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. Ratios are unitless and express the relative magnitude of two quantities.

2. How Does the Calculator Work?

The calculator uses the simple ratio formula:

Where:

• \( a \) — Numerator (first value)
• \( b \) — Denominator (second value)
• \( r \) — Resulting ratio (unitless)

Explanation: The ratio compares the size of two quantities by division. A ratio of 2 means the numerator is twice as large as the denominator.

3. Importance of Ratio Calculation

Details: Ratios are fundamental in mathematics, science, engineering, finance, and everyday life for comparing quantities, analyzing proportions, and making relative measurements.

4. Using the Calculator

Tips: Enter any positive numbers for numerator and denominator. Denominator must be greater than zero. Results are rounded to 4 decimal places.

5. Frequently Asked Questions (FAQ)

Q1: What does a ratio of 1 mean?
A: A ratio of 1 indicates that the two quantities being compared are equal in size.

Q2: Can ratios be greater than 1?
A: Yes, ratios can be any positive number. Values >1 mean the numerator is larger, <1 means denominator is larger.

Q3: What's the difference between ratio and fraction?
A: Mathematically similar, but ratios typically compare different quantities while fractions represent parts of a whole.

Q4: How are ratios used in real life?
A: Common uses include financial ratios (debt-to-income), aspect ratios (16:9 screens), and odds ratios (probability).

Q5: Can ratios be simplified?
A: Yes, ratios can often be simplified by dividing both terms by their greatest common divisor (e.g., 4:2 simplifies to 2:1).