WEBVTT 00:00:06.889 --> 00:00:12.239 Hi, welcome to Math Antics. In this video we’re gonna learn how to do multi-digit addition. 00:00:12.239 --> 00:00:18.108 A multi-digit number is just a number with more than one digit, which is anything greater than 9. 00:00:18.108 --> 00:00:22.560 Two-digit numbers use two number places, like the number 32. 00:00:22.560 --> 00:00:26.300 It has a ‘2’ in the ones place and a ‘3’ in the tens place. 00:00:26.300 --> 00:00:31.440 Three-digit numbers use three number places, for example 215. 00:00:31.447 --> 00:00:32.964 There’s a ‘5’ in the ones place, 00:00:32.964 --> 00:00:34.249 a ‘1’ in the tens place, 00:00:34.249 --> 00:00:36.565 and a ‘2’ in the hundreds place. 00:00:36.565 --> 00:00:41.418 But no matter how many digits a number has, if you know your basic addition facts, 00:00:41.418 --> 00:00:44.858 you can add it to any other multi-digit number easily. 00:00:44.860 --> 00:00:47.200 So let’s start by adding these two numbers together. 00:00:47.200 --> 00:00:48.560 Here’s how it works. 00:00:48.570 --> 00:00:51.589 The first thing we need to do is stack the numbers up. 00:00:51.589 --> 00:00:55.889 And by that, I mean re-writing them so they’re on top of each other like this. 00:00:55.889 --> 00:01:00.440 Ah ah ah - don’t be sloppy! Make sure they line up nice and straight. 00:01:00.440 --> 00:01:01.991 That’s more like it. 00:01:01.991 --> 00:01:04.226 But here’s the most important part. 00:01:04.226 --> 00:01:08.026 Be sure to line up the number places so that they’re directly over each other. 00:01:08.026 --> 00:01:13.729 …so that the ones place of the number on top is directly over the ones place of the number beneath it. 00:01:13.729 --> 00:01:18.864 And if you line up the ones places correctly, then all the other number places will be lined up too. 00:01:18.864 --> 00:01:22.065 The tens places are also lined up, and the hundreds places. 00:01:22.065 --> 00:01:26.034 Well, the bottom number doesn’t have a digit in the hundreds place, but that’s ok. 00:01:26.034 --> 00:01:30.469 We can imagine a zero there as a place holder, but we don’t have to show it. 00:01:30.469 --> 00:01:37.087 After our numbers are lined up, we draw a line just below the bottom number because our answer is going to go below that. 00:01:37.087 --> 00:01:41.222 We also put a plus sign down here on the left side to show that we’re adding. 00:01:41.222 --> 00:01:47.674 By stacking the numbers up, we’ve formed columns for each number place and we’re going to add the digits in each column. 00:01:47.674 --> 00:01:49.475 And this is super important… 00:01:49.475 --> 00:01:54.535 We ALWAYS start with the ones places column and then work our way to the left. 00:01:54.540 --> 00:01:58.660 And in the ones places we have 5 plus 2 which equals 7. 00:01:58.660 --> 00:02:03.700 So we put a ‘7’ in the ones place of our answer which is just below the line. 00:02:03.700 --> 00:02:08.031 Now we can move left to the next number place column, which is the tens place. 00:02:08.031 --> 00:02:13.951 The digits there are a ‘1’ plus a ‘3’, and that gives us a ‘4’ in the tens place of our answer. 00:02:13.951 --> 00:02:17.011 And last of all, we add the hundreds place column. 00:02:17.020 --> 00:02:19.935 But there’s only one digit there, so we don’t really have to add it. 00:02:19.935 --> 00:02:22.853 We just bring the ‘2’ down to our answer like this. 00:02:22.860 --> 00:02:30.720 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. 00:02:30.720 --> 00:02:36.100 There: 215 plus 32 equals 247. 00:02:36.108 --> 00:02:37.709 Let’s try another example. 00:02:37.709 --> 00:02:44.020 This one’s a little harder: 1,850 plus 354 00:02:44.020 --> 00:02:46.120 Okay, the first step is the same. 00:02:46.129 --> 00:02:49.696 We need to stack the numbers up so we can add each number place column. 00:02:49.696 --> 00:02:55.596 Be sure to line up the ones places and draw your line and plus symbol just like in the last example. 00:02:55.600 --> 00:02:59.733 Again, we ALWAYS start by adding the digits in the ones place. 00:02:59.733 --> 00:03:04.973 0 plus 4 equals 4, so a ‘4’ goes in the ones place of our answer. 00:03:04.980 --> 00:03:10.437 Now we move to the next place to the left (the tens place), and here comes the tricky part. 00:03:10.437 --> 00:03:15.173 If you add the digits in the tens places (5 plus 5) you get 10. 00:03:15.173 --> 00:03:20.124 But 10 is a two-digit number, so we would need to use two digits in our answer to write it! 00:03:20.124 --> 00:03:22.884 But we can’t leave a ‘1’ in the hundreds place of our answer 00:03:22.884 --> 00:03:26.376 because we’re going to need that space when we add the hundreds place digits. 00:03:26.376 --> 00:03:28.259 That ‘1’ is gonna be in the way. 00:03:28.259 --> 00:03:30.078 So what do we do? 00:03:30.078 --> 00:03:36.346 The answer is; we carry the digit that we don’t have room for up to the top of the next number place column. 00:03:36.346 --> 00:03:42.114 Instead of putting it in the answer space, we put it above the other digits in our hundreds place column 00:03:42.114 --> 00:03:45.514 so that we can add it with the rest of the digits in that column. 00:03:45.520 --> 00:03:50.818 So you can see, the ‘1’ is gonna go in the hundreds place of the answer, …just not by itself. 00:03:50.818 --> 00:03:56.036 It’s almost like it has to ‘get in line’ so it can be added to the other digits in that column. 00:03:56.036 --> 00:04:01.422 Oh, and carrying the extra digit up to the next column you’re gonna add is often called “re-grouping” 00:04:01.422 --> 00:04:05.807 because it’s really like you’re moving a group of 10 to the next column over, 00:04:05.807 --> 00:04:09.924 and leaving whatever is left in the first column. …in this case, zero. 00:04:09.924 --> 00:04:14.745 Okay, now that we’ve carried that ‘1’, we can add up the digits in the hundreds place column, 00:04:14.745 --> 00:04:20.278 which means adding up three digits now. 1 plus 8 plus 3 which equals 12. 00:04:20.278 --> 00:04:23.058 Hmmm… another two-digit number! 00:04:23.060 --> 00:04:28.580 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. 00:04:28.582 --> 00:04:34.835 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. 00:04:34.835 --> 00:04:36.967 …just one more column to add up now. 00:04:36.967 --> 00:04:40.836 In the thousandths places we have 1 plus 1 equals 2. 00:04:40.836 --> 00:04:48.276 Okay, we’ve added up all our columns, so the answer to our addition problem is 2,204. 00:04:48.280 --> 00:04:53.400 Think you’ve got it so far? Let’s try one more together before you do some of the exercise problems. 00:04:53.408 --> 00:04:59.210 Let’s add up these three numbers: 145, 809 and 77 00:04:59.210 --> 00:05:05.779 We start the same way, stacking the numbers up and making sure all the ones places line up in a column on the right. 00:05:05.779 --> 00:05:09.539 And as always, we add up the digits in the right-hand column first. 00:05:09.540 --> 00:05:13.540 5 + 9 + 7 = 21. 00:05:13.548 --> 00:05:18.433 Because that answer is a two-digit number, we need to carry the first digit to the next column, 00:05:18.433 --> 00:05:22.653 which is like moving a group of 20 over and leaving the ‘1’ behind. 00:05:22.660 --> 00:05:26.080 Now we add the next column, and there are 4 digits to add: 00:05:26.080 --> 00:05:31.020 2 + 4 + 0 + 7 = 13 00:05:31.020 --> 00:05:37.120 Yep, that’s another two-digit answer so we carry the ‘1’ and leave the ‘3’ in the tens place. 00:05:37.120 --> 00:05:39.473 Last, we add the hundreds place column: 00:05:39.473 --> 00:05:42.758 1 + 1 + 8 = 10 00:05:42.758 --> 00:05:49.327 Wow!… another two-digit number. But this time we don’t need to carry, because there’s no more columns left to add, 00:05:49.327 --> 00:05:54.607 so we won’t be getting in the way of any answers by leaving both the digits in the answer like this. 00:05:54.607 --> 00:05:58.127 So our answer is 1,031 00:05:58.130 --> 00:06:01.132 Alright, now you know how to add multi-digit numbers, 00:06:01.132 --> 00:06:04.782 but it’s very important to practice so you’ll remember and get good at it. 00:06:04.782 --> 00:06:07.680 So check out the printable exercises for this section. 00:06:07.680 --> 00:06:12.660 I recommend that you work a few problems each day for several days until you’ve got it down. 00:06:12.668 --> 00:06:16.170 And it’s a great idea to use a calculator to check your answers. 00:06:16.170 --> 00:06:22.472 This will help you find mistakes, and you’ll get practice doing math with a calculator, which is an important skill too. 00:06:22.472 --> 00:06:25.840 Thanks for watching Math Antics and I’ll see you next time. 00:06:26.660 --> 00:06:28.660 Learn more at www.mathantics.com