What Is Inverse Proportion?
Definition
Inverse Proportion: A relationship in which one quantity grows by the same factor as the other shrinks. The product of matching values stays constant: if 4 workers need 12 days, 6 workers need 8.
Inverse proportion is a relationship in which one quantity grows by the same factor as the other shrinks. The product of matching values stays constant: k = a × b. For example, if 4 workers finish a job in 12 days, 6 workers finish it in 8 days; both products are 48.
Where it appears in the formulas
In an inverse proportion a × b = c × x, so x = a × b / c and the constant is k = a × b. A trip that takes 5 hours at 60 km/h takes x = 60 × 5 / 75 = 4 hours at 75 km/h. The constant k = 300 is the length of the trip in kilometres.
A common mistake
Not every relationship where one value falls as the other rises is an inverse proportion; the product has to stay the same. Worker problems assume that everyone works at the same pace.