Fraction Calculator
Add, subtract, multiply and divide fractions. Simplifies to lowest terms and converts to decimal.
How is the fraction simplified?
Once the operation is done, we reduce the result by dividing numerator and denominator by the GCD (Greatest Common Divisor) between them, which brings the fraction to its lowest terms.
Each operation has its own route. Addition and subtraction (+/−) lean on the LCM of the denominators. Multiplication (×) multiplies numerators together and denominators together. Division (÷) multiplies by the reciprocal of the second fraction.
The computation runs 100% locally.
How fraction arithmetic works
A fraction a/b represents the division of a (numerator) by b (denominator, with b different from zero). To add or subtract fractions, both must share the same denominator — the standard procedure is to find the LCM (least common multiple) of the denominators and rewrite each fraction with the common base. Example: 1/2 + 1/3 uses LCM(2,3) = 6, giving 3/6 + 2/6 = 5/6.
Multiplication is direct: multiply numerator times numerator and denominator times denominator — a/b · c/d = (a·c)/(b·d). Division is multiplication by the reciprocal — a/b ÷ c/d = a/b · d/c. To check whether two fractions are equal, use the cross-multiplication rule: a/b = c/d if and only if a·d = b·c. Always simplify the result by dividing numerator and denominator by the GCD (greatest common divisor).
Where fractions are used in real life
Cooking recipes (1/2 cup, 3/4 teaspoon), splitting expenses or project deliverables among team members, building plans and scale drawings, music notation (half, quarter, eighth notes), probability and statistics, and most ENEM and university entrance exams. Any fraction can be converted to a decimal by performing the division, and to a percentage by multiplying the decimal by 100 — 3/4 equals 0.75 or 75%.
Fraction calculator
Working with fractions is where a lot of people get tangled up: finding a common denominator, simplifying, remembering each operation's rule. This calculator takes care of the tedious part. It adds, subtracts, multiplies and divides fractions and returns the result already in lowest terms.
Beyond the operation itself, the tool reduces automatically to the smallest possible expression and also shows the decimal equivalent, which helps you check the result from another angle. It works for homework, for recipes calling for fractional measures, and for any everyday calculation involving parts of a whole.
The calculation runs in the browser. A direct reference for solving fractions without the risk of getting the simplification wrong along the way.
Frequently asked questions
What is an improper fraction?
Can the denominator be negative?
How do I simplify a fraction?
Why can't the denominator be zero?
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.