Ratio Calculator
Solve ratio problems, proportions, and simplify ratios instantly
Solve Proportion (A:B = C:D)
Scale by Ratio
Scaled Values
📐 Quick Answer
The proportion 2:3 = 4:? solves to D = 6. The ratio 1:2 with a value of 10 gives you 10 : 20.
Dr. Snezana Lawrence
Mathematical Historian
15+ years experience
PhD from Yale University. Published mathematical historian ensuring precision in all calculations.
Education
PhD in Mathematical History - Yale University
📑 Table of Contents
🤔 What is a Ratio?
A ratio is a comparison of two or more quantities. It shows how many times one value contains or is contained within another. Ratios can be written in several ways:
Colon notation
Fraction notation
Word notation
Real-World Examples
- Recipe: 2 cups flour to 1 cup sugar (2:1)
- Map Scale: 1 inch = 100 miles (1:100)
- Class: 15 boys to 10 girls (3:2 simplified)
- Odds: 3:1 odds of winning
⚖️ Understanding Proportions
A proportion is an equation stating that two ratios are equal. If a:b = c:d, then these ratios are in proportion.
Cross Multiplication
a : b = c : d → a × d = b × c
The cross products are always equal in a true proportion
Solving for Unknown
2:3 = 4:x
2 × x = 3 × 4
2x = 12
x = 6
Checking Proportion
Is 2:3 = 4:6?
2 × 6 = 12
3 × 4 = 12
Yes! 12 = 12 ✓
🔽 How to Simplify Ratios
To simplify a ratio, divide both numbers by their greatest common divisor (GCD):
- Find the GCD of both numbers
- Divide each number by the GCD
- The result is the simplified ratio
Example: Simplify 24:36
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
GCD = 12
24 ÷ 12 = 2
36 ÷ 12 = 3
Simplified: 2:3
Common Simplified Ratios
📝 Examples and Applications
Cooking Recipe Scaling
A recipe calls for 2 cups flour for 4 servings. How much flour for 10 servings?
2:4 = x:10
4x = 20
x = 5 cups of flour
Map Distance
A map scale is 1:50,000. If two cities are 3 cm apart on the map, what's the real distance?
1 cm : 50,000 cm = 3 cm : x
x = 150,000 cm = 1.5 km
Mixing Paint
Mix blue and yellow in ratio 3:5. If you use 12 oz of blue, how much yellow?
3:5 = 12:x
3x = 60
x = 20 oz of yellow
❓ Frequently Asked Questions
What is a ratio?
A ratio is a comparison of two quantities showing how many times one value contains or is contained within the other. It can be written as a:b, a/b, or "a to b".
How do you solve a proportion?
To solve a proportion a:b = c:d, use cross multiplication: a × d = b × c. Then solve for the unknown variable.
How do you simplify a ratio?
To simplify a ratio, find the greatest common divisor (GCD) of both numbers and divide each by it. For example, 12:18 simplified is 2:3.
What's the difference between ratio and rate?
A ratio compares quantities of the same unit, while a rate compares quantities with different units. For example, 60 miles per hour is a rate, while 3:2 boys to girls is a ratio.
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Dr. Snezana Lawrence
Mathematical Historian | PhD from Yale
Dr. Lawrence is a published mathematical historian with a PhD from Yale University. She ensures mathematical precision and accuracy in all our calculations, conversions, and academic score calculators. Her expertise spans computational mathematics and educational assessment.
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