# Addition

Addition is one of the first things you learn when beginning math education. In

order to add, you must know how to count using traditional counting numbers (1,

2, 3, etc). Once you have a good understanding of counting, you will begin to add

numbers together. To start, we’re going to use one digit plus one digit examples,

and move on to harder examples.

## Adding One Digit Plus One Digit Numbers

Adding one digit to another digit is the first kind of addition problem you’ll learn

how to complete. A basic addition problem looks like this:

2 + 1 = _____

In order to complete this problem, you would first count to two, and then count

one more (adding it), and get to three. If you were to look at it with pictures

instead of numbers, it would look like this:

For beginners, it may be easier to draw dots and then count them all together, like

we did for this one. Let’s try this again. Here’s the problem, in numbers and in

pictures:

Now, count up the dots. How many did you get? You should have gotten five in the

end. If you didn’t, go back and re-count them.

Let’s try this one more time before we move on. We’ll give you the pictures and

numbers, and you give us the answer!

Now, count up all the dots, adding them together. What do you get? If you got 11,

you’re right! If not, recount them, and make sure you’re not skipping any.

## Adding Two Digit Plus One Digit Numbers Without Carrying

Once you can add simple numbers together, you’ll move on to adding two digit plus

one digit numbers. A two digit plus one digit problem would look like this:

In order to complete this problem, you’re first going to add the ones’ columns together.

For this problem, you’d be adding together 5 + 2. You write the answer to this part

in the ones’ column under the answer bar. Then, you move on and add the tens’ column

together. In this problem, the only number in the tens’ column is 1, so you would

bring 1 down and write it in the tens’ column of the answer.

Then, you’re done! Here’s the work for the problem:

Step 1:

Step 2:

Now, we get our final answer of 17.

Let’s try this one more time. This time, we’ll give you the problem, and you can

try working it out. When you’re done, check your answer with our answer. Here’s

the problem:

Remember, follow the same steps we did for the first problem, and see if you can

come up with an answer.

Did you get 19? If you did, you’re right! If you didn’t, go back and re-add the

two steps, make sure you brought the 1 down into your answer, and so on. Here’s

the work for the problem:

Your final answer is 19.

## Adding Two Digit Plus One Digit Numbers With Carrying

After you add two digit plus one digit numbers for a while, you’ll run into a problem

where you have to carry a number. This happens when you get an answer of 10 or more

when you add the ones’ column together. For example, if your ones’ column said 9+3,

that gives you 12, and you’d need to carry. In order to carry, you need to follow

three steps very carefully.

First, after you’ve added and gotten the number, you need to split the number up

into two separate digits. You’re not going to write anything yet; you do this step

in your head. For example, if you got 12 for your answer to the first part of the

problem, you would look at it as 1 and 2 (two separate digits).

Second, you’re going to take the ones’ digit of the number you just split up, and

write it in the ones’ column of your answer. (This should seem normal after doing

addition without carrying).

Last, here’s the different step: you’re going to take the tens’ digit of the number

you just split up, and write it at the top of the tens’ column in your addition

problem.

Congrats, you’ve carried! Now let’s see what it looks like in the problem itself:

Now you need to finish the addition problem. All you have left to do is add together

the numbers in the tens’ column now. Notice that after you’ve carried, there are

now 2 numbers in the tens’ column. In this problem, they are both ones. You would

add these two numbers together, and place the answer in the tens’ column of the

answer. It would look like this:

Now you have a final answer, 22.

Let’s try this a couple more times to make sure you understand.

Go ahead and try this problem on your own. Remember to split up the answer to the

addition of the ones’ column, and put the ones’ digit in the answer while carrying

the tens’ digit up to the next column. We’ll show this one more time, but after

that we’re not going to write it out.

Now try this one as our last practice problem:

Here’s the solution:

Did you get 53? If not, go back and re-add the columns, and make sure you’re splitting

up the number the right way when you do your carrying. Your final answer is 53.

Congrats! Now you know how to carry!

## Adding Two Digit Plus Two Digit Numbers Without Carrying

More advanced addition problems will ask you to add two digit plus two digit numbers.

A problem adding together two two-digit numbers looks like this:

This may look a little harder than before, but don’t worry! It’s not too bad. You

just have to remember to do it in the right order. First, add together the ones’

column, and write the answer beneath the answer bar, like this:

Then, move over to the tens’ column and write that answer in the tens’ column beneath

the answer bar, like this:

The solution would look like this:

Did you get 55? If not, re-add each column to see where your mistake is. Remember

to add each column separately in order to get your answer. Your final answer for

this problem is 55.

Let’s try one more example of this to make sure you understand it. Here’s the new

problem:

Go ahead and try it on your own, and then compare your answer with ours.

Solution:

If you didn’t get 78, make sure you remember to go back and re-add each column,

to find and correct your mistake. Otherwise, if you got 78, you’re right!

## Adding Two Digit Plus Two Digit Numbers With Carrying

Now that you know how to add two digit numbers together, we’re going to practice

doing it when you have to carry a number. It works very similarly to the carrying

shown previously. Here’s a problem to start with, and we’ll go through each step

of solving it.

Start this as you would a normal addition problem, with the ones’ column. Notice

when you add the ones’ column together that you get a number higher than ten, which

means you have to carry. You’re going to carry the same way as we showed in

Adding Two Digit Plus One Digit Numbers With Carrying. Split up the number

and write the ones’ digit under the ones’ column beneath the answer bar, and write

the tens’ digit above the tens’ column in the addition problem. These steps look

like this (the ones’ column is circled in red, and the number in red at the top

of the tens’ column is the number that was carried).

Now, you can go ahead and add the tens’ column together. Notice that now there are

three numbers in the tens’ column that you must add together, 1 + 3 + 2. Here’s

the rest of the solution:

Thus, our final answer is 61.

Let’s try one more example that’s a little bit harder. Here’s the problem:

First, add the ones’ column together. Place the ones’ digit of the answer beneath

the answer bar in the ones’ column, and the tens’ digit of the answer above the

tens’ column in the division problem.

Now, once again, you have 3 digits in the tens’ column to add together, 1 + 6 +

8. When you add these together, you get 15. Next, you simply write 15 in front of

the 6. Now, you have 6 in the ones’ column, 5 in the tens’ column, and 1 in the

hundreds’ column. Your solution looks like this (we’ll put the 15 in red so you

can see how it lines up):

Thus, our final answer is 156.

Now, try this one on your own, following the same steps we just went through. When

you’re done, you can check your answer with ours to make sure you understand completely.

Here’s the problem:

Now try to work it out on your own, and when you’re done, compare it to our work.

Did you get 142 for your final answer? If you didn’t, go back and re-add each column,

and make sure you carried correctly. If you did get 142, congrats! You’re absolutely

right.