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