Back to Math Calculators

Fraction Calculator

All-in-one fraction tool for arithmetic, simplification, mixed numbers & decimal conversion.

Fraction Addition / Subtraction / Multiplication / Division

=
?
?

📖 Fraction Calculator Complete User Guide

This all-in-one fraction calculator supports six core functional modules, covering fraction arithmetic, simplification, mixed number conversion, decimal bidirectional conversion, and ultra-large integer fraction computation. All outputs are auto-reduced to lowest terms with GCD algorithm, and returns mixed number, improper fraction and decimal results simultaneously.

1. Module Tab Button Introduction

Tab Name Core Function & Usage Scenario
Basic Arithmetic Standard fraction + − × ÷ for two simple proper/improper fractions; auto simplify final output
Mixed Numbers Compute arithmetic with mixed numbers (whole number + fraction), convert result to mixed form automatically
Simplify Fraction Input any unreduced fraction, divide numerator & denominator by GCD to get lowest terms
Decimal → Fraction Convert finite positive/negative decimal value to reduced fraction and mixed number
Fraction → Decimal Execute long division to convert fraction to decimal value, show repeating decimal hint if exists
Big Number Fraction Support arbitrary-length large integer inputs without overflow, for ultra-big fraction operation

2. Functional Operation Button Description

Button Function Definition Operation Example
Calculate / Convert / Simplify Trigger computation logic, validate input, output reduced fraction & auxiliary data Input 3/4 + 1/6 → click Calculate → output 11/12
Clear Reset all input boxes and result display of current module to empty state Clear all numerator, denominator & result fields
Operator Dropdown (+ − × ÷) Select mathematical operation between two fractions Select × to compute fraction multiplication
Numerator Input Box Upper input field, represents the top value of fraction (integer, positive/negative) Fraction 5/7 → numerator = 5
Denominator Input Box Lower input field, represents bottom value of fraction; CANNOT be zero Fraction 5/7 → denominator = 7
Mixed Whole Number Input Integer part before fraction for mixed number calculation, supports negative value -2 3/4 → whole number input = -2

3. Core Fraction Mathematical Rules & Formulas

Addition Formula

a/b + c/d = (a×d + c×b) / (b×d)

Example: 3/4 + 1/6 = (18+4)/24 = 22/24 = 11/12

Subtraction Formula

a/b − c/d = (a×d − c×b) / (b×d)

Example: 3/4 − 1/6 = (18−4)/24 = 14/24 = 7/12

Multiplication Formula

a/b × c/d = (a×c) / (b×d)

Example: 3/4 × 1/6 = 3/24 = 1/8

Division Formula

a/b ÷ c/d = a/b × d/c = (a×d) / (b×c)

Example: 3/4 ÷ 1/6 = 18/4 = 9/2

Simplification Rule

Divide numerator and denominator by GCD (Greatest Common Divisor) of both values to get lowest terms.

Example: 220/440, GCD=220 → simplified to 1/2

Decimal To Fraction Conversion Rule

Count decimal digits N, use 10^N as denominator, remove decimal point as numerator, then reduce fraction.

Example: 1.375 has 3 decimals → 1375/1000, GCD=125 → 11/8

📐 Fraction Basic Mathematical Definition

A fraction represents a portion of a whole integer value, split into equal parts. A fraction consists of two core components separated by a dividing line:

Take fraction 3/8 as an example: The whole unit is split into 8 identical slices, and we take 3 slices out of the full set. If 3 slices are eaten, the remaining portion is 5/8.

Fraction Type Classification

❓ Common Input Error Troubleshooting