1. Multiplying Multi-Digit Whole Numbers
5.NBT.B.5

2. Multiplying Multi-Digit Whole Numbers5 7 3 3 8 8 × 7 7 9 9 1 3 4 2 1 +
2 6 6
Here is 38 times 79.
Let’s begin by multiplying 38 by 9.
What is 9 times 8? 72
Let’s mark the 2 …
… and regroup the 7.
Here is 72.
What is 9 times 3? 27
Let’s add the 7. What is 27 plus 7? 34
Now, let’s prepare to multiply 38 times 7.
First, let’s cross off the regrouped digit.
Notice that the 7 is in the tens place, not the ones place. So, let’s mark the ones place with a zero.
What is 7 times 8? 56
Let’s mark the 6 …
… and regroup the 5.
Here is 56.
What is 7 times 3? 21
Let’s add the 5. What is 21 plus 5? 26
Now, let’s add the partial products.
What is 2 + 0? 2
What is 4 + 6? 10
Let’s mark the 0 …
… and regroup the 1 …
… so that it still says 10.
What is ?
What is 1 + 2? 3
Now, let’s mark the comma.
The answer is 3,002. 3 , 2 10
Let’s mark the 0 …
… and regroup the 1 … 26
What is 4 + 6?
… so that it still says 10.
Now, let’s add the partial products.
What is 2 + 0? 2
… so that it still says 10.
Now, let’s mark the comma.
The answer is 3,002.
Let’s add the 5. What is 21 plus 5? 3
What is 1 + 2? 10
Let’s mark the 0 …
… and regroup the 1 …
What is ? 27
… and regroup the 7.
Here is 72.
What is 9 times 3?
Let’s add the 7. What is 27 plus 7?
Let’s mark the 2 … 72
Here is 38 times 79.
Let’s begin by multiplying 38 by 9.
What is 9 times 8? 34
Now, let’s prepare to multiply 38 times 7.
… and regroup the 5.
Here is 56.
What is 7 times 3?
Let’s mark the 6 … 56
First, let’s cross off the regrouped digit.
Notice that the 7 is in the tens place, not the ones place. So, let’s mark the ones place with a zero.
What is 7 times 8? 21

3. Multiplying Multi-Digit Whole Numbers
38 × 79 = 3,002
3,002
79 × 38 = 3,002
3,002 ÷ 38 = 79 38 79
3,002 ÷ 79 = 38
Since we know that 38 x 79 …
… is equal to 3,002 …
… we also know that 79 x 38 …
… is equal to 3,002.
3,002 divided by 38 …
… is equal to 79.
And, 3,002 divided by 79 …
… is equal to 38.
And, 3,002 divided by 79 …
… is equal to 79.
… is equal to 38.
… is equal to 3,002 …
Since we know that 38 x 79 …
… we also know that 79 x 38 …
… is equal to 3,002.
3,002 divided by 38 …

4. Multiplying Multi-Digit Whole Numbers1 2 5 5 3 3 × 4 4 7 7 3 7 1 + 21 2
Here is 53 times 47.
Let’s begin by multiplying 53 by 7.
What is 7 times 3? 21
Let’s mark the 1 …
… and regroup the 2.
Here is 21.
What is 7 times 5? 35
Let’s add the 2. What is 35 plus 2? 37
Now, let’s prepare to multiply 53 times 4.
First, let’s cross off the regrouped digit.
Notice that the 4 is in the tens place, not the ones place. So, let’s mark the ones place with a zero.
What is 4 times 3? 12
Let’s mark the 2 …
… and regroup the 1.
Here is 12.
What is 4 times 5? 20
Let’s add the 1. What is 20 plus 1?
Now, let’s add the partial products.
What is 1 + 0? 1
What is 7 + 2? 9
What is 3 + 1? 4
And, here is 2.
Now, let’s mark the comma.
The product is 2,491. 2 , 4 9 1
Now, let’s add the partial products.
What is 1 + 0? 21 20
What is 4 times 5? 1
Let’s add the 1. What is 20 plus 1?
What is 3 + 1?
Now, let’s mark the comma.
The product is 2,491.
And, here is 2.
Here is 12. 9 4
What is 7 + 2?
… and regroup the 2.
Let’s mark the 1 …
Here is 21.
What is 7 times 5? 21
What is 7 times 3?
Here is 53 times 47.
Let’s begin by multiplying 53 by 7. 35
Let’s add the 2. What is 35 plus 2?
What is 4 times 3? 12
Let’s mark the 2 …
Notice that the 4 is in the tens place, not the ones place. So, let’s mark the ones place with a zero.
First, let’s cross off the regrouped digit. 37
Now, let’s prepare to multiply 53 times 4.
… and regroup the 1.

5. Multiplying Multi-Digit Whole Numbers
53 × 47 = 2,491
2,491
47 × 53 = 2,491
2,491 ÷ 53 = 47 53 47
2,491 ÷ 47 = 53
Since we know that 53 x 47 …
… is equal to 2,491 …
… we also know that 47 x 53 …
… is equal to 2,491.
2,491 divided by 53 …
… is equal to 47.
And, 2,491 divided by 47 …
… is equal to 53.
And, 2,491 divided by 47 …
… is equal to 47.
… is equal to 53.
… is equal to 2,491 …
Since we know that 53 x 47 …
… we also know that 47 x 53 …
… is equal to 2,491.
2,491 divided by 53 …

6. Multiplying Multi-Digit Whole Numbers
4 3 6 ×
9 7 +
The first step in solving this problem is to multiply 436 x 7.
This part of the product is 3,052.
Next, we multiply 436 x 9.
Since the 9 is in the tens place, we will mark the ones place with a 0.
436 x 9 = 3,924
Now, we can add the partial products.
These are the partial products to add together.
The sum of the partial products is 42,292.
So, 42,292 is the product of 436 x 97.
4 2,2 9 2
The sum of the partial products is 42,292.
So, 42,292 is the product of 436 x 97.
Now, we can add the partial products.
These are the partial products to add together.
The first step in solving this problem is to multiply 436 x 7.
Here is 436 x 97.
This part of the product is 3,052.
Next, we multiply 436 x 9.
Since the 9 is in the tens place, we will mark the ones place with a 0.
436 x 9 = 3,924

7. Multiplying Multi-Digit Whole Numbers
6 2 9 ×
5 8 4 +
0 0
Here is 629 x 584.
The first step in solving this problem is to multiply 629 x 4.
This part of the product is 2,516.
Next, we multiply 629 x 8.
Since the 8 is in the tens place, we will mark the ones place with a 0.
629 x 8 = 5,032
Next, we multiply 629 x 5.
Since the 5 is in the hundreds place, we will mark the ones and tens places with 0.
629 x 5 = 3,145
Now, we can add the partial products.
These are the partial products to add together.
The sum of the partial products is 367,336.
So, 367,336 is the product of 629 x 584.
3 6 7,3 3 6
Next, we multiply 629 x 5.
Now, we can add the partial products.
Since the 5 is in the hundreds place, we will mark the ones and tens places with 0.
So, 367,336 is the product of 629 x 584.
629 x 5 = 3,145
This part of the product is 2,516.
The first step in solving this problem is to multiply 629 x 4.
Here is 629 x 584.
Next, we multiply 629 x 8.
Since the 8 is in the tens place, we will mark the ones place with a 0.
These are the partial products to add together.
629 x 8 = 5,032
The sum of the partial products is 367,336.

8. Multiplying Multi-Digit Whole Numbers
Closing Question

9. Multiplying Multi-Digit Whole Numbers
1 0 8 ×
3 7 4
4 3 2
7 5 6 +
3 2 4
0 0
Here is 108 x 374.
The first step in solving this problem is to multiply 108 x 4.
This part of the product is 432.
Next, we multiply 108 x 7.
Since the 7 is in the tens place, we will mark the ones place with a 0.
108 x 7 = 756
Next, we multiply 108 x 3.
108 x 3 = 324
Since the 3 is in the hundreds place, we will mark the ones and tens places with zeros.
Now, we can add the partial products.
These are the partial products to add together.
The sum of the partial products is 40,392.
So, 40,392 is the product of 108 x 374.
4 0,3 9 2
Next, we multiply 108 x 3.
Now, we can add the partial products.
Since the 3 is in the hundreds place, we will mark the ones and tens places with zeros.
So, 40,392 is the product of 108 x 374.
108 x 3 = 324
This part of the product is 432.
The first step in solving this problem is to multiply 108 x 4.
Here is 108 x 374.
Next, we multiply 108 x 7.
Since the 7 is in the tens place, we will mark the ones place with a 0.
These are the partial products to add together.
108 x 7 = 756
The sum of the partial products is 40,392.