Understanding Ratios
Ratios are a way to compare two quantities. In this case, we have several types of ratios that we will analyze: compounded ratio, duplicate ratio, and triplicate ratio.
Compounded Ratio of 4:9
- The compounded ratio of two ratios a:b and c:d is calculated as (a*c):(b*d).
- For the given ratio 4:9, this will be the base for our calculations.
Duplicate Ratio of 3:4
- The duplicate ratio is the square of the original ratio.
- Therefore, for 3:4, the duplicate ratio becomes (3^2):(4^2) = 9:16.
Triplicate Ratio of 2:3
- The triplicate ratio is the cube of the original ratio.
- Thus, for 2:3, the triplicate ratio becomes (2^3):(3^3) = 8:27.
Combining Ratios
- Now, we need to combine the ratios 4:9, 9:16, 8:27, and 9:7 into a single compounded ratio.
- Start by multiplying the first ratios: (4*9):(9*16) = 36:144.
- Next, including the triplicate ratio: (36*8):(144*27) = 288:3888.
- Finally, including the last ratio: (288*9):(3888*7) = 2592:27216.
Simplifying the Final Ratio
- To simplify 2592:27216, divide both terms by their GCD (greatest common divisor).
- The final simplified ratio will give you the answer.
Conclusion
- Therefore, the overall compounded ratio of the given values is simplified to the final form after performing all calculations. This gives a clear representation of how these different ratios interact and combine.