Ratio Calculator
Simplify ratios, solve proportions, and find equivalent ratios
How to Use This Calculator
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Simplify Ratio
Enter two numbers to simplify their ratio. The calculator finds the greatest common divisor (GCD) and divides both numbers by it to get the simplest form.
Example Problems:
- Simplify 6:9 → 2:3 (recipe proportions)
- Simplify 12:18 → 2:3 (mixing ratios)
- Simplify 15:25 → 3:5 (compare quantities)
Solve Proportion
Use this mode to find an unknown value in a proportion. Enter three known values and the calculator will find the fourth value (x) that makes the ratios equal.
Example Problems:
- If 2:3 = 4:x, then x = 6 (scale recipes)
- If 1:5 = 3:x, then x = 15 (unit conversion)
- If 3:4 = 9:x, then x = 12 (scaling dimensions)
Equivalent Ratios
Generate multiple equivalent ratios by multiplying both parts of the ratio by the same number. This helps understand that ratios can be expressed in different forms while maintaining the same proportion.
Example:
1:2 = 2:4 = 3:6 = 4:8 = 5:10
All these ratios represent the same relationship
Frequently Asked Questions
What is a ratio?
A ratio is a comparison of two quantities. It shows how many times one value contains another. Ratios are written as a:b or a/b. For example, a ratio of 2:3 means for every 2 of the first item, there are 3 of the second item.
How do I simplify a ratio?
To simplify a ratio, find the greatest common divisor (GCD) of both numbers and divide both by it. For example, to simplify 6:9, find GCD(6,9) = 3, then divide both: 6÷3 = 2 and 9÷3 = 3, giving the simplified ratio 2:3.
What is a proportion?
A proportion is an equation stating that two ratios are equal. For example, 2:3 = 4:6 is a proportion because both ratios simplify to the same value. Proportions are useful for scaling and unit conversions.
How do I solve for x in a proportion?
Use cross-multiplication: if a:b = c:x, then a × x = b × c, so x = (b × c) ÷ a. For example, if 2:3 = 4:x, then 2x = 3 × 4 = 12, so x = 12 ÷ 2 = 6.
What are equivalent ratios?
Equivalent ratios are ratios that express the same relationship. They're created by multiplying or dividing both parts by the same number. For example, 1:2, 2:4, and 3:6 are all equivalent because they all simplify to 1:2.
What's the difference between a ratio and a fraction?
A ratio compares two separate quantities (a:b), while a fraction represents part of a whole (a/b). However, ratios can be written as fractions. For example, a ratio of 2:3 can be written as 2/3 when comparing the first quantity to the total (2+3=5).
Why use a ratio calculator?
A ratio calculator saves time, ensures accuracy, and shows step-by-step work. It's perfect for homework help, recipe scaling, unit conversions, mixing solutions, and any situation where you need to work with proportional relationships.
What are real-world uses of ratios?
Ratios are everywhere: cooking recipes (ingredient proportions), mixing paint colors, diluting chemicals, map scales, gear ratios in vehicles, aspect ratios in screens, comparing statistics, financial analysis (debt-to-income ratio), and construction blueprints.
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Educational Disclaimer
This calculator is provided for educational purposes and homework assistance. While we strive for accuracy, please verify critical calculations independently. Results should not be used as the sole basis for important financial, academic, or professional decisions. Always check your work and consult with appropriate professionals when needed.