Using place value to add 3-digit numbers: part 1

Let's add 536 to 398. I'm going to do it two different ways so that we really understand what this carrying is all about. So first we'll do it in the more traditional way. We start in the ones place. We say, well, what's 6 plus 8? Well, we know that 6 plus 8 is equal to 14. And so when we write it down here in the sum, we could say, well, look, the four is in the ones place, so it's equal to 4 plus one 10 So let's write that one 10 in the tens place. And now we focus on the tens place. We have 1 ten, plus 3 tens, plus 9 tens. So what's that going to get us? 1 plus 3 plus 9 is equal to 13. Now, we have to remind ourselves, this is 13 tens. This is 13 tens. Or another way of thinking about it, this is 3 tens. This is 3 tens and 100. You might say, wait, wait. How does that make sense? Remember, this is in the tens place. When we're adding a 1 ten plus the 3 tens plus 9 tens, we're actually adding 10 plus 30 plus 90, and we're getting 130. And so we're putting the 30. The 3 in the tens place represents the 30. So this is the 3. The 3 represents the 30. And then we're placing this 1 in the hundreds place. 10 tens is equal to 100. And now we're adding up the hundreds place. 1 plus 5 plus 3 is equal to-- let's see, 1 plus 5 is equal to 6, plus 3 is equal to 9. But we have to remind ourselves, this is 900. This is in the hundreds place. So this is actually 100-- I want to make all colors the same. So this is actually 100 plus 500 plus 300. Let me get the color coding right. Plus 300 is equal to 900. And that's exactly what we got here. 100 plus 500 plus 300 is equal to 900, and we're done. This is equal to 934.