Fraction Calculator — All Types
Select a calculation type, enter your fractions, and get the answer with complete step-by-step working
a/b + c/d
a/b − c/d
a/b × c/d
a/b ÷ c/d
Reduce a/b
Fraction ↔ Decimal
Which is bigger?
and it will be reduced
to its simplest form.
Result Summary
More Useful Results
Visual Breakdown
Step-by-Step Working
What Is a Fraction?
The core concept behind fractions, types, and why they matter in everyday calculations
A fraction represents a part of a whole or, more generally, any number of equal parts. It consists of a numerator (the top number) and a denominator (the bottom number). The denominator tells you how many equal parts the whole is divided into; the numerator tells you how many of those parts you have.
For example, the fraction 3/4 means the whole is divided into 4 equal parts, and you have 3 of them. Fractions appear everywhere — from cooking recipes (½ cup of flour) to finance (¾ of a portfolio) to construction measurements.
Proper Fraction
Numerator is less than denominator. Value is between 0 and 1. Examples: 1/2, 3/4, 7/8.
Improper Fraction
Numerator is greater than or equal to denominator. Value ≥ 1. Examples: 5/3, 9/4, 7/7.
Mixed Number
A whole number combined with a proper fraction. Examples: 1¾, 2½, 3⅔. Can always be converted to an improper fraction.
Equivalent Fractions
Different fractions that represent the same value. 1/2 = 2/4 = 3/6 = 50/100. Multiplying or dividing both parts by the same number creates equivalents.
Fraction Formulas — Complete Reference
All fraction operation rules with worked examples
| Operation | Formula | Example | Result |
|---|---|---|---|
| Addition | a/b + c/d = (ad + bc) / bd | 1/3 + 1/4 | 7/12 |
| Subtraction | a/b − c/d = (ad − bc) / bd | 3/4 − 1/3 | 5/12 |
| Multiplication | a/b × c/d = (a×c) / (b×d) | 2/3 × 3/4 | 6/12 = 1/2 |
| Division | a/b ÷ c/d = (a×d) / (b×c) | 2/3 ÷ 4/5 | 10/12 = 5/6 |
| Simplify (GCD) | (a÷GCD) / (b÷GCD) | 12/18, GCD=6 | 2/3 |
| To Decimal | a ÷ b | 3/4 | 0.75 |
| To Mixed Number | ⌊a/b⌋ remainder (a mod b)/b | 7/3 | 2 1/3 |
How to Use This Calculator
Step-by-step guide to getting the most out of all 7 fraction tools
For Add / Subtract / Multiply / Divide: Select the operation, enter the numerator and denominator for each fraction, and click Calculate. The result is automatically simplified using the GCD. You can also switch to Mixed Number mode to input numbers like 1 3/4 directly.
For Simplify: Enter any fraction (e.g., 24/36) and the calculator finds the GCD and reduces it step by step.
For Convert: Switch between Fraction → Decimal and Decimal → Fraction. Decimal-to-fraction conversion shows the exact fraction (e.g., 0.125 = 1/8) using the GCD method.
For Compare: Enter two fractions to find which is greater, lesser, or if they are equal. Results show cross-multiplication working.
Frequently Asked Questions
Common questions about fractions and how to solve them