The rule of three is one of the oldest and most practical tools in arithmetic, a quick method for solving a proportion when you know three values and need the fourth, and this calculator does it instantly for both direct and inverse relationships. Set it to direct proportion, enter the three known values in the pattern a is to b as c is to the unknown, and it returns the missing value by cross-multiplying. Switch to inverse proportion, where more of one thing means less of the other, and it applies the matching rule. The result updates as you type. The direct rule answers the everyday questions that fill shopping, cooking, maps and currency: if two items cost a certain amount, how much do five cost; if a recipe for four needs so much flour, how much for six; if a scale shows a distance one way, what does it mean on the ground. The arithmetic is just b times c divided by a, the heart of cross-multiplication. The inverse rule handles the situations where increasing one quantity shrinks another in step, so their product stays fixed: more workers finishing a job in fewer hours, a faster speed covering a distance in less time, or more pipes filling a tank quicker. There the answer is a times b divided by c. Knowing which case you are in is the only real skill, and seeing both options side by side makes that choice clear. That makes the tool genuinely useful for primary and secondary students learning ratio and proportion and checking homework, and for anyone scaling a recipe, converting quantities, working out prices, or solving a practical everyday proportion without fuss. Because the result recalculates live, you can change any value and watch the answer follow. The method and a worked example are explained clearly below.
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25
is to this (the unknown x)
How it works
For a direct proportion, a is to b as c is to x, so cross-multiplying gives x = b times c divided by a. For an inverse proportion the products are equal, a times b equals c times x, so x = a times b divided by c. Direct means the two quantities rise and fall together; inverse means one rises as the other falls.
Worked example
Direct: if 2 corresponds to 10, then 5 corresponds to 10 times 5 over 2, which is 25. Inverse: if 4 workers take 6 hours, then 8 workers take 4 times 6 over 8, which is 3 hours, because doubling the workers halves the time.
