Addition means bringing together.   

2 + 3


If we bring together 2 apples and 3 apples, we have 5 apples.

If we put them all in a bag, we have 5 apples.

Before starting: 

You should know the place values of the numbers.

In modeling, shapes and their meanings.

In modeling, shapes and their meanings can be used to represent mathematical concepts or quantities.We generally use cubes to represent 1000, squares for 100, rectangles for 10, and small squares for the units in modeling.

Modeling can help you understand what addition operations mean by providing a visual representation of the numbers and the process of combining them. It can make abstract mathematical concepts more tangible and easier to grasp, especially for those who are visual learners or new to the subject


If we bring these together;


1256  >>>1256 consists of one thousand, two hundreds, five tens, and six ones. 

132 >>>132 consists of one hundred, three tens, and two ones.

When we bring these together, the sum is 1388, which consists of one thousand, three hundreds, eight tens, and eight ones.

The Classic Addition Operation

Now, let's add these numbers as you have learned before, by writing them vertically and aligning the same place values under each other.
 I'm writing the numbers to be added, making sure that the units, tens, hundreds, and thousands are lined up correctly.

If you write the ones place values under each other, the other place values will automatically align vertically as well.

Why should the same place values be aligned vertically?

Units should be added to units, tens to tens, hundreds to hundreds. Numbers take their value according to the place they are written, that is, their place value. If you write them in different places, their meaning changes.

Aligning the same place values ensures that you are adding like terms together, preserving the value and meaning of each digit according to its position in the number. It's a fundamental principle in arithmetic that helps maintain the integrity of the mathematical system.

Incorrect vertical alignment example

In this way of writing,  you are adding 1256 and 1320, it's because you wrote the 1 in the thousands place, making its value 1000. You wrote the 3 in the hundreds place, making its value 300, and you wrote the 2 in the tens place, making its value 20.

Place value is essential in understanding the value of a number, and each digit's value is determined by its position. Writing the numbers in the correct columns ensures that you are adding the corresponding units, tens, hundreds, and thousands together, preserving the true value of the numbers. If the digits are not aligned correctly, it can lead to a misunderstanding of the numbers being added.

Let's begin the addition.

I'm starting the addition by adding the units.

6 units plus 2 units equals 8 units, and it is written in the ones place.

5 tens plus 3 tens equals 8 tens, and it is written in the tens place.

2 hundreds plus 1 hundred equals 3 hundreds, and it is written in the hundreds place.

I have 1 thousand and no other thousands to add to it, so the total is 1 thousand, and it is written in the thousands place.

Carry-Over Addition

In elementary school, you did carry-over addition. Let's see what this "carry-over" actually means.

3567 + 458

Paying attention to the place values, I wrote 3567 and 458 vertically and am starting to add them, beginning with the ones place.

If we add 7 units with 8 units, it makes 15 units. I can't write 15 in the ones place (since only one digit can be written in a place), so I write 5 in the ones place, and I say "carry over 1" for the remaining 10, to add to the other tens. "Carry over 1" means that I now have one ten in my hand And I will add this ten to the other tens.

If we add 6 tens with 5 tens, it makes 11 tens, and there was also one "carried over," so in total, I have 12 tens, which equals 120. Again, I can't write 12 tens in the tens place, so I take the 1 hundred from 120 and say "carry over 1." I write the remaining 20, or 2 tens, in the tens place. Now I have one hundred in my hand, and it will be added to the other hundreds.

If we add 5 hundreds with 4 hundreds, it makes 9 hundreds, and I also had one hundred carried over, so in total, I have 10 hundreds, which equals 1000. I can't write 10 hundreds in the hundreds place, so I say "carry over 1" to add the 1000 to the thousands. Right now, I have no other numbers except 1000, and that 1000 will be added to the other thousands, so I write 0 in the hundreds place.

I have no other thousands to add to the 3 thousands, but I had one thousand carried over from the hundreds. If I add that thousand to the 3 thousands, I have 4 thousands in total, and I write 4 in the thousands place.

Our result is:  4025