Ratio Calculator

Solve proportions, simplify ratios, and find equivalent ratios with step-by-step solutions

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Solve Proportion

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Solve Proportion

Ratio Calculation Results

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How to Use the Ratio Calculator

Master ratios and proportions with step-by-step solutions

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Solve Proportions

Find the missing value in A:B = C:x using cross multiplication

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Simplify Ratios

Reduce ratios to their simplest form using GCD

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Equivalent Ratios

Generate equivalent ratios by multiplying both terms

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Step-by-Step

See detailed calculation steps for learning and verification

Ratio Calculator FAQ

What is a ratio?

A ratio is a comparison between two or more related quantities. It shows how many times one value contains or is contained within another. Ratios can be written as "a:b", "a to b", or as a fraction "a/b". For example, a ratio of 3:2 means the first quantity is 1.5 times the second.

How do you solve a proportion?

To solve a proportion like A:B = C:x, use cross multiplication. Multiply the means (B x C) and extremes (A x x) to get A x x = B x C. Then solve for x: x = (B x C) / A. For example, 3:6 = 9:x gives us x = (6 x 9) / 3 = 18.

How do you simplify a ratio?

To simplify a ratio, find the Greatest Common Divisor (GCD) of both terms using the Euclidean algorithm, then divide each term by the GCD. For example, 8:12 has GCD = 4, so the simplified ratio is 2:3. A ratio is fully simplified when the GCD of its terms is 1.

What is the difference between a ratio and a fraction?

A ratio compares two quantities (written as a:b) while a fraction represents a part of a whole (written as a/b). Every ratio can be expressed as a fraction, but a fraction always represents a single value whereas a ratio expresses a relationship. For example, the ratio 3:4 can be written as the fraction 3/4.

What are equivalent ratios?

Equivalent ratios have the same value when simplified. You create equivalent ratios by multiplying or dividing both terms by the same non-zero number. For example, 2:3, 4:6, 6:9, and 8:12 are all equivalent ratios because they all simplify to 2:3. They represent the same proportional relationship.