Introduction to standard way of multiplying multidigit numbers

What we're going to do in this video is think about how we might multiply 592 times 7. And in general, we're going to think about how we would approach multiplying something that has multiple digits times something that has one digit.

The way we're going to do it is the way that if you were to ask your parents, is probably the way that they do it. The typical approach is you would write the larger multi-digit number on top, and then you would write the smaller single-digit number below that. Since it's in the ones place, to seven, you would put it in the ones place column.

So, you'd put it right below the ones place in the larger number, right below that 2. Then you write the multiplication symbol, and the way you think about it is, “All right, I'm just going to take each of these places and multiply it by the 7.” For example, if I'm taking those two ones and I'm multiplying it times seven, well, that's going to be 14 ones.

Well, like there's no digit for 14. I can only put four of those ones over here, and then the other 10 ones I can express as 1 ten, and so I'd put it up there. Sometimes when people learn it, they say, “Hey, 2 times 7 is 14; I write the 4 and I carry the 1.” But all you're doing is you're saying, “Hey, 14 is 1 hundred plus 4 ones.”

Then you move over to the tens place. You say, “Hey, what's nine tens times seven?” Well, nine times seven is sixty-three. So, nine tens times seven is sixty-three tens. Plus another ten is sixty-four tens; you can only put four of those tens over here. So, the other 60 tens you can express as 600s, so you can stick that right over there.

Now, a lot of people would explain that as saying, “Hey, 9 times 7 is 63, plus 1 is 64. Write the 4 and carry the 6.” But hopefully, you understand what we mean by carrying. You're really trying to write 64 tens; only 4 of those tens can be expressed over here, or that's maybe the cleanest way to do it.

Then, the other 60 tens you can express as six hundreds. Last but not least, five hundreds times seven is going to be 35 hundreds, and then you add 600; you get hundreds, so 4100. So it's 4144.

Now I want to reconcile this or connect it to other ways that you might have seen this. So, let's say that let's do this again. If we were to write 592 times 7, one way that we've approached in the past is we say, "All right, what's 2 times 7?" Well, that's going to be 14. Notice that's the same 14; we're just representing it a little bit differently.

Then we might say, "Well, what is 9 times 7?" Do the same color and it's really 9 tens times 7; that's 63 tens. So you might write it right over there, which is the same thing as 630. Then you could think about what is 5 hundreds times 7? Well, that's 35 hundreds. So, you could write it like that, same thing as three thousand five hundred, and then you would add everything up.

So you have a total of four ones, you have a total of four tens, you have a total of eleven hundreds. So you could write one hundred there and then regroup the other 10 hundreds into the thousands place. It's 1000. 1000 plus 3 thousands is 4,000. So we got the exact same answer.

Because we essentially did the same thing over here when we were carrying it, we were essentially regrouping things from here. You could think about it where we're condensing our writing versus what we did here. Here we just very systematically said, "2 times 7, 9 times 7, 5 times 7," but we made sure to keep track of the places to figure out what each of those, you could think of as partial products would be, and then we added.

Well, here, we carried along the way, essentially regrouping the values when we said, “Hey, two ones times seven ones—that's fourteen ones,” which is the same thing as four ones plus one ten, and so on and so forth. So I encourage you, one, it's good to learn this method; it's the most common way that folks multiply.

Once again, your parents probably learned it this way, but it's really valuable to understand why these two things are the same thing. So really ponder that, think about that, and see if you can—if it all makes sense what's going on—that you're not just blindly memorizing the steps.