Fraction Calculator & Simplifier: what this tool is for
In mathematics, a fraction represents a numerical part of a whole expressed as a ratio a/b between two integers (where b ≠ 0), with 'a' denoting the numerator (count of parts) and 'b' representing the denominator (total equal subdivisions). Fundamental to rational arithmetic, mastering fractions is essential across science, cooking, construction, finance, and engineering.
Arithmetic operations on fractions follow universal mathematical rules: adding or subtracting fractions with unequal denominators requires finding a common denominator via the Least Common Multiple (LCM). Multiplying fractions involves multiplying numerators together and denominators together directly, whereas dividing fractions requires multiplying by the second fraction's reciprocal.
Every fraction can be simplified to its irreducible lowest terms by dividing both terms by their Greatest Common Divisor (GCD). When the numerator exceeds the denominator (an improper fraction), it can be expressed as a mixed number consisting of an integer quotient and a proper fractional remainder.
This free online Fraction Calculator & Simplifier enables you to perform all fractional arithmetic operations (+, -, ×, ÷) and reduce any fraction to lowest terms, complete with mixed numbers, decimal values, percentages, and full step-by-step proofs.
No file stored
Nothing is saved on our servers, during or after processing.
Local processing
The computation runs in your browser whenever the technology allows it.
Instant result
No waiting and no export queue: the result appears live.
Free, no account
No sign-up, no daily limit and no intrusive ads.
What this tool gives you
Complete arithmetic suite (+, -, ×, ÷)
Add, subtract, multiply, and divide two fractions with automated Least Common Multiple (LCM) denominator conversion.
Instant simplification to lowest terms
Reduce any fraction into its simplest irreducible form using Euclidean algorithm Greatest Common Divisor (GCD) extraction.
Mixed number & decimal conversions
Convert improper fractions into clean mixed numbers (e.g., 17/4 = 4 1/4) with exact decimal figures and percentages (425%).
Step-by-step mathematical reasoning
Follow each calculation step: common denominator conversion, numerator arithmetic, cross-cancellation, and GCD simplification.
Real-world examples
Review common benchmark fractions, decimals, and percentage equivalents:
How to use Fraction Calculator & Simplifier
Select your calculation mode
Choose between '2-Fraction Operations (+, -, ×, ÷)' or 'Simplify 1 Fraction (GCD)'.
Input numerators and denominators
Enter your integer values for each term (e.g., 1/2 and 1/3).
Review irreducible results
Inspect the simplified lowest terms, mixed number format, exact decimal value, and percentage.
Follow step-by-step arithmetic
Review common denominator matching and GCD division steps for homework and algebra problems.
Tips and mistakes to avoid
Cross-cancel before multiplying fractions
When multiplying fractions such as (4/9) × (3/8), cross-simplify shared factors first: 4 and 8 reduce by 4 (leaving 1 and 2), while 3 and 9 reduce by 3 (leaving 1 and 3), giving (1×1)/(3×2) = 1/6 directly!
Invert and multiply for division
Dividing by any fraction c/d is identical to multiplying by its reciprocal d/c. For instance, (3/5) ÷ (2/7) = (3/5) × (7/2) = 21/10 = 2 1/10.
Avoid : Adding denominators directly
Never add denominators together: 1/2 + 1/3 is NOT (1+1)/(2+3) = 2/5. You must find a common denominator (6) to compute 3/6 + 2/6 = 5/6.
Avoid : Dividing by zero
A fraction denominator cannot equal zero (a/0 is undefined). Similarly, dividing by a fraction whose numerator is 0 is mathematically impossible.
Frequently asked questions
Answers to the questions people ask about Fraction Calculator & Simplifier.
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Updated on August 2026. See all tools