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 4^th 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

1.  8.57:12, 714:1000
2. 18.24:12, 1520:1000
3. 4:12, 333:1000
4. 9:12, 750:1000
5. 4:12, 333:1000
6. 7.2:12, 600:1000
7. 9:12, 750:1000
8. 10.8:12, 900:1000