Fraction Calculator

Understanding Fraction Arithmetic Rules

A fraction represents a part of a whole, expressed as a numerator (top number) over a denominator (bottom number). Understanding the basic rules of fraction arithmetic simplifies algebra and real-world measurement calculations.

The Four Basic Fraction Formulas

Addition & Subtraction

(a/b) ± (c/d) = (ad ± bc) / bd

Multiplication & Division

(a/b) × (c/d) = ac / bd | (a/b) ÷ (c/d) = ad / bc

Step-by-Step Addition Walkthrough

Let's add 1/4 and 2/3:

Find the Least Common Denominator (LCD): LCD of 4 and 3 is 12.
Convert fractions: 1/4 = 3/12 and 2/3 = 8/12.
Add numerators: 3 + 8 = 11.
Combine over LCD: 11/12.

Frequently Asked Questions

What is the difference between an improper fraction and a mixed number?

An improper fraction has a numerator greater than or equal to its denominator (e.g., 7/4). A mixed number combines a whole integer with a proper fraction (e.g., 1 ¾).

How do you reduce a fraction to lowest terms?

Divide both the numerator and denominator by their Greatest Common Divisor (GCD). For example, to reduce 8/12, divide both numbers by GCD(8, 12) = 4 to get 2/3.

About This Calculator & Guide

About the Fraction— Add, Subtract, Multiply & Divide Fractions Calculator

The Fraction— Add, Subtract, Multiply & Divide Fractions Calculator is a specialized online utility designed to help you free online fraction calculator. add, subtract, multiply, divide, and reduce fractions to simplest form with step-by-step math steps. It performs calculations in real-time to provide immediate, reliable estimates for study, work, or daily tasks.

How to Use

Simply enter your parameters in the input fields of the calculator widget above. The tool evaluates the inputs instantly and displays the results in real-time. You can modify any value to check alternate scenarios and compare figures dynamically.

Data Privacy & Safety

All calculations are executed locally within your web browser. No inputs are sent to our servers or stored externally, ensuring your personal and financial details remain completely private and secure.

Frequently Asked Questions

How do you add or subtract fractions with different denominators?+

To add or subtract fractions with unlike denominators, find the Least Common Denominator (LCD), convert each fraction into an equivalent fraction with that LCD, add or subtract the numerators, and simplify to lowest terms.

How do you multiply two fractions?+

To multiply fractions, multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator: (a/b) × (c/d) = (a×c)/(b×d).

How do you divide one fraction by another?+

To divide fractions, multiply the first fraction by the reciprocal (flip) of the second fraction: (a/b) ÷ (c/d) = (a/b) × (d/c) = (a×d)/(b×c).