Fraction Calculator
Add, subtract, multiply and divide fractions.
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Enter two fractions and an operation to get the answer in lowest terms, as a decimal, and as a mixed number. The calculator uses exact integer arithmetic and the greatest common divisor, so the result is never a rounded approximation.
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How to Calculate With Fractions — The Quick Answer
Multiplying is easiest — multiply the tops, multiply the bottoms. Dividing flips the second fraction and multiplies. Adding and subtracting need a common denominator first. Then simplify by the greatest common divisor.
Shortcut
a/b × c/d = ac/bd | a/b ÷ c/d = ad/bc | a/b ± c/d = (ad ± cb)/bd
Fact-Checking Claims You May Have Seen Online
To add fractions you add the tops and add the bottoms
False
1/2 + 1/3 is not 2/5. You need a common denominator first: 3/6 + 2/6 = 5/6. Only the numerators are added once the denominators match.
Dividing by a fraction makes the answer smaller
False
Dividing by a fraction less than 1 makes the answer bigger: 1/2 ÷ 1/4 = 2. Dividing flips the second fraction and multiplies.
The four operations at a glance
| Operation | Rule | Example |
|---|---|---|
| Add | common denominator, add tops | 1/2 + 1/3 = 5/6 |
| Subtract | common denominator, subtract tops | 3/4 − 1/4 = 1/2 |
| Multiply | tops × tops, bottoms × bottoms | 3/4 × 2/3 = 1/2 |
| Divide | flip the second, then multiply | 1/2 ÷ 1/4 = 2 |
Always simplify at the end by dividing the top and bottom by their greatest common divisor — 6/12 and 1/2 are the same value, but 1/2 is the expected form.
How It Works
The Rules
How each operation works on a/b and c/d
Formula
Add/Subtract: a/b ± c/d = (a·d ± c·b) / (b·d) Multiply: a/b × c/d = (a·c) / (b·d) Divide: a/b ÷ c/d = (a·d) / (b·c) Simplify: divide top and bottom by GCD
Variables
Adding and subtracting
Fractions can only be added or subtracted once they share a denominator. Multiplying each fraction by the other's denominator (b·d) is the reliable way to get there, after which you add or subtract the numerators.
Dividing
To divide by a fraction, keep the first fraction, change ÷ to ×, and flip (reciprocate) the second. 1/2 ÷ 1/4 becomes 1/2 × 4/1 = 4/2 = 2.
Simplifying
Divide the numerator and denominator by their greatest common divisor to express the answer in lowest terms. 6/12 has a GCD of 6, giving 1/2.
Note: Multiplication and division don't need a common denominator — only addition and subtraction do. That's why multiplying fractions is usually the easiest of the four.
Worked Example
1/2 + 1/3, and 1/2 ÷ 1/4
1/2 + 1/3 — common denominator
Multiply the denominators: 2 × 3 = 6. Rewrite as 3/6 + 2/6.
Add the numerators
3/6 + 2/6 = 5/6. The GCD of 5 and 6 is 1, so 5/6 is already in lowest terms (≈ 0.833).
1/2 ÷ 1/4 — flip and multiply
Keep 1/2, flip 1/4 to 4/1: 1/2 × 4/1 = 4/2.
Simplify
4/2 divides by its GCD of 2 to give 2/1 = 2.
Reference Guide
| unit | value | note |
|---|---|---|
| 1/2 + 1/3 | 5/6 | ≈ 0.833 |
| 3/4 − 1/4 | 1/2 | common denominator already |
| 3/4 × 2/3 | 1/2 | 6/12 simplified |
| 1/2 ÷ 1/4 | 2 | flip and multiply |
Key Features
Last updated: October 5, 2026
Creators
Computer Scientist & Developer Tools Author
Reviewers
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Table of Contents
Quick Facts
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Frequently Asked Questions
How do you add two fractions?
Give them a common denominator, then add the numerators. For 1/2 + 1/3, the common denominator is 6, so you rewrite them as 3/6 and 2/6 and add to get 5/6. You never add the denominators themselves.
How do you divide fractions?
Keep the first fraction, change the division to multiplication, and flip the second fraction (use its reciprocal). So 1/2 ÷ 1/4 becomes 1/2 × 4/1 = 4/2 = 2. This 'keep–change–flip' rule works for any two fractions.
How do you simplify a fraction?
Divide the top and bottom by their greatest common divisor (the largest number that divides both exactly). For 6/12, the GCD is 6, so dividing both gives 1/2. This calculator simplifies every answer for you.
What is a mixed number?
A mixed number combines a whole number and a proper fraction, like 1 1/2. It's another way of writing an improper fraction (one whose top is larger than its bottom): 3/2 equals 1 1/2. The calculator shows the mixed-number form whenever the answer is improper.
How do I enter a whole number as a fraction?
Write it over 1. The number 3 is the fraction 3/1, and 5 is 5/1. That lets you add, subtract, multiply, or divide whole numbers and fractions together in the same calculation.