# Area Model Multiplication up to Three-Digits

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Basics on the topic
**Area Model Multiplication up to Three-Digits**

## Content

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.

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Transcript
**Area 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...