by There are concepts you need to understand in duplicate ratios. One is duplicate ratios itself and the other is a sub-duplicate ratio. In duplicate ratios, when the ratio p/q is compounded with itself, the resulting ratio which is p²/q² is called as the duplicate ratio. For example, 16/9 is the duplicate ratio of 4/3.
The duplicate ratio of the ratio of a:b is also defined as the compound ratio of a:b and a:b
=> (a × a) : (b × b) => a² : b²
So, the duplicate ratio of 6:7 = 6²:7² = 36:49
Similarly, for the sub-duplicate ratio, √a/√b is the sub-duplicate ratio of a/b or a:b.
For example 3:4 is the sub-duplicate ratio of 9:16.
Triplicate ratio: The triplicate ratio is the compound ratio of three equal ratios.
The triplicate ratio of the ratio a : b is the ratio a^3: b^3
In other words,
The triplicate ratio of the ratio m : n = Compound ratio of m : n, m : n and m : n
= (m × m × m) : (n × n × n)
= m^3 : n^3
Therefore, the triplicate ratio of 4 : 7 = 4^3: 7^3 = 64 : 343.
One thought on “Duplicate, Triplicate and Sub-duplicate of a ratio”