The ratio compounded of duplicate ratio of 4:5, triplicate ratio of 1:...
Ratio of Ratios
When we talk about a ratio of ratios, we are essentially comparing different ratios with each other. In this case, we have four different ratios that we need to compare to arrive at the final answer. Let's break down each of these ratios and then combine them to get the final answer.
Duplicate Ratio of 4:5
A duplicate ratio is simply a ratio that has been multiplied by 2. In this case, we have a ratio of 4:5 which has been duplicated to give us a new ratio of 8:10. We can simplify this ratio by dividing both sides by 2 to get 4:5.
Triplicate Ratio of 1:3
A triplicate ratio is a ratio that has been multiplied by 3. In this case, we have a ratio of 1:3 which has been triplicated to give us a new ratio of 3:9. We can simplify this ratio by dividing both sides by 3 to get 1:3.
Sub Duplicate Ratio of 81:256
A sub-duplicate ratio is a ratio that has been square rooted. In this case, we have a ratio of 81:256 which has been square rooted to give us a new ratio of 9:16.
Sub Triplicate Ratio of 125:512
A sub-triplicate ratio is a ratio that has been cube rooted. In this case, we have a ratio of 125:512 which has been cube rooted to give us a new ratio of 5:8.
Combining Ratios
Now that we have simplified all four ratios, we can combine them to get the final answer. To do this, we simply multiply all four ratios together to get:
4:5 x 1:3 x 9:16 x 5:8
Next, we can simplify this ratio by multiplying the numerators together and the denominators together:
4 x 1 x 9 x 5 : 5 x 3 x 16 x 8 = 180:1920
We can simplify this ratio by dividing both sides by 60 to get:
3:32
Final Answer
The final answer is the ratio 3:32.