Calculadora de fracciones
Suma, resta, multiplica o divide dos fracciones y obtén el resultado exacto simplificado, además de las formas de número mixto, decimal y porcentaje.
Cómo usar esta calculadora
- 1Enter the numerator and denominator of the first fraction.
- 2Choose the operation you want.
- 3Enter the second fraction the same way.
- 4Read the simplified result, and use the step panel to see how the answer was reached.
Cómo funciona
Aritmética de fracciones
a/b + c/d = (ad + cb) / bd a/b − c/d = (ad − cb) / bd a/b × c/d = ac / bd a/b ÷ c/d = a/b × d/c = ad / bc Simplifica dividiendo ambas partes por su MCD
Para sumar o restar fracciones se necesita un denominador común; para multiplicar, se multiplican numeradores y denominadores por separado; y para dividir, se multiplica por la fracción invertida. En todos los casos, el resultado se simplifica dividiendo el numerador y el denominador por su máximo común divisor, lo que da la forma más reducida y exacta.
Ejemplo resuelto
1/2 + 1/3 = (1·3 + 1·2) / (2·3) = 5/6. Y 2/3 × 3/4 = 6/12, que simplificado es 1/2 (o 0,5, es decir el 50 %).
Calculadora de fracciones: la guía completa
Dividing fractions: why you flip the second one
Dividing by a number means asking how many of it fit into the first quantity. Dividing by 1/2 asks how many halves fit — which is why dividing by a fraction less than one makes the answer larger, a result that feels backwards until you say it out loud.
Mechanically, dividing by c/d is the same as multiplying by d/c, because c/d × d/c = 1. Multiplying by the reciprocal cancels the divisor and leaves the answer. "Keep, change, flip" is the classroom mnemonic: keep the first fraction, change ÷ to ×, flip the second.
Common denominators for adding and subtracting
You cannot add quarters to thirds any more than you can add metres to feet — the pieces are different sizes. Rewriting both fractions over a common denominator makes the pieces the same size, and then the numerators simply add.
Multiplying the two denominators always gives a valid common denominator, and it is what the formula above uses. The least common denominator is the LCM of the two, which keeps the numbers smaller and often means less simplifying at the end. For 1/4 and 1/6, multiplying gives 24 while the LCM is 12 — both work, but 12 is tidier.
Simplifying, mixed numbers, and improper fractions
A fraction is in lowest terms when the numerator and denominator share no factor other than 1. Dividing both by their greatest common factor gets there in a single step — no repeated halving required.
An improper fraction has a numerator at least as large as its denominator, like 12/8. The mixed-number form 1½ is easier to picture, while the improper form is easier to compute with, which is why you convert mixed numbers to improper fractions before multiplying or dividing and convert back only at the end.
Preguntas frecuentes
¿Cómo se suman fracciones con distinto denominador?
Se convierten a un denominador común (el mínimo común denominador es lo más práctico), se suman los numeradores y se simplifica. Por ejemplo, 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
¿Cómo se dividen fracciones?
Se multiplica la primera fracción por la segunda invertida (intercambiando su numerador y denominador). Así, 1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6 = 2/3.
¿Por qué el resultado es exacto?
Porque toda la aritmética se realiza con números enteros y solo se simplifica al final. No se convierte a decimal durante el cálculo, así que no aparece ningún error de redondeo y la fracción resultante es exacta.