Rule of Three

The so-called rule of three is an educational tool utilized historically to verbalize the process of solving basic linear equations with four terms where three of the terms are known. Evidence suggests that there are two "different" rules of three: One direct and one inverse.

The direct rule of three describes the process for finding the fourth term  of a proportion

(1)

given that , , and  are known. In words, the solution is to "multiply the second and third numbers together, and divide product by the first" so that the term  in equation (1) above becomes

(2)

The inverse rule of three describes the process of solving for  when  and , , and  are known. In words, one solves the problem by "multiplying the first and second terms together, and dividing the product by the third" so that

(3)

REFERENCES:

Hersee, J. "Multiplication is Vexation." Paradigm 24, 1997. http://faculty.education.illinois.edu/westbury/paradigm/Hersee.html.