Use this when both quantities move in the same direction. Enter one known pair, add the new value, get X with the ratio check shown.
Write the proportion as A : B = C : X. The tool solves X using cross multiplication.
Load one. Then change a value and solve again.
Ask one question. If the first quantity doubles, does the second also double?
If your answer is yes, direct rule of three is the right tool.
Practical shortcut: look for a fixed unit rate in the story. Cost per item, miles per hour, grams per serving. A stable unit rate usually signals direct proportion.
People often get a wrong answer with perfect arithmetic.
The setup was wrong.
These are the common failure points.
Shopping. If 3 liters of paint cover 36 square meters, how much paint covers 50 square meters? Setup: 3 : 36 = X : 50. Solve X.
Work output. If a machine makes 120 parts in 8 hours, how many parts in 11 hours at the same speed? Setup: 8 : 120 = 11 : X.
Ingredients. If 250 g of flour makes 10 cookies, flour for 18 cookies? Setup: 10 : 250 = 18 : X.
Rule of three is fast. It is not the only path.
| Approach | Best when | What you do |
|---|---|---|
| Unit rate | You want a mental check | Compute B/A, then multiply by C |
| Cross multiplication | You want a single equation | Set A x X = B x C |
| Proportion table | You teach or explain | Build a small ratio table then scale |
If you want to practice cross multiplication without story problems, open Cross Multiplication. If you need a broader ratio workflow, use Proportional Calculator.
Direct rule of three assumes a linear relationship.
It fails when the unit rate changes.
If you suspect inverse behavior, switch to Inverse Rule of Three before you calculate.
