Adding whole numbers by their place values | Math | 4th grade | Khan Academy

What is 19,000 plus 7? To first, let's think about what are 19,000 and what are 7. Then from there, we can add them.

So, 19,000 would quite literally be if we had a thousand 19 times. So, there's a thousand one time. If we had 1,000 two times, we would have 2,000. If we had 1,000 three times, we would have 1,000, 2,000, 3,000. The pattern here should be pretty clear. If we had 19,000, or 1,000 19 times, we would have 19,000.

So, 19,000 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. This one's a little simpler to do than the 19. We only have to list seven tens this time. That's 6 tens and there's 7 tens.

So, 7 tens would be literally 7 tens, or 10, 20, 30, 40, 50, 60, 70. So, 7 T is 70. And then if we wanted to combine these or add these, we would have 19 thousands, 0 hundreds, 7 tens, and 0 ones, or 19,700.

We could have 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 19,000, which means we want our last digit, the nine, to be in the thousand's 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 that can be represented by these three zeros at the end, whereas 70, 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 7 T added one zero to the end. And again, if we combined them, like we saw on the previous one, we'd have 19,000, 0 hundreds, and 7 ones.

So, either way, whether we list out what 19,000 is literally, with 19,000, or 7 T 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 19,700.

Here's one more: we have 5 10,000s plus 22,000. So two ways, again, we could try to solve this one. We could think about what are 5 10,000s. If we had 10,000 five times, another 10,000, another—that's three, four 10,000 and 5 10,000—that would be a total of 50,000: 10,000, 20,000, 30,000, 40,000, 50,000.

So, 5 10,000 is 50,000. Let's write that up here: 50,000 plus 22,000. Remember when we did the 19,000? If we wrote 1,000, it would be a thousand. If we wrote 1,000 two times, it would be 2,000s. If we wrote it 202 times, then it would be 22,000. There will be 22,000.

And we could combine these numbers: 50,000 + 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 5 10,000s look like and what do 22,000 look like to get our numbers and then add them.

Or, the other way we could solve this is with a place value chart, thinking about place value. So, let's put a place value chart in here and then put our first number, which was five 10,000—so we have five in the 10,000 place. 5 10,000.

And we can fill in the zeros behind it in these empty place values. There were no thousands, hundreds, tens, or ones. So for 10,000s, 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.

With thousands, like before, we'll add three zeros to the end. Finally, when we combine these numbers, when we look at the place values, we now have 7 10,000s. We have 2 thousands, still no hundreds, no tens, and no ones.

So, our solution for 5 10,000 plus 22,000 is 72,000.