Whether you are doing simple multiplication or a complicated calculus problem, you must use a predetermined set of rules, called an algorithm, to solve it. An algorithm includes a finite number of steps to solve any given problem.
The word algorithm has an unusual backstory. It seems the 9th Century Persian mathematician Al-Khwārizmī wrote about calculations, and when his work was translated into Latin 300 years later, his name was somehow incorporated into the name of the process as Algoritmi. This got confused with the Greek word for number, arithmos, leading to the evolution of the word as we know it. It's a mish-mash, ironic for a word that stands for a rather rigid set of rules.