yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Introduction to standard way of multiplying multidigit numbers


3m read
·Nov 10, 2024

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.

More Articles

View All
Shopping For Affordable Watches With Teddy Baldassarre
Teddy’s learning he’s the grasshopper; he’s learning from the master. That’s the way I look at it. [Laughter] Garbage! You know, when you’re a fashionista like me, you can pick style out five yards away already. I’m kicking Teddy’s ass here; this is amazi…
Algorithms and selection | Intro to CS - Python | Khan Academy
Imagine you’re playing a word game where you need to guess only three words. What strategy might you use to solve for all the words in this game? One approach might be to just guess all of the letters in alphabetical order. So you start by guessing A, the…
One of the BEST way to save on taxes: What is a 401k
What’s up you guys, it’s Graham here. So, due to popular demand from a video I made about a week ago about why you should open up a Roth IRA, I’m going to make this video to share with you guys one of the best ways to reduce your taxable income and one of…
LearnStorm Growth Mindset: Chef De Cuisine on his career journey
My name is Zia Shaikh. I am 35 years old. I am chef to cuisine at Pawalo Restaurant, and I make $75,000 a year. My main responsibilities at Sheffield Cuisine are to oversee any type of kitchen operation, from menu development to dishwashing, to working al…
The Best and Worst Prediction in Science
How much energy is there in empty space? We believe there is 10 to the minus 8th ergs in every cubic centimeter of empty space. How much is an “erg”? It’s a very small amount. You know, if a mosquito flaps its wings, or a fly I guess flaps its wings, it’s…
Meth Smuggling Model | Locked Up Abroad
At that point in time, my main mission was to get it back to Australia. We bought a whole heap of crystal meth from Zack’s suppliers—big snaplock bags of drugs. So, we bought a whole heap of gift sets that had bath salts in them. There was a process; we w…