Study Guide · Chapter 9
3.1 Definition
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Four quantities a, b, c, d are said to be in proportion if a : b = c : d, written as a : b :: c : d. Here a and d are called extremes, and b and c are called means.
Fundamental rule (cross-product rule): Product of extremes = Product of means, i.e., a × d = b × c.
Example 15: Find x if 5 : x :: 20 : 16. Product of extremes = product of means: 5 × 16 = x × 20 → 80 = 20x → x = 4.
Example 16: Are 8, 12, 10, 15 in proportion? Check 8 × 15 = 120 and 12 × 10 = 120. Since they’re equal, yes, 8 : 12 :: 10 : 15.
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