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Perimeter & area (video) | Perimeter | Khan Academy

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Perimeter is the distance around the outside of a shape. Area measures the space inside a shape. Learn how to calculate perimeter and area for various shapes.

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Thesaurus.com - The world's favorite online thesaurus!

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Thesaurus.com is the world's largest and most trusted online thesaurus for 25+ years. Join millions of people and grow your mastery of the English language.

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Breaking apart 3-digit addition problems

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Sal shows ways to break up addition problems using place value.

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In this video, I'll introduce you to a new way of computing division, especially for larger numbers. And then we'll think a little bit about why it works. So we're going to try to compute what 96 divided by 4 is. And I'm going to write it a little bit differently. I'm going to write 96 divided by-- so I'm going to write this strange-looking symbol right over here, this thing that covers the 96. But you could view this as 96 divided by 4. And I'll show you in a second why we write it this way. This is actually a very useful way of actually computing it. So the first thing we'll do is we'll say, well, how many times does 4 go into 9? Well, we know that 4 times 2 is equal to 8 and that 4 times 3 is equal to 12. So 3 would be too much. We would go above 9. So we want to be below 9 but not have too much left over. We want the largest number that gets us into 9 without going over 9. So we'll say it goes two times. 4 goes into 9 two times. And then we say, what's 2 times 4? Well, 2 times 4 is 8. 4 times 2 is 8. Or 2 times 4 is 8. And now, we subtract. We subtract the 8 from the 9. And we get 1. And now we bring down the next digit, which is the 6. And then we ask ourselves, well, how many times does 4 go into 16? Well, in this case, we know that 4 goes into 16 exactly four times. 4 times 4 is 16. So we say 4 goes into 16 four times. Then we multiply 4 times 4 is 16. We subtract. And 16 minus 16, we have absolutely nothing left over. And there we have our answer. I know it seems kind of magical at this point. But in a few seconds, we're going to think about why this actually worked. We got that 96 divided by 4 is equal to-- I want to do that in a different color-- 24. Now, what I want you to do right now is pause this video and think about why did this actually work. How did we magically get the right answer here? And you can verify this. Multiply 4 times 24, and you will get 96. Well, I'm assuming you gave a go at it. And the important thing always is to keep track of the place value. And it really tells you what's going on when we do this process. When we looked at this 9 right over here, this 9 is in the tens place. This is actually representing 90. It represents 9 tens. So we're saying, well, how many times does 4 go into 90 if we're thinking about multiples of 10? Well, it goes 20 times. 4 times 20 is 80. And so we said, well, 4 times 20 is 80. But we still have 16 left over. You do 96 minus 80. You have 16 left over to divide 4 into. And then 4 goes into 16 four times. So really, a lot of this is just saying, well, we first figured out that we could go 20 times. And then we said, well, that doesn't get us all the way to 96. We have to go another four times. Hopefully, that helps.

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Intro to long division (no remainders) (video) | Khan Academy

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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We've got 24 triangle things right over here. And what I want to do in this video is to divide it into different numbers of groups. So the first thing I want to do is I want to divide this 24 triangle things into 3 groups and think about how many do I end up per group. So let's try that out. So I'm going to divide it into 3 equal groups. So that is one equal group right over there. Then I have another equal group right over here. And then I have a third equal group right over here. So if I divide 24 into 3 equal groups-- 1, 2, 3-- how many are going to be in each group? Well, we can count that. We have 1, 2, 3, 4, 5, 6, 7, 8 in each group. So we could say that 24 divided by 3 is equal to 8. Now, you might say, hey, this is very similar to what we saw in multiplication. In multiplication, we said if we have 3 groups of 8, we could view that as 3 times 8 and get 24. And you are exactly right. Let me do those same colors-- we could also write that 3 times 8-- so if I have 3 groups of 8, that that is going to be equal to 24. So when we started in this video, we had 24 things. We want to divide it into 3 equal groups. We got 8 in each group, or you could say 3 equal groups of 8 is equal to 24. But there's even other ways of thinking about this. So let me clear this up a little bit. So let me clear that. So in the first example, I divided 24 into 3 equal groups. But you could also view 24 divided by 3 as dividing 24 into groups of 3. So let's think about what that looks like. So if we divide it into groups of 3, then, for example, this is a group of 3. That is a group of 3. This is a group of 3. You might see where this is going. That's a group of 3. That is another group of 3. And we're going to think about how many groups of 3 we're actually going to get. So this is another group of 3. And that's another group of 3. So how many groups of 3 did we get? Let's see, we have 1, 2, 3, 4, 5, 6, 7, 8 groups of 3. So another way of viewing 24 divided by 3 is divide 24 into groups of 3. And then you will have 8 groups of 3. And one way of thinking about this-- if you want to express the same thing in terms of multiplication-- is if you have 8 groups of 3, that is also going to be equal to 24. Whether you have 3 groups of 8 or 8 groups of 3, either way, you're going to have 24. Now, let's make things more interesting. What I want you to think about is, based on what we just saw, what is 24 divided by 12? And I encourage you to pause the video, draw out 24 triangles like this, and try to figure out what 24 divided by 12 is. Well, I assume you've paused the video. And there's two ways to think about 24 divided by 12. You could say, well, let's divide 24 into groups of 12 and think about how many groups we have. So we could do that. So let's see. This is one group of 12 right over here. That's one group of 12, and then here is another group of 12. So how many groups of 12 do we have? Well, we have 2 groups of 12. So we could say 24 divided by 12 is 2. But another just as reasonable way of doing this is you could have said, well, let me divide 24 into 12 groups instead of groups of 12. So if I want to divide it into 12 groups, 12 equal groups-- well, let's see. This is 1 equal group, 2 equal groups-- actually let me do it this way. Well, let me do this-- 2 equal groups, 3 4, 5, 6, 7, 8, 9, 10, 11, 12. So once again, if you say, oh, I'm going to divide 24 into 12 equal groups, how many do you have in each group? Well, you have 2. So once again, 24 could be viewed as 24 divided into 12 equal groups. And how many do you have in each group? Or 24 divided into groups of 12, and how many groups would you have? And that's what we saw in the last example. So now, let's make things even more interesting. What I want you to think about-- a couple of things. I want you think about what 24 divided by 6 is. And I also want you to figure out what 24 divided by-- let me use that same color-- 4 is. And once again, I encourage you to pause the video, draw these triangles, and figure it out. What is 24 divided by 6 and 24 divided by 4? So let's tackle 24 divided by 6 first. And let's try to divide 24 into 6 equal groups. So let's see. This could be 1 equal group, 2 equal groups-- in fact, each group here is a group of 4. And we have 6 rows. So 3 equal groups, 4, 5, and 6. And so if you divide 24 into 6 equal groups, how many do you have in each group? Well, it's pretty clear you have 4. You have 4 In each group. Another way we could have thought about that is we could have said, let me divide 24 into groups of 6. So if you divided 24 into groups of 6, you could have viewed it like this. So that's 1 group of 6 right there. That's another group of 6 right over here. That's another group of 6. And I think you see how many groups of 6 we have. How many groups of 6 do we have? We have 4. We have 4 groups of 6. Well, now let's think about what 24 divided by 4 is. Well, if I view 24 divided by 4 as taking 24 and dividing it into 4 equal groups, I've just drawn that. I have 4 equal groups, and in each group I have 6. So notice 24 divided by 6 is 4. 24 divided by 4 is 6. And that's because I could view this as 4 groups of 6 or say that 4 times 6 is equal to 24. Or you could just as equivalently say that 6 times 4 is 24. You could equivalently say that 6 times 4 is equal to 24.

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The idea of division (video) | Khan Academy

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We've got 24 triangle things right over here. And what I want to do in this video is to divide it into different numbers of groups. So the first thing I want to do is I want to divide this 24 triangle things into 3 groups and think about how many do I end up per group.

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I have these three star patches, I guess you could call them, right over here. And so I could say, if I had one group of three star patches, how many star patches do I have? So I literally have one group of three star patches. Well, that means that I have three star patches. 1, 2, 3. This is my one group of three. Now let's make it a little bit more interesting. Let's say that I had two groups. Let's say that I had two groups of three. So that's one group, and then here's a second group. Here's two groups of three. So how many total star patches do I have now? Well, I have two groups of three. Or another way of thinking about it is this is 3 plus 3. This is equal to 3 plus 3, which is equal to 6. So we see 1 times 3-- one group of 3 is 3. Two groups of 3, which is literally two 3's, is 6. Let's make it even more interesting. Let's have three groups of 3. Now, what is this going to be equal to? Well, it's three groups of 3. So I could write this as three groups, 3 times 3. And how many of these star patches do I now have? Well, this is going to be 3 plus 3 plus 3. It's going to be 3 plus 3 plus 3. Notice I have three 3's. I have two 3's. I have one 3. So this is 3 plus 3 plus 3 is equal to 9. And you can count them. 1, 2, 3, 4, 5, 6, 7, 8, 9, or you could just count by 3's. 3, 6, 9. And I think you see where this is going. Let's keep incrementing it. Let's get four groups of 3. So let's think about what 4 times 3 is. 1, 2, 3, and 4. This right over here is four groups of 3. We could write this down as 4 times 3, which is the same thing as 3 plus 3 plus 3 plus 3. Notice I have four 3's. One 3, two 3's, three 3's, four 3's. One 3, two 3's, three 3's, four 3's. So we get 3, 6, 9, 12. So what I encourage you to do now, now that the video is almost over, is to keep going. I want you to figure out what 5 times 3 is, and 6 times 3, and 7 times 3, and 8 times 3, and 9 times 3, and 10 times 3. And I'll give you a little hint. You don't always have to draw the star patches, but it's nice to visualize it. We saw 4 times 3 is literally four 3's. Well, 5 times 3 is going to be five 3's. So 2, 3, 4, 5. Which is equal to 3, 6, 9, 12, 15. So I encourage you to think about what all of these are after this video is done.

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Multiplication as equal groups (video) | Khan Academy

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I have these three star patches, I guess you could call them, right over here. And so I could say, if I had one group of three star patches, how many star patches do I have? So I literally have one group of three star patches.

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Video transcript

Let's try to calculate 3 times 32. And I like to rewrite it, and this is one way of doing it. I like to rewrite it where I have a larger number on top. So in this case it's 32. And I write the smaller number right below it. And since the smaller number is only one digit, it's only a ones digit, I put that below the ones place on the larger number. So I'll put the 3 right over here. And of course, we can't forget our multiplication symbol. And this is essentially a way of saying the same thing. You could read this as 32 times 3. But 32 times 3 is the exact same value as 3 times 32. It doesn't matter what order you multiply in. Now let's try to compute it. And once again, this is only one way of doing it. There's many ways of doing it. And I want you to think about why this works. We'll start with this 3 down here, and we're going to multiply it times each of the digits in 32. So we'll start with 3 times 2. Well, 3 times 2 from our multiplication tables, and you can figure it out even if you didn't know your multiplication tables, is 6. So 3 times 2, I'll write 6 right over here in the ones place. Now we're going to figure out what 3 times 3 is. Well, once again, we know that 3 times 3 is 9. And since I'm multiplying times the tens place right over here, I'm going to put it in the tens place right like this. So we're done. We got 32 times 3 is 96. And I really encourage you to think about why this worked. And I'll give you a little bit of a hint here. I'll give you a little bit of a hint about why this worked. Remember, 3 times 32 is the same thing as 3 times 30 plus 3 times 2. And if you look at it that way, that's essentially what this process did. We did 3 times 2 is 6. 3 times 30 is 90. You add them together, you get 90 plus 6 is 96.

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Multiplying 2-digit by 1-digit (video) | Khan Academy

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