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Adding whole numbers by their place values

Lindsay adds numbers like 19 thousands + 7 tens by thinking about their place values. 

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Video transcript

- [Voiceover] What is 19 thousands plus seven tens? First let's think about what are 19 thousands, and what are seven tens, and then from there we can add them. So, 19 thousands, would quite literally be, if we had a thousand, 19 times. So there's a thousand one time. If we had a thousand two times, we would have 2000. If we had a thousand three times, we would have 1000, 2000, 3000. And the pattern here should be pretty clear. If we have 19 thousands, or a thousand 19 times, we would have 19,000. So, 19 thousands is literally 19 thousands. And then seven tens, same thing, we could have seven tens. We could have 10 seven times. So, 10 plus another 10, plus another 10, and this one's a little simpler to do than the 19, we only have to list seven tens this time. That's six tens, and there's seven tens. So, seven tens would be literally seven tens. Or, 10, 20, 30, 40, 50, 60, 70. So, seven tens is 70. And then if we want to combine these, or add these, we would have 19 thousands, zero hundreds, the seven tens, and zero ones. Or 19,070. We could've also thought about that question in terms of place value instead of listing out all the thousands, and listing out all the tens, we could have thought of the place values. We had 19 thousands, which means we want our last digit, the nine, to be in the thousands place value. And then the other digit, we had one, would go in front of it. So, this is read 19 thousands, and by writing that thousands there, we covered all these empty place values. Or, the three zeros we ended up adding. The thousands can be represented by these three zeros at the end. Whereas, seven tens, we put a seven in the tens place, and again, we have an empty place value behind it. We had no ones with it. The tens, by saying tens, we implied this zero after it. So, the thousands added these three zeros to the end, and seven tens added one zero to the end. And again, if we combined them, like we saw in the previous one, we'd have 19 thousands, zero hundreds, and seven tens. So, either way, whether we list out what 19 thousands is literally with 19 thousands, or seven tens, literally 10 seven times, or we look at it in terms of place value, and add the zeros on the end. Either way, our solution will be 19,070. Here's one more. We have five ten-thousands plus 22 thousands. So, two ways again we could try to solve this. One, we could think about what are five ten-thousands? If we had 10,000 five times, another 10,000, another, that's three. Four ten-thousands, and five ten-thousands, that would be a total of 50,000. 10,000, 20, 30, 40, 50 thousands. So, five ten-thousands is 50,000. Let's write that up here, 50,000. Plus, 22 thousands. 22 thousands, remember when we did the 19 thousands, if we wrote one 1000 it would be a thousand. If we wrote a thousand two times, it would be two thousands. If we wrote it 22 times, then it would be 22 thousands. There'd be 22 thousands. And we could combine these numbers, 50,000 plus 22,000, will be a total of 72,000. So, one way there, that first way we talked about, is to think about what does five ten-thousands look like, and what do 22 thousands look like, to get our numbers and then add them. Or, the other way that we could solve this is with a place value chart. Is, thinking about place value. So, let's put a place value chart in here, and then put our first number, which was five ten-thousands. So, we have five in the ten-thousands place, five ten-thousands. And we can fill in the zeros behind it in these empty place values. There were no thousands, hundreds, tens, or ones. So, for ten-thousands, we added four zeros behind it. And the other number was 22,000, so 22. We read this as 22,000, always saying the place value of the last non-zero digit we see. So, 22 and then thousand. And then, with thousands like before, we'll add three zeros to the end. And finally, when we combine these numbers, when we look at the place values, we now have seven ten-thousands. We have two thousands. Still no hundreds, no tens, and no ones. So, our solution for five ten-thousands plus 22 thousands is 72,000.