Ratio Calculator
Simplify ratios, solve proportions, find missing values, and calculate equivalent ratios with detailed explanations
Ratio Calculator
Simplify Ratio
:
Enter two numbers to find their simplified ratio
Results
Enter values and click "Calculate Ratio" to see the results
Understanding Ratios and Proportions
What is a Ratio?
A ratio is a comparison between two or more quantities, showing how many times one value is contained in another. Ratios can be expressed in different forms.
Colon notation: 3:4
Fraction form: 3/4
Word form: "3 to 4"
Decimal form: 0.75
What is a Proportion?
A proportion is an equation that states two ratios are equal. It's used to find unknown values when ratios are equivalent.
General form: a:b = c:d
Cross multiplication: a × d = b × c
Example: 2:3 = 6:9
Check: 2 × 9 = 3 × 6 = 18
Types of Ratios
Part-to-Part Ratios
Compare one part to another part
Example: In a class of 20 students with 12 boys and 8 girls, the ratio of boys to girls is 12:8 or 3:2
Part-to-Whole Ratios
Compare a part to the total
Example: In the same class, the ratio of boys to total students is 12:20 or 3:5
Real-World Applications
- • Recipe scaling
- • Map scales
- • Financial ratios
- • Mixing solutions
- • Speed and distance
- • Architecture and design
Ratio Properties
- • Order matters: 2:3 ≠ 3:2
- • Can be simplified: 6:9 = 2:3
- • Equivalent ratios: 1:2 = 2:4
- • Unit ratios: express as 1:n
- • Golden ratio: ≈ 1.618:1
Common Mistakes
- • Confusing ratios with fractions
- • Not simplifying ratios
- • Incorrect cross multiplication
- • Wrong order in ratios
- • Adding ratios incorrectly
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