Using place value to add 3-digit numbers: part 2
About this video
This video redoes 536 + 398 by writing each number in expanded form: 500 + 30 + 6 and 300 + 90 + 8. Adding the ones gives 10 + 4, adding the tens gives 100 + 30, and adding the hundreds gives 900, so the answer is 900 + 30 + 4 = 934. It shows that carrying the 1 really moves a 10 or a 100.
You'll be able to
- write a 3-digit number in expanded form.
- add numbers in expanded form, column by column.
- explain that 'carrying the 1' moves a ten or a hundred into the next column.
Key words
- expanded form
- Writing a number as the sum of its place values, like 536 = 500 + 30 + 6.
- carrying
- Moving a group of ten into the next place so you don't lose track of it.
- multiple of 10
- A number you get by counting in tens, like 10, 30 or 90.
- column
- A line of digits that all have the same place value, like the ones column.
Transcript
Now, let's do the exact same addition problem that we did in the last video. But I'm going to expand out these numbers so that we really understand what's going on when we're doing all of this carrying. So this 5 is in the hundreds place. So it really represents 5 hundreds or 500.
3 represents 3 tens because it is in the tens place. So it represents 30. And the 6, well, it just represents 6 ones or 6. Likewise, this 3 represents 300. This 9 is 9 tens or 90. And this 8 just represents 8 ones or 8. And now we can add these two up. Now let's start in the right-most column-- this ones column.
6 plus 8, we've already figured out, is equal to 14, which is the same thing as 10 plus 4. So let's write the part that's not a multiple of 10 in this ones column. So let's put that 4 there. And the part that is a multiple of 10, we can now carry into this tens column.
And that's just to keep track of it-- just to make sure that we don't lose that 10, we're putting it into the tens column. Now we can add all the tens. 10 plus 30 plus 90, we've already figured out is 130. Well the part that is not a multiple of 100, we can write in this tens column-- so the 30 part.
And then the part that is a multiple of 100, we can put in the hundreds column. So we could put the 100 right over here. Notice, we've just carried the 1. But essentially, we've carried 100, because we put a 1 in the hundreds place. 10 plus 30 plus 90 is 100 plus 30.
This is equal to 100 plus 30. That's all we've done. Now we can add the hundreds. 100 plus 500 plus 300 we've already figured out is 900. So we can write it as 900. And we're done! We've figured out that 500 plus 30 plus 6, plus 300 plus 90 plus 8, is equal to 900 plus 30 plus 4, which is the same thing as 934.
So hopefully this gives you a little bit more sense of what we're doing when we "carry the 1" every time. 6 plus 8 is 14. We carried the 1. That 1 represents 10. It represents this 10 right over here. Just so we don't lose track of it. Then we say that 10 plus 30 plus 90 is equal to 130.
So that's 30 plus 100. Then we add the hundreds together and we get 900.
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