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%.
FAQ
What is an improper fraction? One whose numerator is greater than or equal to the denominator, such as 7/4. It can be converted to a mixed number (1 and 3/4) by performing the integer division.
Can the denominator be negative? Technically yes, but the convention is to keep the negative sign in the numerator — 2/-3 is rewritten as -2/3.
How do I simplify a fraction? Divide numerator and denominator by their GCD. For 8/12, GCD is 4, so the simplified form is 2/3.
Why can't the denominator be zero? Division by zero is undefined in mathematics — there is no number that, multiplied by zero, equals a non-zero numerator.
Related Tools
Rent Adjustment Calculator
Compute annual rent adjustment by IGP-M or IPCA accumulated in the last 12 months (manually configurable).
Pregnancy Calculator
Compute estimated due date (EDD), gestational age and trimester from the last menstrual period (LMP).
Fertile Period Calculator
Compute fertile window and ovulation day from the first day of the last cycle and the average cycle length.
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.