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MasterMath

Inverse Proportion Calculator

When one quantity goes up and the other goes down in step, what stays constant is their product. Six workers take half as long as three.

The value you want

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The value you want—
Constant product—
The proportion—
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How this was worked out

    The rule

    a × b = c × x, so x = (a × b) ÷ c

    Why it works

    In an inverse proportion the product of the paired values never changes. Double one and the other halves, so the product survives untouched — and that constant is what lets you solve for the missing value.

    How to do it by hand

    1. Multiply the first pair to get the constant
    2. Divide it by the third value
    3. That is the missing value
    4. Check: the new pair should multiply to the same constant

    What is worth knowing

    Inverse proportions are everywhere once you look: speed and travel time, workers and days, pressure and volume at fixed temperature. The last is Boyle's law, which is exactly this relationship with a name. The trap is assuming a relationship is inverse just because the quantities move oppositely — they also have to move in exact step. Doubling the workers rarely halves the time in practice, because communication overhead grows, which is Brooks's law and the reason the model is an idealisation.

    Frequently asked questions

    What is an inverse proportion?

    One where the product of the two quantities stays constant. Double one and the other halves.

    How is it different from a direct proportion?

    In a direct one the ratio stays constant; in an inverse one the product does.

    What are some real examples?

    Speed and travel time, pressure and volume at constant temperature, workers and days for a fixed job.

    Does doubling the workers really halve the time?

    In the model, yes. In practice coordination overhead means it rarely does, which is Brooks's law.