What happens when you multiply one number by another? Is there a right answer to this question? What does it tell us about how you should think about multiplication? Keep on reading to find out.
Quick question: How do you prefer to think about multiplication? In other words, how do you like to picture the meaning of multiplication so that you too get that awesome deep-down-in-the-gut feel for it?
In truth, I’m pretty sure multiplication isn’t a topic that most people particularly like to think about at all. If you are like most people, you memorized the multiplication table way back in the day and haven’t given it much thought since. If that sounds familiar, rest assured that I don’t think any less of you. In fact, I’d say you’re perfectly normal.
But I’d also say that it’s good for all of us to spend a few minutes thinking about what we’re actually doing when we’re doing stuff. It’s a healthy habit to get into and it’s actually kind of fun too. And besides, memorization can only take us so far in math … and in life—thinking is a much better option in the long run.
So today let’s think about multiplication.
Is Multiplication (Just) a Handy Way to Add Faster?
People often like to think about multiplication as being nothing more than a sort of shortcut for adding some number to itself some other number of times. For example, you can think of the expression 3 • 5 as a request for you to add 5 to itself 3 times—that is, as 3 • 5 = 5 + 5 + 5 = 15. If you want a picture to have in your head for this view of multiplication, think of the process as stacking up three 5-box-long rows and then counting up all the boxes:
Clearly this picture gives the correct answer—that is, 3 • 5 really does equal 15. Of course, we can extend this idea to the problems 4 • 5 = 5 + 5 + 5 + 5 = 20, 5 • 5 = 5 + 5 + 5 + 5 + 5 = 25, and so on by stacking more and more 5-box-long rows onto the pile. If you think about it, you’ll see that we’re just using multiplication as a convenient way to save ourselves from having to write a bunch of extra terms in an addition problem.
So that’s how we should think about multiplication? It’s just a handy way to do addition more efficiently? No, not exactly—multiplication is certainly this, but it’s a lot more too.