Finance Health Math Other Blog
Login

Fraction Calculator

Simplify & Solve Fraction Operations

Enter your fractions and choose an operation to get the simplified result.

Format: numerator/denominator or whole number
Format: numerator/denominator or whole number

Calculation Result

Enter your fractions to see the result here.

Mastering Fractions: A Complete Guide

What is a Fraction?

A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.

A common or simple fraction consists of a numerator displayed above a line (or before a slash), and a non-zero denominator, displayed below (or after) that line.

How to Perform Fraction Operations

Addition & Subtraction

To add or subtract fractions, they must have a common denominator. If they don't, find the Least Common Multiple (LCM) of the denominators.

a/b ± c/d = (ad ± bc) / bd
Multiplication

Simply multiply the numerators together and the denominators together. No common denominator is needed.

a/b × c/d = (a × c) / (b × d)
Division

To divide by a fraction, multiply by its reciprocal (flip the second fraction).

a/b ÷ c/d = a/b × d/c = (ad) / (bc)
Simplification

Divide both the numerator and denominator by their Greatest Common Divisor (GCD) to reach the simplest form.

Types of Fractions

  • Proper Fraction: The numerator is smaller than the denominator (e.g., 3/4).
  • Improper Fraction: The numerator is greater than or equal to the denominator (e.g., 5/2).
  • Mixed Number: A whole number and a proper fraction combined (e.g., 2 1/2).
  • Equivalent Fractions: Fractions that have the same value (e.g., 1/2 and 2/4).

Converting Fractions to Decimals

To convert a fraction to a decimal, simply divide the numerator by the denominator. For example, 1/4 becomes 1 ÷ 4 = 0.25. Some fractions result in repeating decimals, like 1/3 = 0.333...

Why Use Our Fraction Calculator?

Manual fraction math can be tedious and prone to errors, especially when finding common denominators or simplifying large numbers. Our tool uses Python's fractions module to ensure exact precision and automatic simplification, giving you the most accurate result every time.

Frequently Asked Questions

Currently, our calculator accepts simple fractions (a/b) or whole numbers. To enter a mixed number like 2 1/2, convert it to an improper fraction first (5/2).

A reciprocal is what you get when you flip a fraction. The reciprocal of 3/4 is 4/3. Multiplying a number by its reciprocal always equals 1.

No, the denominator of a fraction can never be zero because division by zero is undefined in mathematics.

To simplify a fraction, find the largest number that divides both the numerator and denominator evenly (the GCD) and divide both by that number. Our calculator does this automatically!

The LCD is the smallest number that is a multiple of all the denominators in a set of fractions. It is used to make addition and subtraction possible.

Fraction Tips

  • Multiply across for multiplication.
  • Keep-Change-Flip for division.
  • Common denominator for +/-.
  • Whole numbers have a denominator of 1.
  • Always simplify your final answer.

Related Tools

Percentage Calculator Scientific Calculator All Math Tools GPA Calculator
Learn More

Fraction Mathematics Resources:

Disclaimer

This tool is designed for educational purposes. While we use high-precision libraries, always verify critical mathematical results for professional or engineering applications.