# Area Model Multiplication up to Three-Digits

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Area Model Multiplication up to Three-Digits
CCSS.MATH.CONTENT.4.NBT.B.5

## Basics on the topicArea Model Multiplication up to Three-Digits

Mr. Squeaks is trying to travel to the Stone Age by fueling his time machine with stones, clocks, and shoes. Before he does that, he needs to calculate how many he has of each. Let’s practice area model multiplication and learn to Multiply 1-Digit by 3-Digit Numbers.

## How Do You Multiply a 3 Digit Number by a 1 Digit Number?

When multiplying 3-digit by 1-digit numbers, we can use an area model. An area model is a rectangular model that helps us find the product of two numbers. Let’s look at a 3 by 1 digit multiplication example.

### 3 Digit by 1 Digit Multiplication Example

Let's help Mr. Squeaks calculate by multiplying two hundred forty-five times three.

The first step is to set up our area model. Start by drawing a rectangle. Next, split it into the number of parts based on how many place values are in each number. Two hundred forty-five has three place values: hundreds, tens, and ones, so we split our rectangle in three parts. Three has one place value so we don't break the rectangle into any more parts.

[line 42 (imagined): two-hundred-forty-five-times-three-rectangle-split-in-three-parts-multiplication-multi-digit-number-with-1-digit-number]

Next, label each part by writing the factors in expanded form. The top is labeled using the expanded form two hundred plus forty plus five and the three goes on the left.

[line 42 (imagined): two-hundred-forty-five-times-three-rectangle-split-in-three-parts-two-hundred-plus-forty-plus-five-on-the-top-three-on-the-left-multiplication-multi-digit-number-with-1-digit-number]

The second step is to multiply each corresponding pair to find the partial products. Partial products are the answers we get when each pair of factors is multiplied.

In the box on the left, we multiply three times two hundred to get six hundred. Now we multiply three times forty which is one hundred twenty. Last multiply three times five to get fifteen.

[line 42 (imagined): two-hundred-forty-five-times-three-rectangle-split-in-three-parts-three-times-two-hundred-equals-six-hundred-three-times-forty-is-one-hundred-twenty-three-times-five-equals-fifteen-multiplication-multi-digit-number-with-1-digit-number]

After we find all the partial products, the third step is to add them. The sum of the partial products is seven hundred thirty-five, which means two hundred forty-five times three is seven hundred thirty-five.

Now that we’ve practiced multiplication 3 digit by 1 digit, let’s review!

## Summary

Remember, when we solve a multiplication problem using an area model, the first step is to set up the area model. The second step is to multiply each corresponding pair to find the partial products. The third step is to find the sum of the partial products.

Want some more multiplication multi digit number with 1 digit number practice? On this website you can find 3 digit by 1-digit multiplication worksheets pdf along with activities and exercises.

### TranscriptArea Model Multiplication up to Three-Digits

What is Mr. Squeaks doing with all those supplies? Oh... Imani needs them to fuel the time machine so they can travel to the Stone Age! Before he gives them to Imani, he needs to calculate how many stones, clocks, and shoes he has. In order to do that, we will practice "Area Model Multiplication up to Three-Digits". An "area model is a rectangular model that helps us find the product of two numbers." Mr. Squeaks has five boxes with thirty-eight clocks in each. Let's help Mr. Squeaks calculate by multiplying thirty-eight times five. The first step is to set up our area model. Start by drawing a rectangle. Next, split it into the number of parts based on how many place values are in each number. Thirty eight has two place values...TENS and ONES, so we split our rectangle in two parts. Five has one place value so we don't break the rectangle into any more parts. Next, label each part by writing the factors in expanded form. The value of the three in the tens place is thirty and the value of the eight in the ones place is eight... so we label the TOP thirty plus eight. Then, we label the five on the LEFT SIDE. The second step is to multiply each corresponding pair to find the partial products. Partial products are the answers we get when each pair of factors is multiplied. In the box on the LEFT, we multiply five times thirty. (...) Remember, you can ignore the zeros at first to get fifteen... and then annex one zero to your answer. Five times thirty equals one hundred fifty. Now we multiply "five times eight" in the box on the RIGHT,(...) which equals forty. After we find all the partial products, the third step is to ADD them. This will give us the answer to our multiplication problem. One hundred fifty PLUS forty is one hundred ninety so (...) they have one hundred ninety clocks. Mr. Squeaks has eight boxes with seventy-six shoes in each. We need to find the product of seventy-six times eight. First, let's set up our area model by drawing a rectangle, (...) breaking it into parts, (...) and labeling it. When we label using expanded form, we have seventy plus six on the TOP and eight on the LEFT. The second step is to multiply each corresponding pair to find the partial products. Let's find the partial product for the box on the LEFT. What is eight times seventy? (...) Eight times seventy equals(...) five hundred sixty. Now let's find the partial product for the box on the RIGHT. Eight times six equals (...) forty-eight. Last, what is the sum of the partial products? (...) Five hundred sixty PLUS forty-eight equals(...) six hundred eight. That means Mr. Squeaks has six hundred eight shoes for the time machine. Last, Mr. Squeaks has three boxes with two hundred forty-five stones in each. We need to find the product of two hundred forty-five times three. The first step is to set up our area model (...) but how does this look with a three-digit number? We still label it using expanded form, (...) but now the model is broken into THREE parts since we are calculating a THREE-digit number. How do we label it? The TOP is labeled using the expanded form two hundred PLUS forty PLUS five... and the three goes on the LEFT. The second step is to multiply to find the partial products. This time, try multiplying on your own. The partial products are six hundred (...) one hundred twenty (...) and fifteen. Now, what do we do with the partial products? The last step is to find the sum of the partial products. (...) The sum of the partial products is seven hundred thirty-five, (...) which is the number of stones Mr. Squeaks has for the time machine. Remember(...) when we solve a multiplication problem using an area model, the first step is to "set up the area model". The second step is to "multiply each corresponding pair to find the partial products". The third step is to "find the sum of the partial products". Let's see if the time machine has enough fuel. It looks like it's working...

## Area Model Multiplication up to Three-Digits exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Area Model Multiplication up to Three-Digits.
• ### Can you solve the multiplication problem?

Hints

Have you multiplied each side of the area model?

After you have multiplied each side, your area model should look like this.

Have you added the partial products together?

Don't forget any zeros!

Solution

First of all, solve the equation on the left:

• 4 x 30 = 120
Then solve the equation on the right:

• 4 x 9 = 36
120 and 36 are the partial products, so we then need to add them together.

• 120 + 36 = 156
Therefore, 4 x 39 = 156

• ### Can you complete the area model and solve the problem?

Hints

Multiply each part separately. In this example 20 is being multiplied by 4, then 2 is being multiplied by 4.

At the bottom we need to add the partial products, and then complete the original multiplication problem.

Solution

Mr. Squeaks had 5 boxes with 68 pencils in each. This is how the area model looks when it is completed.

• We multiply 5 by 60 to get 300.
• Then we multiply 5 by 8 to get 40.
• We then add 300 and 40 to get 340.
• 68 x 5 = 340.
• ### Can you spot the mistakes in the area model?

Hints

Think about how we partition a three digit number, has it been done correctly here? What should 248 be partitioned into?

What should the first digit in each of the three area model equations be?

Have the zeros been included on if necessary?

Solution

The image above shows the mistakes highlighted.

• When partitioning a three digit number we need only the hundreds in the first box, so this should have been 200, both above the box and in the first box.
• 4 x 40 is 160, not 16. We can multiply 4 x 4 first to make it easier, but the 0 needs adding onto the end again.
• In the third box the first number should have been 4, as that is what we are multiplying 248 by.
• The final answer at the end is incorrect because of the mistakes in the area model. 248 x 4 = 992.
• ### Can you find the correct answers to the multiplication problems?

Hints

Have you partitioned the two or three digit number?

This example shows how we could set up 32 x 3 using an area model.

Solution

The grid above has been filled in for the problem 42 x 7. 42 has been partitioned into tens and ones to give 40 and 2.

To solve:

• First of all we multiply 7 by 40 to get 280.
• We then multiply 7 by 2 to get 14.
• Now we need to add 280 and 14 to get 294.
• Therefore 42 x 7 = 294.
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• 83 x 3 = 249
• 113 x 4 = 452
• 207 x 2 = 414
• 325 x 3 = 975
• ### Can you complete the area model and find the answer?

Hints

Remember to multiply 3 by the tens and the ones of the two digit number.

Solution

Here is the completed area model:

• 3 x 30 = 90
• 3 x 5 = 15
• We then add 90 and 15 to get 105.
• So, 35 x 3 = 105.
• ### Can you solve the multiplication problems?

Hints

Remember to partition your two or three digit number.

Solution

For the first problem:

• We need to partition 39 into 30 and 9.
• We then multiply 8 by 30 to get 240, and 8 by 9 to get 72.
• Next, add 240 and 72 to get 312.
• Therefore, 39 x 8 = 312

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For the second problem:

• Partition 76 into 70 and 6.
• Multiply 4 by 70 to get 280, and 4 by 6 to get 24.
• Add 280 and 24 to get 304.
For the third problem:
• Partition 122 into 100, 20 and 2.
• Multiply 6 by 100 to get 600, 6 by 20 to get 120, and 6 by 2 to get 12.
• Add 600, 120 and 12 to get 732.
For the fourth problem:
• Partition 341 into 300, 40 and 1.
• Multiply 7 by 300 to get 2,100, 7 by 40 to get 280, and 7 by 1 to get 7.
• Add 2,100, 280 and 7 to get 2,387.