Why do I need a common denominator to add fractions but not to multiply them?

Addition combines parts of the same whole, so the pieces need to be the same size (same denominator) before combining. Multiplication scales quantities directly, so numerators and denominators can multiply straight across without matching first.

How do I simplify a fraction to lowest terms?

Divide both the numerator and denominator by their greatest common factor. For example, 8/12 has a greatest common factor of 4, so dividing both by 4 gives 2/3.

How do I divide fractions?

Flip the second fraction to its reciprocal, then multiply straight across. Dividing by 1/4 is the same as multiplying by 4/1.

Fraction Calculator

Add, subtract, multiply, or divide fractions — with full step-by-step working shown.

How to use

Arithmetic — Enter numerator and denominator for each fraction, choose an operation, and click Calculate.
Step-by-step working is shown below the result so you can follow the math.
Simplify — Enter any fraction and reduce it to its lowest terms using the GCD.
Convert — Convert a fraction to a decimal/percentage, or turn a decimal into a fraction.
Results include the simplified fraction, decimal equivalent, and mixed number where applicable.

About this Fraction Calculator

Fraction arithmetic follows different rules depending on the operation — adding and subtracting require a common denominator, while multiplying and dividing do not, which is where most manual mistakes happen.

The four operations

Addition/subtraction: convert both fractions to a common denominator first, then add or subtract the numerators. 1/4 + 1/6 becomes 3/12 + 2/12 = 5/12.
Multiplication: multiply numerators together and denominators together directly — no common denominator needed. 2/3 × 3/4 = 6/12, which simplifies to 1/2.
Division: flip the second fraction (its reciprocal) and multiply. 1/2 ÷ 1/4 becomes 1/2 × 4/1 = 4/2 = 2.

Simplifying to lowest terms

A fraction is in lowest terms when the numerator and denominator share no common factor other than 1. 6/12 simplifies to 1/2 by dividing both numbers by their greatest common factor (6). Calculators and worksheets almost always expect answers in simplified form.

Where fraction math shows up outside the classroom

Cooking recipes scaled up or down (3/4 cup × 1.5), construction and woodworking measurements (adding 3/8 in and 5/16 in), and splitting quantities in recipes or materials all rely on the same fraction arithmetic taught in school, just applied to real physical quantities instead of homework problems.