Lesson Objectives
 Demonstrate an understanding of place value
 Demonstrate an understanding of singledigit multiplication
 Learn how to set up multidigit multiplication problems in a vertical format
 Learn how to perform multidigit multiplication with regrouping (carrying)
How to Multiply MultiDigit Whole Numbers with Regrouping (Carrying)
At this point, you should be fairly comfortable with the singledigit multiplication facts covered in our
properties of multiplication lesson.
In that lesson, we saw a basic times table for the numbers 1  9. We also learned several properties of multiplication
such as: the commutative property of multiplication, the associative property of multiplication, the identity property of
1, the multiplication property of 0, and the distributive property of multiplication.
Once we have mastered our singledigit multiplication facts, it’s time to move on to multiplying multidigit whole numbers.
When we multiply multidigit whole numbers together, we generally use a process known as vertical multiplication. This process will allow us to break our multidigit multiplication problem down into a series of singledigit multiplication problems. In order to completely understand the process, it is imperative to have a good understanding of place value.
Example 1: Multiply 113 x 12
Let's try an example with carrying involved.
Example 2: Multiply 305 x 49
When we multiply multidigit whole numbers together, we generally use a process known as vertical multiplication. This process will allow us to break our multidigit multiplication problem down into a series of singledigit multiplication problems. In order to completely understand the process, it is imperative to have a good understanding of place value.
Vertical Multiplication
 Set up the vertical multiplication by stacking the factors vertically and lining up the digits by place value. Although multiplication is commutative (order is not important) we want to place the number with more digits on top. If the two numbers have the same number of digits, either number can be on top.
 Draw a multiplication symbol "x" to the left of the bottom number and a horizontal line underneath the bottom number.
 We start our multiplication with the ones' place digit (rightmost) in the bottom column. We will multiply this digit by each digit
in the top number working right to left. After each multiplication, we write the individual answers below the horizontal line
working right to left. The placement here is very important to maintain the proper place value.
 If the result of a particular multiplication is larger than 9, we will use regrouping (carrying). When this occurs, write the right digit of the number down into the answer. We then carry the left digit above the next column to the left. This digit will be added to the result of the next multiplication.
 We continue our multiplication by shifting to the next digit left in the bottom number. We will repeat the process of multiplying this digit by each digit in the top number and regrouping (carrying) when needed. The most important thing here is to start the placement of the answers from this multiplication on a new row and one place to the left. This is done to ensure proper place value in our answer.
 Once we have completed the process and multiplied each number in the bottom row by each number in the top row, we are ready to add. We now set up a vertical addition and find the sum of the amounts in the answer section.
Example 1: Multiply 113 x 12
 Set up the vertical multiplication by stacking the factors vertically and lining up the digits by place value. Although multiplication is commutative (order is not important) we want to place the number with more digits on top. If the two numbers have the same number of digits, either number can be on top.
 Draw a multiplication symbol "x" to the left of the bottom number and a horizontal line underneath the bottom number.
 We start our multiplication with the ones' place digit (rightmost) in the bottom column. We will multiply this digit by each digit
in the top number working right to left. After each multiplication, we write the individual answers below the horizontal line
working right to left. The placement here is very important to maintain the proper place value.
 If the result of a particular multiplication is larger than 9, we will use regrouping (carrying). When this occurs, write the right digit of the number down into the answer. We then carry the left digit above the next column to the left. This digit will be added to the result of the next multiplication.
 Multiply starting with the rightmost digit of the bottom number 2. This digit will multiply each digit of the top number.
 2 x 3 = 6
 2 x 1 = 2
 2 x 1 = 2
 After each multiplication, the result is written directly below the horizontal line working right to left.

We continue our multiplication by shifting to the next digit left in the bottom number. We will repeat the process of multiplying
this digit by each digit in the top number and regrouping (carrying) when needed. The most important thing here is to start the
placement of the answers from this multiplication on a new row and one place to the left. This is done to ensure proper place value in our answer.
 Move one digit left in the bottom number (1). This digit will multiply each digit of the top number.
 We start a new row to write our answers. We start the answers one place left (tens' place) and work right.
 1 x 3 = 3
 1 x 1 = 1
 1 x 1 = 1
 Once we have completed the process and multiplied each number in the bottom row by each number in the top row, we are ready to add. We now set up a
vertical addition and find the sum of the amounts in the answer section.
 Find the sum of 226 and 1130.
 6 + 0 = 6 (or you can just bring the 6 down)
 2 + 3 = 5
 2 + 1 = 3
 1 + 0 = 1 (or you can just bring the 1 down)
 226 + 1130 = 1356
Let's try an example with carrying involved.
Example 2: Multiply 305 x 49
 Set up the vertical multiplication by stacking the factors vertically and lining up the digits by place value. Although multiplication is commutative (order is not important) we want to place the number with more digits on top. If the two numbers have the same number of digits, either number can be on top.
 Draw a multiplication symbol "x" to the left of the bottom number and a horizontal line underneath the bottom number.
 We start our multiplication with the ones' place digit (rightmost) in the bottom column. We will multiply this digit by each digit
in the top number working right to left. After each multiplication, we write the individual answers below the horizontal line
working right to left. The placement here is very important to maintain the proper place value.
 If the result of a particular multiplication is larger than 9, we will use regrouping (carrying). When this occurs, write the right digit of the number down into the answer. We then carry the left digit above the next column to the left. This digit will be added to the result of the next multiplication.
 Multiply starting with the rightmost digit of the bottom number 9. This digit will multiply each digit of the top number.
 9 x 5 = 45
 Since 45 is a two digit number, place the 5 directly below and carry the 4 into the next column left
 9 x 0 = 0
 We then add the 4 which was carried over. This results in 0 + 4 which is 4. This will be written directly below
 9 x 3 = 27
 Since there are no more columns we can simply write the 27 and move on to the next step

We continue our multiplication by shifting to the next digit left in the bottom number. We will repeat the process of multiplying
this digit by each digit in the top number and regrouping (carrying) when needed. The most important thing here is to start the
placement of the answers from this multiplication on a new row and one place to the left. This is done to ensure proper place value in our answer.
 Move one digit left in the bottom number (4). This digit will multiply each digit of the top number.
 We start a new row to write our answers. We start the answers one place left (tens' place) and work right.
 4 x 5 = 20
 Since 20 is a two digit number, place the 0 below and carry the 2 into the next column left
 4 x 0 = 0
 We then add the 2 which was carried over. This results in 0 + 2 which is 2. This will be written below
 4 x 3 = 12
 Since there are no more columns we can simply write the 12 and move on to the next step
 Once we have completed the process and multiplied each number in the bottom row by each number in the top row, we are ready to add. We now set up a
vertical addition and find the sum of the amounts in the answer section.
 Find the sum of 2745 and 12,200.
 5 + 0 = 5 (or you can just bring the 5 down)
 4 + 0 = 4
 7 + 2 = 9
 2 + 2 = 4
 1 + 0 = 1 (or you can just bring the 1 down)
 2745 + 12,200 = 14,945
Ready for more?
Watch the Step by Step Video Lesson
Take the Practice Test