Hi, welcome to Math Antics. In this video we’re gonna learn how to do multi-digit addition.
A multi-digit number is just a number with more than one digit, which is anything greater than 9.
Two-digit numbers use two number places, like the number 32.
It has a ‘2’ in the ones place and a ‘3’ in the tens place.
Three-digit numbers use three number places, for example 215.
There’s a ‘5’ in the ones place,
a ‘1’ in the tens place,
and a ‘2’ in the hundreds place.
But no matter how many digits a number has, if you know your basic addition facts,
you can add it to any other multi-digit number easily.
So let’s start by adding these two numbers together.
Here’s how it works.
The first thing we need to do is stack the numbers up.
And by that, I mean re-writing them so they’re on top of each other like this.
Ah ah ah - don’t be sloppy! Make sure they line up nice and straight.
That’s more like it.
But here’s the most important part.
Be sure to line up the number places so that they’re directly over each other.
…so that the ones place of the number on top is directly over the ones place of the number beneath it.
And if you line up the ones places correctly, then all the other number places will be lined up too.
The tens places are also lined up, and the hundreds places.
Well, the bottom number doesn’t have a digit in the hundreds place, but that’s ok.
We can imagine a zero there as a place holder, but we don’t have to show it.
After our numbers are lined up, we draw a line just below the bottom number because our answer is going to go below that.
We also put a plus sign down here on the left side to show that we’re adding.
By stacking the numbers up, we’ve formed columns for each number place and we’re going to add the digits in each column.
And this is super important…
We ALWAYS start with the ones places column and then work our way to the left.
And in the ones places we have 5 plus 2 which equals 7.
So we put a ‘7’ in the ones place of our answer which is just below the line.
Now we can move left to the next number place column, which is the tens place.
The digits there are a ‘1’ plus a ‘3’, and that gives us a ‘4’ in the tens place of our answer.
And last of all, we add the hundreds place column.
But there’s only one digit there, so we don’t really have to add it.
We just bring the ‘2’ down to our answer like this.
Of course we could add the ‘2’ to the zero that we imagined there as a place holder, but 0 plus 2 will just give us 2 also.
There: 215 plus 32 equals 247.
Let’s try another example.
This one’s a little harder: 1,850 plus 354
Okay, the first step is the same.
We need to stack the numbers up so we can add each number place column.
Be sure to line up the ones places and draw your line and plus symbol just like in the last example.
Again, we ALWAYS start by adding the digits in the ones place.
0 plus 4 equals 4, so a ‘4’ goes in the ones place of our answer.
Now we move to the next place to the left (the tens place), and here comes the tricky part.
If you add the digits in the tens places (5 plus 5) you get 10.
But 10 is a two-digit number, so we would need to use two digits in our answer to write it!
But we can’t leave a ‘1’ in the hundreds place of our answer
because we’re going to need that space when we add the hundreds place digits.
That ‘1’ is gonna be in the way.
So what do we do?
The answer is; we carry the digit that we don’t have room for up to the top of the next number place column.
Instead of putting it in the answer space, we put it above the other digits in our hundreds place column
so that we can add it with the rest of the digits in that column.
So you can see, the ‘1’ is gonna go in the hundreds place of the answer, …just not by itself.
It’s almost like it has to ‘get in line’ so it can be added to the other digits in that column.
Oh, and carrying the extra digit up to the next column you’re gonna add is often called “re-grouping”
because it’s really like you’re moving a group of 10 to the next column over,
and leaving whatever is left in the first column. …in this case, zero.
Okay, now that we’ve carried that ‘1’, we can add up the digits in the hundreds place column,
which means adding up three digits now. 1 plus 8 plus 3 which equals 12.
Hmmm… another two-digit number!
Alright, it looks like we'll have to carry again because we’re gonna need this answer spot for the next column to the left.
So we carry the ‘1’ up to the top of the next column and leave our ‘2’ where it is in the hundreds place of the answer.
…just one more column to add up now.
In the thousandths places we have 1 plus 1 equals 2.
Okay, we’ve added up all our columns, so the answer to our addition problem is 2,204.
Think you’ve got it so far? Let’s try one more together before you do some of the exercise problems.
Let’s add up these three numbers: 145, 809 and 77
We start the same way, stacking the numbers up and making sure all the ones places line up in a column on the right.
And as always, we add up the digits in the right-hand column first.
5 + 9 + 7 = 21.
Because that answer is a two-digit number, we need to carry the first digit to the next column,
which is like moving a group of 20 over and leaving the ‘1’ behind.
Now we add the next column, and there are 4 digits to add:
2 + 4 + 0 + 7 = 13
Yep, that’s another two-digit answer so we carry the ‘1’ and leave the ‘3’ in the tens place.
Last, we add the hundreds place column:
1 + 1 + 8 = 10
Wow!… another two-digit number. But this time we don’t need to carry, because there’s no more columns left to add,
so we won’t be getting in the way of any answers by leaving both the digits in the answer like this.
So our answer is 1,031
Alright, now you know how to add multi-digit numbers,
but it’s very important to practice so you’ll remember and get good at it.
So check out the printable exercises for this section.
I recommend that you work a few problems each day for several days until you’ve got it down.
And it’s a great idea to use a calculator to check your answers.
This will help you find mistakes, and you’ll get practice doing math with a calculator, which is an important skill too.
Thanks for watching Math Antics and I’ll see you next time.
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