This is the video for lesson four on my web site, Basic Addition. It's a two part lesson on my site.

Many students are allowed to use calculators in class and on exams but it's very important to understand how basic arithmetic works and how to do it quickly by hand. What you’ll see later is that many standard exams like the GRE and the G math don’t allow calculators. And if you don’t know how to do basic computations quickly and easily on paper by hand, you’re really be in trouble. Let’s start with some very basics.

One way that we can add is just a count on a number line. So for example to add two plus three, we would just start two, move three spaces to the right and end up on five. That’s all addition really is. We’re just combining by counting. Let me show you a trick that I find I use quite bit when I need to add certain numbers.

Let’s say I want to add nine plus seven. Now it's certainly good to be able to that in your head and just to know what it is. What I find visible to shortcut that I find, I use just in my head when I need to add these numbers. What I'll do is I’ll make the nine a ten and what I actually did was I added one to the nine. And then to compensate for that, I’ll subtract one from the seven to make it a six. Make sure that you fully see why you’re allowed to do that, why that works.

Okay. Now that it's 10 plus six, it's very easy to see that the answer is 16. So that’s just a little trick that you can keep in mind whenever you need to add numbers such as nine plus seven. Increase one, decrease the other one and you’ll have much simpler equivalent problem.

Now, let’s see how to add some larger numbers. Let’s say I want to add 128 plus 35. Now, notice what I did. I lined up the one’s places over the 1’s and the 10’s places over 10’s. In the case of the second number, there are no 100’s but I do have the one, the 100 place for the top number where it should be. So it's very important to line your up your numbers otherwise you’ll get a completely wrong answer.

Now when adding, we always start on the right. We always start with the ones place. I'm going to add eight plus five which is 13. Now, I'm not allowed to write the entire 13 in the one’s place so what I can do is I can write the three in my answer. That represents the 3 ones and then I have to carry the one the little one in the 10’s place to show that I still have 110.

Okay. Now, we’ll add up this column here, the 10’s column. I have the one that I carried plus two plus three and that’s six. There's nothing to carry there. It’s just plain six. And now on the 100’s column, I have 100 and there's actually no 1’s—there’s actually no 100’s in the second number so I can just write one as my answer.

Now, let’s try another addition problem. For this one, I’d like to add 98 plus 49. Again, notice how I lined up the ones column—the one’s place on top of the one’s place and the ten’s place on top of the ten’s place.

As always, we’ll start adding on the right. I have eight plus nine which is 17. All I can do is write the seven down here in the one’s place and carry the one 10. Now, add one plus nine which is 10 plus 4 is 14.

Now, we could just write 14 down there and that would be correct but what we really have is a four in this column and then we have to carry the one. One plus nothing here gives us one and the answer is 147.

It’s important to understand that when we added one plus nine plus four, we are in the 10’s column and what we really got was 14 10’s. Now, 14 tens is equal to a 140 that’s why we had four 10’s and we have 100. That maybe a little tricky but it's very important to understand the connection between the place of values.

This is just a very basic introduction to addition. Make sure you feel fully comfortable with everything that I've shown you in this lesson and then you can do problems like this very quickly and easily without a calculator.