Ratio Simplifier Calculator

How to Simplify Ratios

Simplifying ratios is an essential mathematical skill used in various fields, from basic arithmetic to advanced sciences. Here's a comprehensive guide on how to simplify ratios:

Simplification Formula

To simplify a ratio, we use the following formula:

\[ \frac{a}{b} = \frac{a \div GCD(a,b)}{b \div GCD(a,b)} \]

Where:

• a and b are the two numbers in the ratio
• GCD(a,b) is the Greatest Common Divisor of a and b

Calculation Steps

Let's go through an example to simplify the ratio 24:36:

Step 1: Identify the ratio

The original ratio is 24:36.

Step 2: Find the Greatest Common Divisor (GCD)

Calculate the GCD of 24 and 36:

\[ GCD(24, 36) = 12 \]

Step 3: Divide both parts of the ratio by the GCD

Divide both the numerator and denominator by the GCD:

\[ \frac{24}{12} : \frac{36}{12} = 2 : 3 \]

Step 4: Express as a simplified ratio

The simplified ratio is:

\[ 2 : 3 \]

Visual Representation

A visual representation can help understand the relationship between the original and simplified ratios:

The top bar shows the simplified ratio (2:3), while the bottom bar shows the original ratio (24:36).

This diagram illustrates how the simplified ratio 2:3 represents the same proportion as the original ratio 24:36, but in its simplest form.