The Proportion Equation
The proportion equation is useful in a variety of situations. In these examples, it will be used to convert any slope to a unit slope (over 12 in imperial, or 1000 in metric).
To set up a proportion equation, think of this:
There are 4 slots. Greens are the same, and blues are the same. For example:
- The “unit” rise and run are on one side together. The “total” rise and run on the other.
- Rise is on top, on both sides. Run is on the bottom, on both sides.
If you know 3 items, you can figure out the 4th using this method:
- Cross multiply the two numbers
- Divide by the third.
Example:
Consider a construction with slope 3:4. The total run is 4’. What is the total rise?
Set up the proportion equation:
Cross multiply and divide:
4 × 4 ÷ 12 = 1.333’ or 1’ – 4”.
Example:
In the above example, you can use the proportion equation to find the rise (or gable stud length) of any arbitrary point. Say for example, there was a stud at 1.5 ft. How long is it? Find the rise for run at 1.5 ft.
4 × 1.5 ÷ 12 = 0.5’ or 6”. The gable stud is 6” long.
Example:
Convert the unusual slope 6:7 to a unit slope (over a run of 12)
6 × 12 ÷ 7 = 10.3. The unit run is . Naturally, this is not a practical slope. However, the
numbers demonstrate the process.
Proportion Equation Exercise Set 1
Change the following ratios to a unit slope in imperial, and metric.
|
|
|
|
|
|
|
|
Answers
- 8.57:12, 714:1000
- 18.24:12, 1520:1000
- 4:12, 333:1000
- 9:12, 750:1000
- 4:12, 333:1000
- 7.2:12, 600:1000
- 9:12, 750:1000
- 10.8:12, 900:1000