Ratio Simplification

Executive Summary

Ratios describe the quantitative relationship between two amounts, showing how many times one number contains another. Simplification reduces ratios to their lowest whole number terms for clarity.

Key Takeaways
  • relative proportion: A ratio compares the quantitative size of two quantities.
  • lowest terms: Ratios are simplified by dividing both parts by their Greatest Common Divisor.
  • scale factor: Ratios preserve relative proportions regardless of the absolute numbers compared.
Formula
Simplified Ratio = (A / GCD) : (B / GCD)

Ratio Simplification Formula

Variable Glossary
SymbolMeaning & Description
AFirst ratio value
BSecond ratio value
GCDGreatest Common Divisor
Step-by-Step Worked Example
1. Mapped Variables
Value A
A12
Value B
B16
2. Equation Substitution
Equation with standard inputs
Ratio = (12 ÷ 4) : (16 ÷ 4)
3. Calculation Steps
Step 1: Compute Greatest Common Divisor (GCD)

GCD(12, 16) = 4

Step 2: Divide both parameters by GCD

A_reduced = 12 ÷ 4 = 3. B_reduced = 16 ÷ 4 = 4.

Step 3: Format simplified terms

Reduced ratio = 3 : 4

Final Resolved Simplified Ratio3 : 4
Live Simulation

Ratio Calculator Sandbox

Tweak variables below to see the formula calculate instantly.

Value A12
Value B16
Calculating...
Common Mistakes to Avoid

Order of Comparison: Ratios are order-dependent. A ratio of 3:4 (A to B) is completely different from 4:3 (B to A).

Frequently Asked Questions
Interactive Tool

Ratio Calculator

Simplify ratios into their lowest integer terms using Greatest Common Divisors.

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