Calculadora de Razões
Simplifique razões, compare-as e escale para qualquer valor alvo
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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O que é uma razão?
Uma razão expressa a relação entre duas quantidades. Escrita como A:B (ou A/B), ela mostra quantas vezes um valor contém o outro. As razões estão em todo lugar: proporções de tela (16:9), medidas de receitas (1:2 de farinha para açúcar), alavancagem financeira em investimentos e escalas de mapas (1:50.000) que permitem medir distâncias reais em papel.
Esta calculadora simplifica razões à sua forma mais reduzida dividindo ambas as partes pelo máximo divisor comum (MDC). Também compara duas razões para verificar se são equivalentes, e escala uma razão para se ajustar a qualquer total — para que você saiba imediatamente quanto precisa de cada parte quando a quantidade-alvo muda.
Como usar a calculadora de razões
- Insira os dois valores da razão — A e B.
- Selecione a operação: simplificar, comparar ou escalar.
- Para escalar, insira o total alvo que deseja atingir.
- Clique em Calcular para ver o resultado simplificado ou escalado na hora.
Fórmulas e referência
Simplificar A:B — dividir ambos pelo MDC(A, B)
Exemplo: 12:8 → MDC = 4 → 3:2
Razões equivalentes — multiplicar cruzado para verificar
A:B = C:D se A × D = B × C
Escalar para o total T:
Parte A = (A / (A + B)) × T
Parte B = (B / (A + B)) × T
Parte sobre o total:
A / (A + B) = fração do total correspondente a AUma razão A:B equivale à fração A/(A+B) como parte do total, ou A/B como comparação direta entre as duas partes.
Exemplos resolvidos
Simplificar 15:10
MDC(15, 10) = 5. Dividir os dois lados: 15 ÷ 5 = 3, 10 ÷ 5 = 2. Razão simplificada: 3:2. Para cada 3 unidades de A há 2 unidades de B.
Misturar cimento e areia na proporção 3:5 para 40 kg no total
Total de partes = 3 + 5 = 8. Cimento = (3/8) × 40 = 15 kg. Areia = (5/8) × 40 = 25 kg. Verificação: 15 + 25 = 40 kg. ✓
Proporção de tela 1920:1080 simplificada
MDC(1920, 1080) = 120. Dividir ambos: 1920 ÷ 120 = 16, 1080 ÷ 120 = 9. Resultado: 16:9 — a proporção widescreen padrão usada em praticamente todas as telas modernas.