Define both quantities first
The rule of three relates quantity A to value B and asks what value X corresponds to another quantity C. Write down what each field measures: people and hours, units and cost, or distance and time.
Units within the same quantity must be consistent. If A is meters and C is centimeters, convert one before calculating. A correct formula with mixed units can produce a misleading result.
Direct proportion
If doubling A doubles B, the relationship is direct. Calculate X = B × C / A. For example, if 2 units cost 6, 3 units cost 9 provided the price per unit stays the same.
Not every purchase follows that condition: a bulk discount or fixed shipping charge breaks simple proportionality. Check what conditions keep the relationship constant before using the result.
Inverse proportion
If doubling A halves B, the relationship is inverse. Calculate X = A × B / C. Two people completing a job in 6 hours would correspond to three people in 4 hours if work rate and coordination stay constant.
This is a simplified model. Adding people does not always reduce time proportionally: some tasks cannot be divided or space may be limited. Choose the formula based on the problem, not your preferred result.
A quick result check
For a direct case, compare ratios B/A and X/C. In the example, both 6/2 and 9/3 equal 3. For an inverse case, compare products A × B and C × X: both 2 × 6 and 3 × 4 equal 12.
A zero denominator is rejected. Results display limited precision; for physical measurements, round the final result according to the actual detail in your data.
- Identify quantities and units.
- Choose direct or inverse according to what happens when one quantity increases.
- Enter A=2, B=6 and C=3 to test both models.
- Check ratios or products and review the problem’s assumptions.
Criteria for reviewing and delivering the result
Write both quantities and the condition maintaining their relationship. For direct proportion, explain why the ratio remains constant. For inverse proportion, explain why the product remains constant. Three available numbers are insufficient if neither model can be justified. A fixed component or capacity constraint can break proportionality that seemed plausible on a quick reading. Establishing the model is part of the solution rather than a result returned by the calculator.
Prepare a small example verifiable through ratios or products. Transfer the same correspondence to the actual problem, converting units before entering quantities. Retain A with B and C with X to detect swapped fields. Check divisors and result signs. The tool solves the selected model but cannot determine whether it describes a situation adequately. Weighted average combines differently weighted values, while Unit converter handles equivalent measurements. Keep a sentence stating the assumption beside the calculation because another reviewer needs the relationship, not merely a precise looking final number. A correct arithmetic result becomes useful when the quantity, unit and proportionality condition are all clear to the reader.
The same data with two different relationships
Enter A=2, B=6 and C=3. Calculate using a direct proportion first, then switch to inverse.
The direct proportion gives X=9; the inverse gives X=4. The tool displays the formula used so you can distinguish why the result changes.
Do not choose a model just because its number looks plausible. Describe what each quantity means and check whether ratios or products should remain constant.
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