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Given: 8 : 12
Find x where 8 : 12 = 12 : x
Solution:
Given: 3 : 4 = 9 : x
Solution:
A proportion is a mathematical statement that two ratios are equal. Understanding proportions is crucial for solving various real-world problems, from scaling recipes to calculating distances on maps. The basic form of a proportion is a:b = c:d or a/b = c/d.
| Concept | Definition | Example |
|---|---|---|
| Direct Proportion | When two quantities increase or decrease in the same ratio | Time and distance at constant speed |
| Inverse Proportion | When one quantity increases as the other decreases in the same ratio | Speed and time for fixed distance |
| Cross Product | Product of means equals product of extremes | In a:b = c:d, ad = bc |
The Golden Ratio (approximately 1.618) is perhaps the most famous proportion in mathematics and art. It appears in nature, architecture, and design, creating what many consider to be perfectly balanced proportions.
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