**Instructions:**

- Enter the values for A, B, C, and D in the input fields.
- Click the "Calculate" button to perform the ratio calculations.
- The simplified ratio will be displayed below along with whether the ratios are equivalent.
- You can also see the calculation history below the results.
- Click "Clear Results" to reset the inputs and results.
- Click "Copy Results" to copy the result to the clipboard.

**Calculation History**

## Introduction

The Ratio Calculator is a versatile mathematical tool that plays a crucial role in various fields such as finance, engineering, and science. This tool simplifies complex calculations involving ratios, providing a straightforward means of analyzing and comparing quantities.

## Understanding Ratios

Ratios are a fundamental mathematical concept used to express the relationship between two or more quantities. A ratio is written in the form of “a:b” or “a to b,” where ‘a’ and ‘b’ are two numbers representing the quantities being compared. Ratios can be used to compare a wide range of attributes, such as distance, speed, concentration, and more.

## The Formulae Behind the Ratio Calculator

The Ratio Calculator relies on several essential formulae to perform its calculations:

### 1. Simple Ratio

The simplest form of a ratio is expressed as ‘a:b,’ where ‘a’ and ‘b’ are integers. This ratio is used for direct comparisons, such as the ratio of boys to girls in a classroom or the ratio of red to blue balls in a bag.

### 2. Compound Ratio

A compound ratio involves multiple ratios combined together. If you have two ratios, ‘a:b’ and ‘c:d,’ the compound ratio is ‘a:b::c:d.’ Compound ratios are useful in scenarios where multiple comparisons need to be made simultaneously.

### 3. Proportions

Proportions are mathematical statements that two ratios are equal. The general proportion formula is ‘a:b = c:d.’ Solving proportions allows you to find an unknown value when other three values are known.

### 4. Percentage

Percentages are ratios expressed as a fraction of 100. The formula to convert a ratio into a percentage is: Percentage (%) = (a / b) * 100. This is used in finance and statistics to express values in a more intuitive way.

### 5. Cross Multiplication

Cross multiplication is a technique used to solve proportions. For a proportion ‘a:b = c:d,’ you can use cross multiplication to find the unknown value: ‘ad = bc.’

## Example Calculations

Let’s illustrate the application of these formulae with some practical examples:

### Example 1: Simple Ratio

Suppose you have a basket of fruits with 5 apples and 3 bananas. The ratio of apples to bananas is 5:3.

### Example 2: Compound Ratio

In a chemistry experiment, you mix chemicals A and B in a 2:1 ratio and chemicals C and D in a 3:2 ratio. The compound ratio of A:B to C:D is 2:1::3:2.

### Example 3: Proportions

If the ratio of the length to width of a rectangle is 3:2, and the width is 4 meters, you can use proportions to find the length: 3:2 = x:4, where x is the length. Solving the proportion, you find that x = 6 meters.

### Example 4: Percentage

You have a test score of 36 out of 50. To express this as a percentage, use the formula: Percentage (%) = (36 / 50) * 100 = 72%.

### Example 5: Cross Multiplication

To find the missing value in the proportion 4:6 = 8:x, you can cross-multiply: 4 * x = 6 * 8. Solving for ‘x,’ you get x = 12.

## Real-World Use Cases

The Ratio Calculator is a powerful tool with numerous real-world applications:

### Finance

- Financial analysts use ratios to evaluate the performance of companies, such as the price-to-earnings ratio (P/E ratio) or the debt-to-equity ratio.
- Investors use ratios to make informed decisions when buying or selling stocks.

### Engineering

- Engineers use ratios to design and analyze mechanical systems, such as gear ratios in machines.
- Structural engineers use ratios to determine the load-bearing capacity of materials.

### Medicine

- Medical professionals use ratios to calculate drug dosages based on patient weight and age.
- Researchers use ratios to analyze the effectiveness of treatments and interventions.

### Education

- Teachers use ratios to assess student performance, such as the student-to-teacher ratio in a classroom.
- Educational institutions use ratios to allocate resources efficiently.

### Cooking

- Chefs and home cooks use ratios to scale recipes up or down based on the number of servings needed.
- Bakers use ratios to maintain the balance of ingredients in recipes.

## Conclusion

The Ratio Calculator is an indispensable tool that simplifies complex mathematical operations involving ratios. With its diverse applications in finance, engineering, medicine, education, and everyday life, understanding and using ratios is essential. By leveraging the formulae and examples provided in this guide, individuals can harness the power of ratios to make informed decisions and solve practical problems.