How do you solve a proportion with a missing value?

Use cross multiplication. If A:B = C:D, then A x D = B x C. To find a missing value, multiply the two known diagonal values and divide by the remaining known value. For example, if 2:3 = x:9, then x = (2 x 9) / 3 = 6.

How do you simplify a ratio?

Divide both numbers in the ratio by their greatest common factor (GCF). For example, to simplify 12:8, find the GCF (4), then divide: 12/4 : 8/4 = 3:2. The simplified ratio represents the same proportion in lowest terms.

What is the golden ratio?

The golden ratio is approximately 1:1.618 (or 1.618:1). It appears naturally in spiral patterns, flower petals, and is considered aesthetically pleasing. The Great Pyramid of Giza and the Parthenon both incorporate proportions close to the golden ratio.

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How Ratios Work

A ratio compares two quantities. If A:B = C:D, then:

A × D = B × C

This is called "cross multiplication" and is used to solve for unknown values in proportions.

Common Ratio Uses

Recipes: Scale ingredients up or down
Maps: 1:100,000 means 1 inch = 100,000 inches
Finance: Price-to-earnings ratios
Mixing: Paint, concrete, cocktails
Photography: Aspect ratios (16:9, 4:3)

Did You Know?

The golden ratio (1.618...) appears in spiral galaxies, hurricanes, and flower petal arrangements.
The Great Pyramid of Giza's base-to-height ratio closely approximates the golden ratio.
Aspect ratio 16:9 is used for modern screens because it's close to the average of common film ratios.

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The Ugly Empire Team

Software engineers and data specialists with backgrounds in financial services, mathematics, and educational technology. Our team builds tools using industry-standard formulas verified against authoritative sources.

Last reviewed: January 2026

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Disclaimer: This calculator provides estimates for informational purposes only. Results should not be considered financial, legal, medical, or professional advice. Always consult qualified professionals for important decisions. We strive for accuracy but cannot guarantee results will match real-world outcomes due to varying factors and individual circumstances.

Ratio Calculator

How Ratios Work

Common Ratio Uses

Did You Know?

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