We are going to analyze the "standard" multiplication algorithm. There are actually several multiplication algorithms, and it’s not necessarily the case that the way it’s presented here is the way you learned it. But this is the most common way it’s taught in the United States.
Most people who can do this calculation have a difficult time describing it in terms other than the specific steps. (For example, multiply this by that, then this by that, then make sure you write a zero...) But we want to take the time to actually understand why these steps are what they are. To help, we are going to put the standard algorithm side-by-side with the grid method.
In performing the standard algorithm, you compute four separate multiplication calculations: \(7 \times 8\text{,}\)\(3 \times 8\) (don’t forget the carried terms), \(7 \times 2\text{,}\) and \(3 \times 2\) (again, don’t forget the carried terms). Explain how the four boxes in the grid method correspond to the four products in the standard algorithm. Be sure to explain the roles of the zeros after the numbers in the grid method compared to the standard algorithm.
2.
In the "middle" portion of the standard algorithm, we come across the numbers 296 and 740. Those numbers do not directly appear in the grid method, but those values do correspond to a certain aspect of the grid method. Explain how you can get the numbers 296 and 740 from the grid method.
3.
The last step of the standard algorithm is to add the two values from the "middle" portion. The last step of the grid method is to add the values in the boxes together. Verify that you get the same result using both methods.
