Ratio Calculator

Simplify ratios to their simplest form or solve for an unknown value.

Simplify a Ratio

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Frequently Asked Questions

What is a ratio and how is it simplified?

A ratio shows the relative sizes of two or more values. To simplify a ratio, divide both numbers by their greatest common divisor (GCD). For example, the ratio 8:12 simplifies to 2:3 because both numbers can be divided by 4 (the GCD of 8 and 12).

How does cross-multiplication work in ratio problems?

Cross-multiplication is used to solve proportion problems. If you have A:B = C:X, you can cross-multiply to get A × X = B × C, then solve for X by dividing both sides by A: X = (B × C) / A. This method ensures the ratios remain equivalent.

What are some practical applications of ratios?

Ratios have many real-world applications:
• Cooking: Scaling recipes up or down
• Finance: Analyzing financial statements and ratios
• Construction: Mixing materials like concrete or paint
• Maps: Scale representations of distances
• Photography: Aspect ratios for images
• Education: Grade distributions and test scores

Can ratios include decimal numbers?

Yes, ratios can include decimal numbers. However, it's often preferred to convert them to whole numbers by multiplying both parts by a common factor. For example, the ratio 1.5:2.5 can be converted to 3:5 by multiplying both numbers by 2. This makes the ratio easier to understand and work with.

What's the difference between ratio and proportion?

A ratio is a comparison of two quantities (e.g., 3:4), while a proportion is an equation stating that two ratios are equal (e.g., 3:4 = 6:8). Ratios show the relationship between quantities, while proportions show the equality between two ratios.

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Ratio Calculator

Simplify a Ratio

Solve for an Unknown

Frequently Asked Questions

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