Recipe scaling: 3/4 cup oil + 1/2 cup water - total liquid?
3/4 + 1/2. Common denominator: 4. So 3/4 + 2/4 = 5/4 cups = 1 1/4 cups total liquid. As decimal: 1.25 cups.
Fraction Calculator - Calculadora online gratis
Add, subtract, multiply or divide two fractions and get the result simplified to its lowest terms - plus a decimal and percent equivalent. Mixed numbers (like 2 1/4) and improper fractions (like 9/4) are both supported. Designed for school homework, recipes, and any DIY measurement task that mixes fractions.
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First fraction
/
Whole · Numerator / Denominator (set whole to 0 for a simple fraction)
Operation
Second fraction
/
Whole · Numerator / Denominator (set whole to 0 for a simple fraction)
Reduced fraction
7 / 4
Mixed: 1 3/4
Decimal
1.75
≈ 175%
Parte del contenido aún se muestra en inglés.
Entender: Fraction Calculator
Fractions show up in school math (Class 4-8 mathematics core), recipes (1/4 cup oil + 3/4 cup water), carpentry and DIY measurements (1/2 inch plywood vs 3/4 inch), engineering drawings, and many real-world ratios. Despite their everyday use, fraction arithmetic - especially addition and subtraction with different denominators - trips up students and adults alike. This calculator handles all four operations (+, −, ×, ÷) on fractions, supports both improper fractions (9/4) and mixed numbers (2 1/4) as inputs, and shows the result in multiple forms (reduced fraction, mixed number, decimal, percent).
Beyond simple computation, this tool is useful as a learning aid. The displayed formula shows the underlying method (common denominator for addition, reciprocal-multiply for division, etc.), and the multi-form result helps build intuition about how fractions, decimals and percents relate. Students preparing for board exams or competitive entrance tests can use it to verify homework answers; cooks scaling recipes can compute portions; DIYers can sum measurements without converting to decimals first.
Cómo usar Fraction Calculator en 5 pasos
Type the first fraction - numerator and denominator (and optional whole-number part for mixed numbers).
Pick an operation: + − × ÷.
Type the second fraction.
The result shows in reduced form, as a mixed number, decimal and percent.
Swap operands or change operation any time - the answer updates instantly.
Cómo funciona Fraction Calculator
All four operations work by first finding a common form, then reducing to lowest terms using the Greatest Common Divisor (GCD). Addition and subtraction need a common denominator (we use the product, then reduce). Multiplication multiplies straight across. Division flips the second fraction and multiplies. The Euclidean algorithm computes GCD efficiently even for very large numbers.
Formula
+: (a/b)+(c/d) = (ad+bc)/(bd) ×: (a/b)×(c/d) = ac/bd
- a/bFirst fraction
- c/dSecond fraction
- ÷Multiply by reciprocal: a/b × d/c
- ReduceDivide numerator and denominator by GCD(a, b)
Cómo obtiene Fraction Calculator su resultado
Addition and subtraction require a common denominator. The calculator uses the product of the two denominators (b × d) as the common denominator, then computes (a×d + c×b)/(b×d) for addition and (a×d − c×b)/(b×d) for subtraction. The result is then reduced to lowest terms using the Greatest Common Divisor (GCD), computed via the Euclidean algorithm. Multiplication is straightforward: (a/b) × (c/d) = (a×c)/(b×d), then reduce. Division uses the reciprocal: (a/b) ÷ (c/d) = (a/b) × (d/c) = (a×d)/(b×c).
Mixed numbers (e.g., 2 1/4) are first converted to improper fractions before computation. The conversion: whole × denominator + numerator, all over denominator. So 2 1/4 = (2×4 + 1)/4 = 9/4. After the operation, the calculator can show the result both as an improper fraction (e.g., 7/4) and a mixed number (1 3/4) - Indian school textbooks vary in which form is preferred, so showing both removes ambiguity.
The Euclidean algorithm for GCD: GCD(a, b) = GCD(b, a mod b), repeating until the remainder is 0. Example: GCD(48, 36). 48 mod 36 = 12. GCD(36, 12) = GCD(12, 0) = 12. So 48/36 reduces by 12 → 4/3. The algorithm runs in logarithmic time, handling numerators and denominators of any reasonable size instantly.
Ejemplos resueltos
Carpentry: 5 boards of 7/8 inch - total thickness?
5 × 7/8 = 35/8 = 4 3/8 inches = 4.375 inches. Useful when planning stacked board projects.
Splitting a bill: 1 1/3 hours work at ₹600 - total cost?
1 1/3 × 600. Convert mixed to improper: 4/3. So 4/3 × 600 = 2400/3 = ₹800. Verify: 1 hour = ₹600, extra 1/3 hour = ₹200, total ₹800.
Cuándo usar Fraction Calculator
- School homework - Class 4-8 fraction arithmetic.
- Recipe scaling - multiplying or adding fractional measurements.
- Carpentry, plumbing, electrical work - adding fractional inch measurements.
- Sewing and fabric work - fractional yard or metre calculations.
- Time arithmetic - combining hours and partial hours expressed as fractions.
- Music notation - adding fractional note durations (1/4 + 1/8 + 1/8 = 1/2 note total).
- Engineering drawings - combining or converting fractional dimensions.
Errores y trampas habituales
- Adding numerators and denominators directly. 1/3 + 1/4 ≠ 2/7. Always find a common denominator first.
- Forgetting to reduce final answers. 6/8 should be reduced to 3/4 unless context demands otherwise.
- Confusing 'of' (multiplication) with 'and' (addition). '1/2 of 1/3' = 1/2 × 1/3 = 1/6, not 1/2 + 1/3.
- Mishandling negative fractions. −1/2 ≠ 1/(−2) for some operations; track signs carefully.
- Dividing by a fraction by direct division. Flip-and-multiply: a/b ÷ c/d = a/b × d/c.
Saca más partido a esta herramienta
- Always reduce the final answer unless the context requires unreduced form (some textbook answer keys do).
- For addition/subtraction, finding the LCM of denominators is more elegant than using their product - same answer, smaller intermediate numbers.
- Convert mixed numbers to improper fractions before computing, then convert back if needed.
- When in doubt, convert fractions to decimals for a sanity check - 7/8 ≈ 0.875 should match the decimal output.
- Pair this calculator with the percentage, ratio and proportion calculators on this site for related arithmetic.
Preguntas sobre Fraction Calculator
How do I add fractions with different denominators?
Multiply each fraction by the form of 1 needed to give a common denominator. Example: 1/3 + 1/4 → multiply first by 4/4 and second by 3/3 → 4/12 + 3/12 = 7/12. The calculator does this automatically and reduces if needed.
How do I convert a mixed number to an improper fraction?
Multiply the whole part by the denominator, add the numerator, keep the denominator. Example: 2 3/4 = (2 × 4 + 3)/4 = 11/4.
How do I convert an improper fraction to a mixed number?
Divide the numerator by the denominator. The quotient is the whole part, the remainder over the denominator is the fractional part. Example: 11/4 = 2 remainder 3 → 2 3/4.
How do I simplify a fraction?
Divide numerator and denominator by their GCD. Example: 18/24 → GCD(18, 24) = 6 → 3/4. Already-reduced fractions like 7/12 stay the same.
What is 1/3 as a decimal?
0.333... (repeating). The calculator shows 0.333333 by default. As a percent, that's 33.3333%.
Can I divide by zero?
No. Division requires a non-zero second fraction (numerator can be zero, denominator cannot). The calculator flags an undefined result if you try.
Why does the answer sometimes look different from my textbook?
Both forms are correct as long as they reduce to the same fraction. Some textbooks leave answers as improper fractions (e.g. 7/4), others convert to mixed numbers (1 3/4). This calculator shows both.
Math in your browser
From simple percentages to scientific notation, statistics, geometry and big-number arithmetic - every common math problem you'd reach for a calculator for, runs in your browser with no installs. The fraction calculator preserves exact rationals, the big-number calculator uses BigInt for hundreds of digits without precision loss, and the scientific calculator's expression evaluator is a hand-written shunting-yard parser (no eval) that supports trig, log, factorial and parentheses.
If you're a student, double-check your work without paying for a graphing calculator. If you're a professional, use these tools as a sanity check on spreadsheet formulas. Every result is shown alongside its formula and inputs, so the math is always auditable.
The Fraction Calculator is part of the Math suite on Online Calculator Tools, alongside 6 related calculators. All tools share the same UI patterns, the same privacy-first rendering (nothing is sent to a server), and the same commitment to showing the formula and assumptions behind every result.