifies results automatically.
Type the whole number, a space, then the fraction — for example 2 1/3. For a negative mixed number type -2 1/3, which means −(2 + 1/3).
Division by zero is undefined, so a fraction such as 3/0 has no value. The calculator will flag it as an error.
To add or subtract fractions, you need a common denominator. Find the Least Common Multiple (LCM) of both denominators, convert each fraction, then add or subtract the numerators. For example: 1/3 + 1/4 → 4/12 + 3/12 = 7/12. This calculator performs these steps automatically and simplifies the result.
Did you know?
The fraction 1/7 produces the repeating decimal 0.142857142857... and if you multiply 142,857 by 2, 3, 4, 5, or 6, you get the same digits in a different cyclic order.
Fractions have been used since ancient Egypt around 1800 BCE. The Egyptians primarily used unit fractions (1/n) and had special symbols for common fractions. The modern fraction notation with a horizontal bar (vinculum) was introduced by Arab mathematicians and popularized in Europe by Fibonacci in his 1202 book Liber Abaci.
Every rational number can be expressed as a fraction of two integers. Irrational numbers like π and √2 cannot be expressed as fractions.
The ancient Egyptians could only use unit fractions (like 1/2, 1/3, 1/7) and had to express other fractions as sums of unit fractions.
The fraction bar also serves as a division symbol — 3/4 literally means "3 divided by 4."
Finding the Greatest Common Divisor (GCD) to simplify fractions uses an algorithm first described by Euclid around 300 BCE.