Simplify Ratio Calculator
Reduce ratios to their simplest form, convert to 1:n or n:1 format, and work with 2 or 3 number ratios
Simplify Your Ratio
Enter Ratio Values
Enter positive numbers. Decimals will be converted to whole numbers for GCF calculation.
Example Calculations
Two Number Ratio Example
Problem: Simplify the ratio 24 : 18
Step 1: Find GCF of 24 and 18
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 18: 1, 2, 3, 6, 9, 18
GCF = 6
Step 2: Divide both numbers by GCF
24 ÷ 6 = 4, 18 ÷ 6 = 3
Answer: 4 : 3
Three Number Ratio Example
Problem: Simplify the ratio 12 : 18 : 30
Step 1: Find GCF of 12, 18, and 30
GCF(12, 18) = 6
GCF(6, 30) = 6
Overall GCF = 6
Step 2: Divide all numbers by GCF
12 ÷ 6 = 2, 18 ÷ 6 = 3, 30 ÷ 6 = 5
Answer: 2 : 3 : 5
Real-World Application
Recipe Scaling: A recipe calls for 3 cups flour, 2 cups sugar, and 1 cup butter
Ratio: 3 : 2 : 1 (already in simplest form, GCF = 1)
To double the recipe: Multiply each by 2 → 6 : 4 : 2
Simplified: 6 : 4 : 2 = 3 : 2 : 1 (same proportions)
Understanding Ratios
Definition
A ratio compares quantities or amounts
Simplification
Divide by GCF to get lowest terms
Proportions
Maintain relationships between quantities
GCF Quick Facts
GCF is the largest factor common to all numbers
Also called Greatest Common Divisor (GCD)
Used to reduce ratios to simplest form
Euclidean algorithm is efficient for calculation
Ratio Forms Guide
Simplified Form
Lowest terms using GCF division
1 : n Form
Shows proportion per 1 unit of first quantity
n : 1 Form
Shows proportion per 1 unit of second quantity
3-Number Forms
1:n:m, n:1:m, or n:m:1 formats available
Understanding Ratio Simplification
What is a Ratio?
A ratio is a way to compare two or more quantities by showing the relationship between their sizes. Ratios are written as A : B (read as "A to B") and tell us how many parts of one quantity exist relative to another quantity.
Why Simplify Ratios?
- •Makes ratios easier to understand and work with
- •Reveals the true proportional relationship
- •Enables easier comparison between different ratios
- •Standard form for mathematical calculations
Simplification Process
A : B = (A ÷ GCF) : (B ÷ GCF)
Step 1: Find the Greatest Common Factor (GCF) of all numbers
Step 2: Divide each number by the GCF
Step 3: Write the result as the simplified ratio
Alternative Forms
- 1 : n form: Divide by first number
- n : 1 form: Divide by second number
- Percentage form: Convert to percentages
- Decimal form: Express as decimal ratios
Real-World Applications
Cooking & Recipes
Scale ingredients proportionally: 2 cups flour : 1 cup water = 2:1 ratio
Business & Finance
Compare profit margins, debt-to-equity ratios, or market share proportions
Science & Engineering
Chemical reaction ratios, gear ratios, concentration ratios