Proportion
A proportion is a statement or equation showing that two ratios are equal to one another.
Fundamental Principles
Proportion Rule
If a : b = c : d, then the four quantities a, b, c, and d are in proportion. This is written as a : b :: c : d. The outer terms 'a' and 'd' are called extremes, and the inner terms 'b' and 'c' are called means.
Mean Proportion
The mean proportion between two numbers 'a' and 'b' is the square root of their product, calculated as √(a * b).
Essential Formulation Tips
- Product of Extremes = Product of Means. For a : b :: c : d, this means a * d = b * c.
- If three numbers a, b, and c are in a continuous proportion (a : b :: b : c), then b² = a * c.
Shortcut Execution Techniques
- Fourth Proportion Shortcut: To find the missing fourth term 'd' in a : b :: c : d, calculate it directly as d = (b * c) / a.
Contextual Inquiries (FAQs)
Q: What is the difference between a ratio and a proportion?
A: A ratio compares two specific values, while a proportion is an equation that sets two ratios equal to each other.
Example Breakdown: Finding a Missing Fourth Proportion
Standard missing proportion layout.Set up the proportion equation: 4 : 9 :: 12 : d.
Apply the product rule: Product of Extremes = Product of Means (4 * d = 9 * 12).
Multiply the values: 4 * d = 108.
Solve for d: d = 108 / 4 = 27.
Proportion and Mean Rules
Practice finding missing terms and calculating mean proportions.
Q1. What is the mean proportion between the numbers 4 and 16?