# What Is an Inverse Relationship?

Inverse relationships are equations in which one variable increases, while the other decreases so that the ultimate product remains the same. For example, if an equation calls for the length of an object to decrease as its width increases while keeping the product of the two the same, the length and width have an inverse relationship. Inverse relationships are common in both mathematics and the natural world.

One example of an inverse relationship in the natural world is reproductive output. For instance, a rat may give birth to five babies that weigh 2 grams each, or it may give birth to two babies that are 5 grams each. Because the total reproductive output of the animal must remain constant, the birth weight and number of young are inversely proportional to each other. If the average baby weight increases, the average number of young must decrease.

In economics, the law of supply and demand is an inverse relationship. As the demand for a given product or service rises, the supply for the product or service decreases. The opposite effect also occurs. If the supply of a product or service rises, the relative amount of demand for each individual good or service must fall.

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