Question

the ratio compounded of 4:9 the duplicate ratio of 3:4 the triplicate ratio of 2:3 and 9:7 is

Answer 1

Compounded ratio is for two given ratios, for example a:b and c : d are two ratios, then their compounded ratio = ac : bd.

Duplicate ratio for a given ratio a : b is a² : b²

Triplicate ratio for a given ratio a : b is a³ : b³

sub-duplicate ratio for a given ratio a : b is √a : √b

sub-triplicate ratio for a given ratio a : b is ∛a : ∛b

========================================

Ratio compounded of ratio 4 : 9 with itself will be its duplicate ratio

Duplicate ratio of 3 : 4 is 3² : 4² or 9 :16

Triplicate ratios of 2/3 and 9/7 will be 2³ : 3³ and 9³ : 7³ ,i.e., 8/27 and 729 / 343.

However, if you want to find compounded ratio of 2/3 and 9/7, then it will be (2x9) / (3x7) = 18 / 21 = 6/7