Ratios and proportional reasoning — Introduction to Ratios + 5 more topics

Inverse variation is a relationship where if you multiply two quantities, their product is always a constant. We usually write it as $y = k/x$ or $xy = k$, where $k$ is the constant of variation.

You'll know you're dealing with inverse variation if:
* As one quantity increases, the other decreases.
* The product of the two quantities remains constant.

Example: If you're driving 100 miles.
* At 50 mph, it takes 2 hours (50 * 2 = 100).
* At 25 mph, it takes 4 hours (25 * 4 = 100).
* At 100 mph, it takes 1 hour (100 * 1 = 100).

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When we say two quantities are proportional, we mean their ratio is constant. If you have two ratios that are equal, you have a proportion. We often write proportions as two fractions set equal to each other:

$\frac{a}{b} = \frac{c}{d}$

Here, $a, b, c, d$ are numbers, and $b$ and $d$ can't be zero.

Direct variation is a special kind of proportion. It describes a relationship where one quantity is a constant multiple of another. If $y$ varies directly with $x$, we can write it as: