# Calculations

Upon completing the first piece, *...(Multiplication)*, I realized I could check its answer by performing the reverse calculation, i.e. division. Specifically, if *...(Multiplication)*’s answer was correct, dividing it by one of the initial two numbers would result in the other number. So I constructed the second piece, *...(Division)*, using the long division method, also taught to me in elementary school. With this method, you calculate the answer one digit at a time, with intermediate steps of subtraction and remainders, writing these below one another and shifting one place to the right each step. After completing a significant amount of the calculation, the answer I was constructing suddenly diverged from *...(Multiplication)*. After checking my work and ruling out any error in *...(Division)*, I had to admit that *...(Multiplication)* had an error. I decided to work back into the first piece, changing its answer, which in turn, changed the second piece being constructed. Continuing on, I discovered more errors, and it quickly became apparent that *...(Division)* and *...(Multiplication)* were inextricably linked, one guiding the other to completion. The only assurance on the accuracy of both answers was if *...(Division)* ended with its final subtraction having no remainder, i.e. zero, which it thankfully did.