Fraction Operations Calculator

Perform basic arithmetic operations like addition, subtraction, multiplication, and division on two fractions with this easy-to-use online calculator. Get your results simplified to their lowest terms.

Numerator 1

Enter the top number of the first fraction.

Denominator 1

Enter the bottom number of the first fraction (cannot be zero).

Operation

Choose the arithmetic operation to perform.

Numerator 2

Enter the top number of the second fraction.

Denominator 2

Enter the bottom number of the second fraction (cannot be zero).

How it works

Perform basic arithmetic operations like addition, subtraction, multiplication, and division on two fractions with this easy-to-use online calculator. Get your results simplified to their lowest terms.

The Formula

Addition: a/b + c/d = (ad + bc) / bd
Subtraction: a/b - c/d = (ad - bc) / bd
Multiplication: a/b × c/d = ac / bd
Division: a/b ÷ c/d = ad / bc

Worked Example

Example: Adding 1/2 and 3/4
To add 1/2 and 3/4, input 1 as Numerator 1, 2 as Denominator 1, select 'Add', then 3 as Numerator 2 and 4 as Denominator 2. The calculator will show the steps and the simplified result: 5/4, which is 1 1/4 as a mixed number.

Tips, Assumptions & Limitations

Always simplify your final fraction to its lowest terms.
Ensure denominators are not zero.
This calculator handles both proper and improper fractions.
For division, the second numerator cannot be zero.

FAQ

Fraction operations refer to the basic arithmetic calculations—addition, subtraction, multiplication, and division—performed on two or more fractions. These operations follow specific rules to combine or separate fractional quantities.

To add or subtract fractions, they must have a common denominator. If they don't, you find the least common multiple (LCM) of the denominators and convert the fractions to equivalent ones with this common denominator. Then, you add or subtract the numerators and keep the common denominator. Finally, simplify the result.

Multiplying fractions is straightforward: multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. Always simplify the resulting fraction to its lowest terms.

To divide fractions, you 'invert and multiply.' This means you take the reciprocal of the second fraction (flip its numerator and denominator) and then multiply it by the first fraction. Simplify the result if possible.

Yes, this calculator can handle improper fractions (where the numerator is greater than or equal to the denominator). While it doesn't directly accept mixed numbers as input, you can convert them to improper fractions first (e.g., 1 1/2 becomes 3/2) and then input them. The calculator will also output mixed numbers when appropriate.