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Place value | 4th grade | Math | Khan Academy

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Let's do a bunch more of these addition problems. So let's say I have 9,367 plus 2,459. So we can do this the exact same way we've done in the last few videos. We start in the 1's place or you can even think of it as the 1's column. So you're going to add the seven 1's plus the 9 1's. So you're going to have 7 plus 9, which we hopefully know by now is 16. So what we do is we write the 6 in the 1's place and we carry the 1. Let me switch-- if this 1 is going to be the same thing as that 1 right there. And this might look like a little bit of a mystery or magic, and the whole reason we did that is that this is the 10's place. And when you write 16 you have six 1's and one 10. If you view this as money, what's the best way to get $16 in a world where there weren't $5 bills? Where you only had $1 bills, $10 bills, $10 bills, and so on. Only multiples of 10. And we don't have any $5 bills. In that world you would represent 16 as one $10 bill just like that. And then six $1 bills. So that's two $1 bills. That's two more $1 bills. And then that's two more $1 bills. The whole reason why I'm drawing it this way or I'm even using this analogy or drawing the dollar bills is to show you what these places mean. When I say that this right here is the 10's place, I'm essentially telling you how many $10 bills do I have? If I've $16 and I'm doing it as efficiently as I can in a world without $5 bills. I only have $1's, $10's, and $100's and $1,000 bills and so forth. And this is the 1's. So when I write it this way I'm literally telling you, I have one $10 bill and I have six $1 bills. That's what $16 is. And so when I have 7 plus 9 is equal to 16 I say that I have six $1 bills and I have one $10 bill. And I add that one $10 bill to everything else in the ten space. And the tens place is essentially telling you how many-- that's the tens. I could write it like that or I could write the 10's place. When I have 67-- 67 means I have six $10 bills plus another seven $1's. So that's six 10's, five 10's. So I add up everything in the tens place. So 1 plus 6 plus 5. Let me do that in a new color. 1 plus 6 plus 5 is equal to-- 1 plus 6 is 7. 7 plus 5 is 12. So I write the 2 in the 10's place because remember, this is twelve $10 bills because we're in the 10's place. So I have two in the 10's place and I put the 1-- I carried this 1 right here into the 100's place. Because if I have twelve $10 bills, I have $120. I have one $100 bill. And I have two $10 bills. I'll stop going to the dollar bill analogy just so we can make sure we understand the process. But I think you see how it works. You start at the right, you add the two numbers up. If it's a two-digit answer you carry the left most digit up to the next column. And you just keep doing that. So let's do this one right here. 1 plus 3 is 4. Let me write this down in another color. 1 plus 3 plus 4. 1 plus 3 is 4. Plus 4 is 8. So 1 plus 3 plus 4 is 8. Nothing to carry. It was a one-digit number. And then finally, I have 9 plus 2. That's equal to 11, so I write the 1 down there. I write this 1 and then if there was anything left here I would carry the 10's or the other 1-- the 1 in the 10's place in 11-- I would carry it. But there's no where to carry it to, so I write it down just like that. So 9.367 plus 2,459 is 11,826. And I just put that comma there because it's easier for me to read. Let me do a bunch more of these. Let's do a really, really daunting problem. Let's do something in the millions. Just to show you that you can do any problem. So let's say we have 2,349,015. Let's throw a 0 in there. We have nothing in the hundreds place there. And I want to add that to-- let me switch colors just for fun. I want to add that to 7,-- let's put a 0 there-- 15,999. Let's add these two numbers. It seems like a hard problem, but if we just focus on each of the places I think you'll find that it's not too bad. So we start off with 5 plus 9. That's equal to 14. Write the 4 down here, carry the 1. Then you go into the 10's place. 1 plus 1 is 2. 2 plus 9-- let me switch colors. 1 plus 1 is 2. 2 plus 9 is 11. Carry the 1. Now we're in the 100's place. 1 plus 0 is 1. Plus 9 is 10. So we write the 0 from the 10, carry the 1. Let me switch colors again. 1 plus 9 is 10. 10 plus 5 is 15. Now we're in the 10,000's place. 1 plus 4 is 5. And 5 plus 1 is 6. And there's nothing to carry. Now we're in the 100,000's place. 3-- we have nothing to carry, so we just have the three 100,000's plus zero 100,000's. Well, that's just three 300,000. And then finally, we're in the millions place. 2,000,000 plus 7,000,000 is 9,000,000. Just like that. So this was a super crazy number. 2,349,015 plus 7,015,999. Just by keeping track of our places and carrying the two-digit numbers or the second digit in the two-digit numbers as necessary, we were able to figure out that the answer is 9,365,014. So hopefully this gives you a pretty good sense. And let me just do one more, just to really make sure that we really understand how all of this carrying business works. So let's do 15,999,001 plus 6,888,999. Let's just see how this one's going to turn out. This seems like a like a difficult problem. But once again, if we just focus and don't get lost, we're going to get the right answer hopefully. So 1 plus 9 is 10. Write the 0, carry the 1. 1 plus 0 plus 9 is 10. Write the 0, carry the 1. 1 plus 0 plus 9. That's 10 again. Write the 0, carry the 1. Now 1 plus 9 is 10, plus 8. 10 plus 8 is 18. Write the 8, carry the 1. 1 plus 9 is 10. Plus eight is 18. Write the 8, carry the 1. 1 plus 9 is 10. Plus 8 is 18. Write the 8, carry the 1. Now we're in the 1,000,000's place. 1,000,000 plus 5,000,000 is 6,000,000. Plus 6,000,000 is 12,000,000. Write the 200,000,000 and then carry the 1 because 12,000,000 is 2,000,000 plus 10,000,000. 10,000,000 plus 10,000,000. This is one 10,000,000 plus another one 10,000,000. That's 1 plus 1 is 2. And then we are done. 15,999,001 plus 6,888,999 is 22,888,000. So you just saw, we're just doing 7 and 8 digit number additions, but you could apply this-- if I had a number with 100 digits in it, you could do the exact same thing. You just have to start at the right, go each column by each column, and then if you end up with a two-digit answer when you add the two one-digit numbers, you just carry the 10's place. You just doing that and work your way left. And if you make no errors, you'll get the right answer.

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Multi-digit addition with regrouping (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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Let's try to subtract 659 from 971. And as soon as you start trying to do it, you face a problem. You go to the ones place, and you say, how am I going to subtract a 9 from a 1? And the answer lies in regrouping, taking value from one of the other places here and giving it to the ones place. And to understand that a little bit better, let me rewrite these two numbers. Let me expand it out. So this 9 is in the hundreds place, so it represents 900. The 7 is in the tens place, so it represents 7 tens. And then, this 1 is in the ones place, so it just represents 1. And then down here, this 6 represents 600. This 5 represents 5 tens, or 50. And then, this 9-- well, it still just represents 9 ones, or 9. And we're subtracting this. We're subtracting 600 plus 50 plus 9. Or another way of thinking about it, we're subtracting 600, we're subtracting 50, we are subtracting 9. So let's work it out over here. So this is the exact same problem, just written a little bit differently. And we still have the same issue. How do we subtract a larger number from a smaller number? And the solution lies in trying to take value from one of the other places. And the easiest place to go is-- look, we've got 70 here. Why don't we take 10 from here, and we'll be left with 60, and give that 10 to the ones place. So if you add 10 to 1, what do we have? Well, then we're going to have 11. Notice, I have not changed the value of the number. 971 is the same thing as 900 plus 60 plus 11. It's still 971. And now we can actually subtract. 11 minus 9 is 2. 60 minus 50 is 10. And 900 minus 600 is 300. So this subtraction should result in 300 plus 10 plus 2, which is 312. Now, let's do the exact same thing here, but we're going to do it without expanding it out. So same issue-- how do we subtract a 9 from a 1? Well, let's take a 10 from the tens place. We're going to regroup. So we're going to get rid of one of these tens, so we're only going to have 6 tens left in the tens place. And we're going to give that 10 to the ones place. So 10 plus 1 is 11. Now we are ready to subtract. 11 minus 9 is 2. 6 minus 5 is 1. 9 minus 6 is 3. We get-- let me do that same color-- 312.

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Worked example: Subtracting 3-digit numbers (regrouping) (video) | Khan Academy

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Let's try to subtract 659 from 971. And as soon as you start trying to do it, you face a problem. You go to the ones place, and you say, how am I going to subtract a 9 from a 1?

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Common Core Sheets - Free Math Worksheets

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Free math worksheets for almost every subject. Create your own daily (spiral) reviews, test, worksheets and even flash cards. All for free! No signup or app to download.

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Subtraction worksheets are an important tool for helping students learn and practice subtraction. These worksheets can be used in the classroom or at home, and are available for a range of grade levels. Our subtraction worksheets cover basic subtraction facts, multi-digit subtraction, and subtraction with regrouping (borrowing) and more. Each subtraction worksheet has a set of problems for students to solve with space to show their work, and answer keys are provided. In addition to the subtraction worksheets, we also offers printable subtraction flashcards and online assignments help students further practice their subtraction skills.

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Understanding Subtraction Link

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Let's try to subtract 164 from 301, and I encourage you to pause this video and try it on your own first. So let's go place by place, and we can realize where we have to do some borrowing or regrouping. So in the ones place, we have an issue. 4 is larger than 1. How do we subtract a larger number from a smaller number? We also an issue in the tens place. 6 is larger than 0. How do we subtract 6 from 0? So the answer that might be jumping into your head is oh, we've got to do some borrowing or some regrouping. But then you might be facing another problem. You'd say, OK, well, let's try to borrow from the tens place here. So we have a 1. If we could borrow 10 from the tens place, it could be 11. But there's nothing here in the tens place. There's nothing to borrow, so what do we do? So the way I would tackle it is first borrow for the tens place. So we have nothing here, so let's regroup 100 from the hundreds place. So that's equivalent to borrowing a 1 from the hundreds place. So that's now a 2. And now in the tens place, instead of a 0, we are going to have a 10. Now, let's make sure that this still makes sense. This is 200 plus 10 tens. 10 tens is 100, plus 1. 200 plus 100 plus 1 is still 301. So this still makes sense. Now, the reason why this is valuable is now we have something to regroup from the tens place. If we take one of these tens, so now we're left with 9 tens, and we give it to the ones place, so you give 10 plus 1, you're going to be left with 11. And we can verify that we still haven't changed the value of the actual number. 200 plus 90 is 290, plus 11 is still 301. And what was neat about this is now up here, all of these numbers are larger than the corresponding number in the same place. So we're ready to subtract. 11 minus 4 is-- let's see, 10 minus 3 is 7, so 11 minus 4 is 7. 9 minus 6 is 3, and 2 minus 1 is 1. So we are left with 137.

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Worked example: Subtracting 3-digit numbers (regrouping from 0) (video) | Khan Academy

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Let's try to subtract 164 from 301, and I encourage you to pause this video and try it on your own first. So let's go place by place, and we can realize where we have to do some borrowing or regrouping. So in the ones place, we have an issue.

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Addition using groups of 10 and 100 (video) | Khan Academy

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Adding and Subtracting on a Number Line 

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Adding and Subtracting on a Number Line 

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Adding and subtracting on number line (video) | Khan Academy

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Adding 3-digit numbers (video) | Khan Academy

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Subtraction by breaking apart (video) | Khan Academy

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