Ratio Calculator

Understanding Ratios

What is a Ratio?

A ratio is a comparison between two or more quantities. It shows the relative sizes of two or more values and is often expressed as "a to b" or "a:b".

Mathematical Definition

Mathematically, a ratio of \(a\) to \(b\) can be expressed as:

\[a:b\]

Where:

• \(a\) is the first quantity (antecedent)
• \(b\) is the second quantity (consequent)

Simplifying Ratios

To simplify a ratio:

1. Find the greatest common divisor (GCD) of the numbers in the ratio.
2. Divide both numbers by the GCD.

Example with Visual Representation

Let's consider a ratio of 6:9

1. Find the GCD: GCD(6, 9) = 3
2. Divide both numbers by 3: 6 ÷ 3 = 2, 9 ÷ 3 = 3
3. Simplified ratio: 2:3

This diagram visually represents the simplified ratio 2:3, showing the relative sizes of the two quantities.