Calculadora de Razones
Simplifica razones, compáralas y escálalas a cualquier valor objetivo
Ratio Calculator
Simplify and solve ratios
Simplify a ratio A:B to its lowest terms
Divide both A and B by their GCDWhat is a Ratio Calculator?
A Ratio Calculator is a math tool that helps you compare two or more quantities and express their relationship in a simple form. A ratio shows how much of one thing there is compared to another. Ratios are commonly written using a colon, such as 3:2, or as a fraction, such as 3/2.
Ratios are used in everyday life and many fields: cooking recipes (2 cups flour to 1 cup sugar), mixing solutions (1 part concentrate to 4 parts water), map scales, financial comparisons, and geometry. They are especially useful when you need to scale something up or down while keeping the same relationship between values.
A ratio calculator can simplify ratios, create equivalent ratios, and help solve 'missing value' problems (often called proportion problems). It saves time and reduces mistakes when working with large numbers or decimals.
How to Use This Ratio Calculator
- Enter the ratio values -- Input the two (or more) numbers you want to compare (example: 24 and 36)
- Choose an option (if available) -- such as simplify ratio, find equivalent ratio, or solve for missing value
- Click 'Calculate' -- the calculator processes the ratio
- Review the simplified ratio -- example: 24:36 becomes 2:3
- Use the result -- apply the ratio for scaling recipes, mixing, comparing quantities, or solving proportions
Tips:
- Ratios work best when the values represent the same type of measurement (e.g., both in grams, both in dollars)
- If you use decimals, the calculator may convert them to a simplified whole-number ratio
- If a ratio is used to scale something (like a recipe), make sure you multiply or divide both parts by the same factor
Ratio Formulas
Ratio Simplification
To simplify a ratio a:b, divide both numbers by their greatest common divisor (GCD):
Simplified = (a / gcd(a,b)) : (b / gcd(a,b))
Example: a = 24, b = 36
gcd(24, 36) = 12
24:36 → (24/12):(36/12) = 2:3
Equivalent Ratios
Multiply or divide both parts by the same number k:
(a:b) → (a × k : b × k)
2:3 × 5 → 10:15
Proportions (Missing Value)
A proportion compares two equal ratios: a/b = c/d
Solve using cross-multiplication:
a × d = b × c
If d is unknown: d = (b × c) / a
Example Calculations
Example 1: Simplify a Ratio
Input: 24:36
GCD: gcd(24, 36) = 12
Calculation: 24 ÷ 12 = 2, 36 ÷ 12 = 3
Result: 2:3
Example 2: Create an Equivalent Ratio
Input: 3:8, scaled by 4
Calculation: 3 × 4 = 12, 8 × 4 = 32
Result: 12:32 (simplifies back to 3:8)
Example 3: Recipe Scaling (Real-World Use)
Setup: A drink mix uses a ratio of 1:5 (concentrate : water)
Problem: If you have 3 cups of concentrate, how much water?
Calculation: 1 part → 5 parts, so 3 parts → 3 × 5 = 15 parts
Result: 15 cups of water
Example 4: Solve a Proportion (Missing Value)
Problem: Solve for x in 2/3 = 10/x
Cross-multiply: 2x = 3 × 10 = 30
Solve: x = 30 ÷ 2 = 15
Result: x = 15
Frequently Asked Questions
What's the difference between a ratio and a fraction?
A fraction represents a part of a whole (3/4). A ratio compares two quantities (3:4). Ratios can be written as fractions, but they often represent comparisons rather than parts.
How do I simplify a ratio?
Divide both parts by their greatest common divisor (GCD). For example, 18:24 simplifies to 3:4 because gcd(18,24) = 6, and 18/6 = 3, 24/6 = 4.
Can ratios include more than two numbers?
Yes. You can have ratios like 2:3:5, often used to compare three quantities (for example, ingredient proportions). Simplification usually divides all terms by their common factor.
What does a ratio like 1:5 mean?
It means for every 1 unit of the first quantity, there are 5 units of the second. For example, 1 cup of concentrate to 5 cups of water.
What is a proportion, and why is it useful?
A proportion states that two ratios are equal (a/b = c/d). It's useful for scaling, converting, and solving for unknown values in real-world situations like recipes, maps, and unit conversions.
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¿Qué es una razón?
Una razón expresa la relación entre dos cantidades. Se escribe como A:B (o A/B) y muestra cuántas veces un valor contiene al otro. Las razones están en todas partes: las proporciones de pantalla (16:9), las medidas de recetas (1:2 de harina a azúcar), el apalancamiento financiero en inversiones y las escalas de mapas (1:50,000) que te permiten medir distancias reales en papel.
Esta calculadora simplifica razones a su mínima expresión dividiendo ambas partes entre su máximo común divisor (MCD). También compara dos razones para verificar si son equivalentes, y escala una razón para ajustarse a cualquier total dado, para que puedas saber al instante cuánto necesitas de cada parte cuando cambia la cantidad objetivo.
Cómo usar la calculadora de razones
- Introduce los dos valores de la razón — A y B.
- Selecciona la operación: simplificar, comparar o escalar.
- Para escalar, introduce el total objetivo que quieres alcanzar.
- Haz clic en Calcular para ver el resultado simplificado o escalado al instante.
Fórmulas y referencia
Simplificar A:B — dividir ambos entre MCD(A, B)
Ejemplo: 12:8 → MCD = 4 → 3:2
Razones equivalentes — multiplicar en cruz
A:B = C:D si A × D = B × C
Escalar al total T:
Parte A = (A / (A + B)) × T
Parte B = (B / (A + B)) × T
Parte sobre el total:
A / (A + B) = fracción del total que corresponde a AUna razón A:B equivale a la fracción A/(A+B) como parte del total, o a A/B como comparación directa entre las dos partes.
Ejemplos resueltos
Simplificar 15:10
MCD(15, 10) = 5. Dividir ambos lados: 15 ÷ 5 = 3, 10 ÷ 5 = 2. Razón simplificada: 3:2. Por cada 3 unidades de A hay 2 unidades de B.
Mezclar cemento y arena en proporción 3:5 para 40 kg en total
Total de partes = 3 + 5 = 8. Cemento = (3/8) × 40 = 15 kg. Arena = (5/8) × 40 = 25 kg. Verificación: 15 + 25 = 40 kg. ✓
Relación de aspecto 1920:1080 simplificada
MCD(1920, 1080) = 120. Dividir ambos: 1920 ÷ 120 = 16, 1080 ÷ 120 = 9. Resultado: 16:9 — la relación de aspecto panorámica estándar usada en casi todas las pantallas modernas.