Ratio Calculator

A ratio is a mathematical comparison of two or more numbers that indicates their sizes in relation to each other. Ratios are used in everything from cooking recipes and construction blueprints to financial analysis and chemistry. This calculator helps you perform the most common ratio-related operations quickly and accurately.

Understanding Ratios

A ratio can be expressed in several ways:

1. Colon Notation: $2:3$
2. Fractional Form: $\frac{2}{3}$
3. Word Form: "2 to 3"

Regardless of the notation, the relationship remains the same. If you have a ratio of $2:3$ of red marbles to blue marbles, it means for every 2 red marbles, there are 3 blue marbles.

The Formulas

1. Simplifying Ratios

To simplify a ratio, you find the Greatest Common Divisor (GCD) of the terms and divide both by that number. $\text{Simplified Ratio} = \frac{A}{GCD(A, B)} : \frac{B}{GCD(A, B)}$

2. Solving Proportions (Missing Value)

A proportion is an equation stating that two ratios are equal: $A:B = C:D$. If one value is unknown ($x$), we use cross-multiplication: $\frac{A}{B} = \frac{C}{x} \implies x = \frac{B \times C}{A}$

3. Dividing a Total into a Ratio

To divide a total amount $T$ into the ratio $A:B$: $\text{Part 1} = T \times \left(\frac{A}{A + B}\right)$ $\text{Part 2} = T \times \left(\frac{B}{A + B}\right)$

How to Use This Calculator

1. Select Mode: Choose whether you want to simplify, solve for a missing value, scale a ratio, or divide a total sum.
2. Enter Values: Input the known parts of your ratio.
3. View Results: The calculator provides the simplified form, decimal equivalents, and a step-by-step breakdown of the logic.

Worked Examples

Example 1: Simplifying

Problem: Simplify the ratio $24:36$.

• Step 1: Find the GCD of 24 and 36. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The GCD is 12.
• Step 2: Divide both by 12.
• $24 \div 12 = 2$
• $36 \div 12 = 3$
• Result: $2:3$

Example 2: Dividing a Total

Problem: Divide $500 into a ratio of$2:3$.

• Step 1: Add the parts: $2 + 3 = 5$.
• Step 2: Calculate Part A: $500 \times (2/5) = 200$.
• Step 3: Calculate Part B: $500 \times (3/5) = 300$.
• Result: $200 and$300.

FAQ

What is a golden ratio?

The golden ratio is a special number approximately equal to $1.618$. It appears frequently in geometry, art, and nature.

Can ratios have decimals?

Yes, but they are usually converted to whole numbers for simplification. For example, $1.5 : 2$ can be scaled by 2 to become $3 : 4$.

What is the difference between a ratio and a proportion?

A ratio is a comparison of two numbers. A proportion is a statement that two ratios are equal.

How do you convert a ratio to a percentage?

Divide the first number by the second number and multiply by 100. For $1:4$, $1 \div 4 = 0.25$, which is $25\\%$.

Why is simplifying ratios important?

Simplifying makes the relationship between numbers easier to understand and communicate, much like simplifying fractions in algebra.

Limitations

• This calculator currently supports two-part ratios ($A:B$).
• Inputs must be positive real numbers for most standard applications.
• Ratios do not imply absolute quantities, only relative proportions.