1. What is a Ratio?

A ratio is a quantitative relationship between two numbers showing how many times one value contains or is contained within the other. It expresses the proportional relationship between two quantities.

2. How to Calculate Ratio

The ratio between two numbers is calculated using the formula:

Where:

• \( a \) — First quantity
• \( b \) — Second quantity
• \( r \) — Resulting ratio (unitless or with units)

Explanation: The ratio determines the proportional relationship between two values by dividing the first value by the second value.

3. Importance of Ratios

Details: Ratios are fundamental in mathematics, science, engineering, finance, and everyday life for comparing quantities, analyzing relationships, and making proportional calculations.

4. Using the Calculator

Tips: Enter both values in the same units. The calculator will compute the ratio a:b. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What does a ratio of 1 mean?
A: A ratio of 1 means the two quantities are equal in value (a = b).

Q2: How do you simplify ratios?
A: Divide both numbers by their greatest common divisor to simplify the ratio to its smallest whole number terms.

Q3: Can ratios have units?
A: Ratios can be unitless when comparing similar quantities, or can have units when comparing different quantities (e.g., km/h).

Q4: What's the difference between ratio and fraction?
A: A ratio compares two quantities, while a fraction represents a part of a whole. Ratios can compare different things, while fractions typically represent portions of the same thing.

Q5: How are ratios used in real life?
A: Ratios are used in cooking (recipes), finance (debt-to-income), maps (scale), medicine (drug dosages), and many other applications.