Lesson Objectives
• Demonstrate an understanding of place value
• Learn how to add two multi-digit whole numbers
• Learn how to add two multi-digit whole numbers with regrouping (carrying)

## How to Add Multi-Digit Whole Numbers

Once we have memorized all of the single-digit addition facts, we are ready to add multi-digit whole numbers. In most cases, we perform multi-digit addition using a vertical format. This process is known as vertical addition. Vertical Addition will allow us to simplify the multi-digit addition problem into a series of smaller single-digit addition problems.

1. Arrange the addends (numbers being added) vertically and line up the digits by place value
2. Draw a horizontal line underneath the bottom number and place a "+" to the left of the bottom number
3. Add the digits in the rightmost column, this will contain the ones' place digit for each number
4. Place the result directly below the horizontal line
5. Repeat the addition process in each column moving left until there are no more columns to add
Example 1: Find each sum.
35 + 23
1. Arrange the addends (numbers being added) vertically and line up the digits by place value
2. Draw a horizontal line underneath the bottom number and place a "+" to the left of the bottom number
3. Add the digits in the rightmost column, this will contain the ones' place digit for each number
4. Place the result directly below the horizontal line
5. Repeat the addition process in each column moving left until there are no more columns to add
35 + 23 = 58
Example 2: Find each sum.
613 + 84
1. Arrange the addends (numbers being added) vertically and line up the digits by place value
2. Draw a horizontal line underneath the bottom number and place a "+" to the left of the bottom number
3. Add the digits in the rightmost column, this will contain the ones' place digit for each number
4. Place the result directly below the horizontal line
5. Repeat the addition process in each column moving left until there are no more columns to add

In the last part of this example, we added a 0 in front of the 8 in the number 84. This can be done to show there are zero hundreds in the number 84. Since adding zero to a number leaves the number unchanged, we can skip this step in the future and simply bring the 6 down into the answer.
613 + 84 = 697

In many cases, the result of adding in a single column is more than 9. When this occurs, we utilize a process known as regrouping or carrying. In order to use the carrying procedure, we simply take our addition answer and split the digits up. The rightmost digit goes down into the answer. We then carry the leftmost digit into the next column on the left. The notation can vary, but this carried number is generally written as a number on top of the next column to the left. Let's take a look at an example to see exactly what's taking place.
Example 3: Find each sum.
397 + 425
1. Arrange the addends (numbers being added) vertically and line up the digits by place value
2. Draw a horizontal line underneath the bottom number and place a "+" to the left of the bottom number
3. Add the digits in the rightmost column, this will contain the ones' place digit for each number
4. Place the result directly below the horizontal line
5. Here we have an issue, we cannot place 12 in the ones' place of our answer. Now we will use our carrying procedure.
Think about what the number 12 represents: 1 ten and 2 ones. This means we can split the digits up. We will place the 2 (rightmost digit) directly into the answer. This 2 is in the ones' place of the answer and represents the 2 ones. The 1 or leftmost digit will get carried into the next column on the left. This next column is the tens place and our 1 has its correct value of 1 x 10 or 10.
6. Repeat the addition process in each column moving left until there are no more columns to add

397 + 425 = 822

Example #1

Find each sum.

46 + 70

A
24
B
116
C
96
D
122
E
126

Example #2

Find each sum.

447 + 286

A
733
B
713
C
823
D
1053
E
623

Example #3

Find each sum.

2,838 + 6,110

A
9,038
B
8,738
C
8,148
D
8,948
E
9,958