2.4 Compounding (Combining) Ratios

If a : b and c : d are two ratios, their compound ratio is (a × c) : (b × d).

Special compound ratios of a ratio a : b with itself: - Duplicate ratio = a² : b² - Sub-duplicate ratio = √a : √b - Triplicate ratio = a³ : b³ - Sub-triplicate ratio = a^(1/3) : b^(1/3) - Inverse (reciprocal) ratio of a : b is b : a

Example 7: Find the compound ratio of 2 : 3 and 4 : 5. Compound ratio = (2 × 4) : (3 × 5) = 8 : 15.

Example 8: Find the duplicate ratio of 5 : 6 and the sub-duplicate ratio of 16 : 25. Duplicate ratio of 5 : 6 = 25 : 36. Sub-duplicate ratio of 16 : 25 = √16 : √25 = 4 : 5.

Example 9: If a : b = 2 : 3 and c : d = 5 : 7, find the compound ratio of (a : b), (c : d), and the duplicate ratio of (2 : 3). Compound ratio = 2 × 5 × 4 : 3 × 7 × 9 = 40 : 189 (using duplicate ratio 4:9 for the third component). This shows how three or more ratios multiply together term-by-term.