Khan Academy Presents: More on subtracting 4-digit numbers
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Let’s do some more subtraction problems. So lets say I had, I don’t know, well actually I do know because I’m looking at the problem at the problem on the Singapore math book. It say’s 6,000—I’ll do it in a new color. So it’s 6,004 – 2,678. And I’m going to do it with a Sal expansion but it’s really the same thing as when we do the Singapore math place value buckets with the little circles and they tell us how much of each place we have. If we expand this out 6,004, that equals six thousand + zero hundreds + zero tens + four—well that’s going to take forever. Well anyway, plus four. I wanted to add some extra space here because I realized in the last problem that’s where the problem was. I’m going to subtract from it 2,000 + 600 + 70 + 8. So let’s do the problem.
2 < 6, that’s cool, 6 is not less than zero. So we have to do something there. Seven is not less than zero so we have to do something there. Seven is not less than zero. Eight is not less than four. So we’re going to have to do some regrouping. So let’s take a thousand from here from the thousands place. So all were left is with five thousand. And let’s put that thousand in the hundreds place. So we’ll have a thousand here. And how does that look here? Well we have 5,000 left and now we’re going to have 10 hundreds.10 hundreds is the same thing as a thousand.
And so now these two, I guess if we say columns it look alright but the 70 is still greater than the zero so what can we do? Well let’s take a hundred from this thousand and turn it into 10 hundreds or turn it into a hundred. So let’s take a hundred from here, so we have 900 left and then put that hundred here. So that looks good but then we have an eight is being less than a four—I’m sorry—an eight being greater than the four. I just had some dark chocolate and I apologize if you hear some pauses in m voice. Anyway, so how do we fix that? Well the same way we’ve done in all of everything else. Let’s take 10 from this place and put it into the ones place. If we take 10 from a hundred, we get 90 or we’re going to put the 10 here so that becomes 14, oh wait I forgot to do it on this side right?
So if we took a thousand from the 6,000, we have 5,000 left and we get 10 hundreds or a thousand, then what we needed—we took a hundred from there, so lets take a hundred out of 10 hundred, we have 900 left and then we put, we make, and then 100 becomes 10 tens but then we had to borrow one of those, not borrow, take one of those 10 tens and put it into the ones place. So we have 4 + 10 is fourteen. So if these two things are equivalent and now we are ready to subtract. That’s the hard part, this is the fun part now.14 – 8 is 6, 90 – 70 is 20, 900 – 600 is 300 and 5,000 – 2,000 is 3,000. And we’re pointed here, 14 – 8 is 6, 9 – 7 is 2, which is really the 20 here, 9 – 6 is 3. This three is actually this 300 and then 5 – 2 is three which is really this 3,000. Right because, it is in the thousands place. Let’s do some more and maybe I won’t expand it out but I’ll talk it though.
I have 4,000–3,092, so we immediately see that these zeros are not going to help us because they are less than the number below it so what can we do? Let’s take a thousand from the 4,000 so that means we have 3,000 left—I’ll switch colors, we took a thousand and if you put a thousands in a hundreds place it becomes 10 hundreds. So these two columns look alright but now we need some tens so we can subtract here. So let me take one of the hundred, we have 10 hundreds right. let me take one of them, so we have nine hundreds left and make this, and then 100 is 10 tens so that looks okay. But we need to borrow for the ones place, so let’s take one of those 10 tens so it’s a nine, we have 9 tens left and then we add that 10 here. And now we are ready to subtract.10 – 2 is 8, 9 – 9 or 90 – 90 is zero, 900 – 300 is 600 and 3,000 – nothing is 3,000.
Let’s do another one, 3,020 – 2,430. Well this column works out, zero minus zero, that we can do that. But this three is greater than this two. This four is greater than zero, so we have to do something similar. So let’s take one of the thousands, so were going to have two left and make 10 hundreds out of it. Ten we need to make this 10 space bigger. So let’s take one of our hundreds, so only have 9 left and turn that into 10 tens so this 2 becomes 2 tens, become 12 tens and we’re all set. Now we can subtract, zero minus zero is zero, 12 – 3 is 9, 9 – 4 is 5 and 2 – 2 is zero so we don’t have to write it. So our answer is 590.
Let’s keep going, I’m just going to keep going until I used up 15-minutes. And now, I'm actually going to write it out with the Sal expansion style just because, I figured it doesn’t hurt to so. Because I really want to understand what you are doing because if you know what you’re doing, you’ll never get confused, you’ll never say, oh my God, what was the next step I forgot what the next step was because they won’t just be steps to you, they will be actual sense making operations. 5,000 – 2,074, now let me write the expansion. That equals 5,000 thousand plus zero hundreds plus zero tens, plus zero one’s. And the bottom number is 2,000 plus zero hundreds plus 70 plus four.
Okay, so what’s the situation here? Well this column is fine—my phones ringing, it’s my mom, I’ll talk to her later—this column is fine 2 < 5, zero is at least equal to zero so we could subtract there but these two columns are giving a problem right? And what’s interesting here, you might say okay, I don’t have enough tens here so let me take something from the hundreds but like wait I don’t have anything in the hundreds place but you do have a lot of thousands. So what were going to do is we’re going to borrow for the thousands place. So let’s do that. We’re not borrow, we’re going to take from the thousands place. So we’re going to take a thousand, so we’re going to have four thousands left. So we’re going to take a thousand, so we’re going to have four thousands left. So we have a thousand to play with right. And what we can do is, well just for simplicity, let’s take all of that thousands and write in the tens place. Oh sorry the hundreds place.
So if we took a thousand from the thousands place, and let’s put it into the hundreds place. So in the hundreds place, it’ll be represented as 10 hundred. So we took a thousand, so we could write that thousand right here. That’s 10 hundred, that’s why it’s a ten here and that’s why there’s a thousand here. But this isn’t where we need it, we need it over here at these areas. So let’s take, out of this thousand, let’s take a hundred to put in the tens place, so let’s take a hundred, so this becomes 900 and stick it here. 100, and the way that we’d represent it here, we have ten hundreds, we’re taking one of the hundreds, we have 9 hundreds left and we’re putting that hundred here so it’s 10 tens.
And I really want you to understand that this 9 is the same thing as 900, why? Because it is in the hundreds place. This 4 is the same thins as 4,000, this is a 4,000 because it is in the thousands place. This 10 is the same thing as a hundred because it is in the tens place. It’s 10 tens and we are almost done, now why don’t we take one of these tens, so we have nine left and put that 10 in the ones place. Or if we take one of the 10’s, the hundred becomes a 90. And we put it into the tens place. And now we are ready to subtract.
So let’s see it becomes 10 – 4 is 6, 90 – 70 is 20, 900 – nothing is 900 and then 4,000 – 2,000 is 2,000. Or we could do it here 10 – 4 is 6, 9 – 7 is 2, 9 – 0 is 9, 4 – 2 is 2, 2,926, 2,926 same number. And frankly this is one of the harder problems you encounter and you know, if you just learn of well I didn’t carry—take away, borrow all of that, you get confused because you try to borrow from the zero and then what do I do? But when you think about it in terms of, no I’m just going to regroup, I’m just going to take a thousand from here and put it into the hundreds place. We took a thousand from here and we wrote the thousand in the hundreds place. And then ewe took a hundred from here and put in the tens place. And then we took 10 from here and we put it into the tens place. That’s all we did we just rearranged where the numbers are, what place value of each of our numbers are.
Let’s do another one, let’s do, I don’t know, we’ll pick a good one. Let’s do—Let me do the problem that they give us, 5,200 – 948. So that equals, 5,000 + 200 + zero tens + zero ones, and then the bottom number is 900 + 40 + 8. So once again, where are we going to need to borrow? Well pretty much on the hundreds, tens and ones place. Because all of these numbers are bigger than all of these numbers. So let’s take a thousand from the 5,000. We have 4,000 left and put it into the hundreds place. So we took a thousand so we have to put it some place. So lets add it here, so a thousand plus 200 is equal to 12 hundred and using our place notation over here, the 5,000 becomes a 4,000.And at the 200 becomes a12 hundred.
And now let’s borrow a hundred from the 12 hundred so we have 11 hundred. We have to put it someplace. We’ll put it here so this becomes 100 or you could say we borrowed a hundred from the 12 hundred so we have 11 hundred left and then we’re putting the hundred in the tens place so it’s 10hundred. That hundred is the same thing as 10 tens right there, and then finally, let’s borrow 10 from this hundred so it becomes 90 and put the 10 there. So that becomes 10. Similarly, let’s take 10 from here so it’s 9 tens and put the 10 here. Now we are ready to subtract, 10–8 is 2, 90–40 is 50,1100–900, that’s 200 and then you have 4,000. Here 10–8 is 2, 9–4 is 5, 11–9 is 2, 4–nothing is 4. 4252, 4252.
Hopefully you have a sense of what’s going on now and frankly, these are, if you find this pretty straight forward you are ready to tackle almost any subtraction problem especially with four digits. See you in the next video.