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Ratio Calculator
Method: Divide both by their GCD
Formula: (12 ÷ 3) × 5 = 20
Results
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Ratio Formulas & Concepts
Simplifying a Ratio
Divide both numbers by their Greatest Common Divisor (GCD).
Example: 12:18, GCD = 6, so 12:18 = 2:3
Comparing Ratios
Convert both ratios to decimal form to compare.
Example: 2:3 = 0.667 vs 3:4 = 0.75, so 3:4 is larger
Scaling a Ratio
Multiply both numbers by the scale factor.
Example: Scale 2:3 by 5 = (2×5):(3×5) = 10:15
Finding Missing Value (Proportion)
Use cross multiplication: A/B = X/Y, solve for Y.
Example: If 3:5 and first is 12, then second = (12 × 5) ÷ 3 = 20
Key Ratio Concepts
- Ratio: Comparison of two quantities (A:B or A/B)
- Equivalent Ratio: Same relationship but different numbers (2:3 = 4:6)
- Proportion: Two equal ratios (A:B = C:D)
- Scale Factor: Number used to multiply a ratio
- Simplest Form: Ratio with GCD = 1
How to Use the Calculator
For Simplifying Ratios
Step 1: Stay in the "Simplify" tab.
Step 2: Enter the first and second numbers of the ratio.
Step 3: Click "Calculate" to get the simplified ratio.
For Comparing Ratios
Step 1: Click the "Compare" tab.
Step 2: Enter the first ratio (A : B).
Step 3: Enter the second ratio (C : D).
Step 4: Click "Calculate" to see which ratio is larger.
For Scaling Ratios
Step 1: Click the "Scale" tab.
Step 2: Enter the original ratio (A : B).
Step 3: Enter the scale factor.
Step 4: Click "Calculate" to get the scaled ratio.
For Finding Missing Values
Step 1: Click the "Missing Value" tab.
Step 2: Enter the known ratio (A : B).
Step 3: Enter the proportional value.
Step 4: Click "Calculate" to find the missing value.
Understanding Results
- Calculation Type: Shows which ratio operation was performed
- Formula Used: Shows the mathematical formula applied
- Breakdown: Shows step-by-step calculation
- Explanation: Explains what the result means
Understanding Ratios & Proportions
What is a Ratio?
A ratio is a comparison of two quantities. It shows how much of one thing there is compared to another. Ratios can be written as A:B, A/B, or A to B.
What is a Proportion?
A proportion states that two ratios are equal. If A:B = C:D, then A/B = C/D. This is often used to solve for unknown values.
Common Ratios in Everyday Life
- 1:1 Equal amounts (50:50)
- 2:1 Twice as much (2 to 1)
- 3:2 Golden ratio related (art/design)
- 16:9 Widescreen video format
- 4:3 Standard screen format
Simplifying Ratios
To simplify a ratio, divide both numbers by their GCD (Greatest Common Divisor). Example: 12:18 becomes 2:3 (divided by 6).
Equivalent Ratios
Ratios that express the same relationship. Example: 2:3, 4:6, 6:9, and 8:12 are all equivalent.
Real-World Applications of Ratios
Cooking & Recipes
Recipe ratios like 3:2:1 (flour:butter:sugar) scale easily for different batch sizes.
Architecture & Design
Aspect ratios (16:9 screens), golden ratio (1.618:1) for aesthetically pleasing designs.
Maps & Scale Models
Map scales like 1:100,000 show real distances compared to map distances.
Business & Finance
Profit ratios, debt-to-income ratios, and price-to-earnings ratios for financial analysis.
Medicine & Chemistry
Medication dosages by weight (mg/kg), chemical compound ratios in formulas.
Photography & Art
Aspect ratios for images, mixing paint colors (blue:white = 1:3 for light blue).
Sports & Games
Win-loss ratios, points per game ratios, odds in betting (3:1 odds).
Manufacturing & Quality
Quality control ratios, defect rates, production ratios between products.
Frequently Asked Questions
What's the difference between ratio and fraction?
A ratio compares two quantities (2:3), while a fraction shows one part of a whole (2/5). Though written similarly, they mean different things.
Can ratios have decimals?
Yes! Ratios can be whole numbers, decimals, or fractions. Example: 2.5:3.75 or 1/2:3/4. They're often simplified though.
What does equivalent ratio mean?
Equivalent ratios express the same relationship. Example: 2:3, 4:6, 6:9 are equivalent (multiply/divide both by same number).
How do I scale a recipe using ratios?
If recipe is 2:3:1 (flour:butter:sugar) and you want to double it, multiply all by 2: 4:6:2. The ratio stays the same!
What's cross multiplication in proportions?
If A/B = C/D, then A×D = B×C. Used to solve for unknown values. Example: 3/5 = 12/X, then 3×X = 5×12, so X = 20.
Can ratios be written in different ways?
Yes! 2:3 can be written as 2/3 or "2 to 3". They all mean the same thing - a comparison of 2 to 3.
What's the simplest form of a ratio?
When the GCD of both numbers is 1. Example: 2:3 is simplest, but 4:6 is not (GCD=2, simplifies to 2:3).
Are order matters in ratios?
Yes! 2:3 is different from 3:2. Order shows which quantity is being compared to which.
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