Step 1. Write Down the Numbers

Write down the numbers to be added on atop of the other, these are called the "Addends". Vertically align each digit into columns, starting from the right and moving left.

When we are adding single digit numbers, we simply place one atop of the other in a single column.

When adding multi-digit numbers, we still place them atop each other; however, we place them digit-by-digit with each digit having its own column. When we're adding whole numbers we fill in the right-most column first and move left-ward.

Aligning the numbers like this allows us to add the one's place of every number together at once, then the ten's place, and so on. Any vacancies left by numbers with more digits than others are ignored, or treated as zeros.

Step 2. Place the Plus Sign and Equals Bar

Once all the numbers that we want to add are written down, draw a line underneath them. This line is called the "Equals Bar" and the answer will be written below it.

Also, we place a "Plus Sign" just to the left of the bottom number to show the operation being performed.

Once the symbols are placed we are ready to begin adding.

Step 3. Add the Right-Most Column

In long addition, we add numbers column-by-column moving right to left. We start with the right-most column, which consists of the one place digits; then, we place the sum in the column below the answer bar.

If the sum is longer than a single digit, then we only place the one's place digit and "carry over" the rest. Carrying over means that only the right-most digit is placed below the bar in the answer row; once this is done the digit is dropped from the sum and the remaining digits are added to the next column.

4. Add the Next Column

We are finished with the single digit examples without carry overs, the number below the answer bar is the final sum. If we are adding numbers which are longer than a single digit or have any carry overs, then we must repeat the process with the next column (the ten's place).

Also, like before, we place the one's place of the sum below in the column below the equals bar and carry over the rest to the next column.

5. Repeat

We repeat the process until every digit of every number is added, including any carry overs from the last column. Once this is done the value left below the answer bar is considered the final sum of the addition.