Vertical Addition

Sometimes we encounter relatively complex addition exercises like:
$4356+213$
or $3434+7123$
that will be difficult for us to add horizontally.
This is exactly why we will use the vertical addition method, which should simplify the addition exercises for us. By writing the numbers vertically and aligning them by place value, we can break down a large problem into several simple single-digit additions, making the calculation much easier to manage.

When we encounter an exercise like this: $2734+9763=$
We need to write it with numbers aligned under each other in an organized way.
The main rule in writing vertical exercises is to write the numbers in the correct order:
The ones digit under the ones digit, the tens digit under the tens digit, the hundreds digit under the hundreds digit, and the thousands digit under the thousands digit.
For example, the exercise $2734+9763=$ we will write like this:

Note - we will write the + sign on the left side to show that this is an addition exercise.
And now, Let's solve it!
We always start with the ones digit and add them together, meaning $4+3$
Write the result under the ones digit.

Continue to the next digit - the tens digit.
Add them together $3+6$ and write the result below:

Proceed to the hundreds digit and add them together.
Notice - $7+7=14$
Since $14$ is a two-digit number, we won't write $14$ instead
we'll only write the ones digit $4$ and carry the $1$ to the thousands column by writing it above the thousands digit, as seen below:

Pay attention -
We wrote $1$ above the thousands digit and now we'll add it together with the thousands digits.
That is:
$1+2+9=12$
Even though $12$ is a two-digit number, given that there are no more digits to add in the exercise, we'll simply write it in the results line as follows:

We're done!
The result of the exercise is $12,497$

1. Write the numbers vertically one under the other, aligning ones under ones, tens under tens, hundreds under hundreds, and thousands under thousands.
2. Don't forget to mark + on the left side and draw a line separating the exercise from the results row.
3. Start adding the ones digit of the first number with the ones digit of the second number and so on, working from right to left.
4. At each step check: did we obtain a two-digit number?
   If yes, write only its ones digit in the results row and write the $1$ (the tens digit) above the next column to remember to add it.
5. Only when there are no more digits to add, we can write the two-digit number we obtained (if it's a two-digit result) as is in the results row.

Did you know?
"Did you know? This method is also called column addition because we arrange the numbers in vertical columns by place value.

And now let's practice!
Solve the following exercise using vertical addition:
$5290+4993=$

Solution:
To begin, we will write the problem vertically according to what we've learned.
Remember - align ones under ones, tens under tens, hundreds under hundreds, and thousands under thousands

Now we will start adding the ones digits

$3+0=3$

Let's continue adding the tens digits:
$9+9=18$
Since $18$ is a two-digit number, we'll write $8$ and carry the $1$ above the hundreds digit.

Let's add the hundreds digits, and don't forget to add the $1$ that we wrote above:
$1+2+9=12$
Since $12$ is a two-digit number, we'll write the digit $2$ and write the $1$ above the thousands digit.

Now we'll move on to adding the thousands digits not forgetting to add the $1$ that we wrote above:
$1+5+4=10$
Since we don't have any more digits to add, we'll write $10$ as is in the results row.

We're done! The result is $10,283$.
Notice how we broke down a complex addition into simple single-digit additions by working column by column!