Area Model Multiplication

Area model multiplication, also known as rectangle model multiplication, is a visual technique used to simplify multiplication, particularly with multi-digit numbers. It is based on the concept of finding the area of a rectangle, which is length × width, where the product is area. The Multiplication Area Model makes complex multiplication easy and interesting.

In this blog, you will learn about the area model math concept and multiplication with area model. 

What is the Area Model for Multiplication

The area model for multiplication is a visual representation of multiplication in which the multiplication of numbers is shown as the length and width of a rectangle, and the product as its area. 

In the multiplication area model, instead of solving the whole multiplication problem at once, it breaks numbers into parts using place value. Each part is solved separately and then added together to get the final product.

How to Use the Area Model of Multiplication

The area model of multiplication is an interesting and simple way to do multiplication, especially for kids. Here, you will learn how to use an area model for multiplication in easy steps.

• Break the number into the tens and ones place value. For example, 25= 20 + 5
• Draw a rectangle and divide it into parts according to the place value. 
•  Multiply each pair and write the product in each box.
• Add all the products in each box to get the answer.

Area Model Multiplication 2 Digit by 1 Digit

Finding the product by multiplying 2 digits by 1 digit is easy with the help of the area model of multiplication. Let’s look at the example of area model multiplication 2 digit by 1 digit. 

Example: 

Use the area model to find the product of 32 x 6.

To find the product of 32x6, we will follow the steps below.

• Convert the numbers into place value.

32=30+2 

• Make a rectangle and divide it into two parts. Write the 30+2 on the top and 6 on the left side. 

• Now multiply the top digits by the number on the left side.

• Multiply the numbers inside the boxes.

• Now, add the numbers in the box together to get the product.

180+12=192

Area Model Multiplication 2 Digit by 2 Digit

We can use the area model to multiply multi-digit numbers. We will look at the area model multiplication 2 digit by 2 digit in detail with the help of a visual example.

Example: 

Solve 34x17 using an area model. 

We will follow steps to find the product of 34x17 using the area model.

• First, we will convert the numbers into place value. 

34= 30 + 4 and 17= 10 +7.

• Now, we will write 30 + 4 on the top of the area model and  10 + 7 on the left side of the area model.

• Next, we will multiply the numbers. For this, take the first digit on the top of the area model and multiply it by the first number on the left side, and write the product in the first box. Now multiply the top second number with the left fist number and write the product in the second box. Follow the steps for the second left number and write the product in the respective box.

• Now, multiply the number in each box. 

• Add all the numbers together to get the product.

300+40+210+28=578

So, we found the product of 34x17 with the help of multiplication with area model. 

Area Model Multiplication 3 Digits by 2 Digits

We can also multiply 3 digits by 2 digits using the area model to multiply. You will learn to find the product by area model multiplication 3 digits by 2 digits. Let’s look at the example.

Example: 

Solve 325 x 12   

We will follow the simple steps.

• First, convert the 3 digits into hundred, ten, and unit place units.

325=300+20+5

12=10+2

• Now represent three digits on the top of the area model and two digits on the left side.

• Multiply the first digit on the top with the first on the left, and multiply the second and third of the top with the first on the left. Now multiply the first, second, and third digit of the top with the second digit on the left.

• Now multiply the number in each box.

• Add all the numbers in the box and get the result. 

3000+200+50+600+40+10=3900

Area Model Multiplication Worksheets

We learned how to do area model multiplication in easy steps. Now you can find the product of multiple digits using this method. Here we provide you with the area model multiplication worksheets so you can practice them and enhance your multiplication skills. 

You can download the area model multiplication PDF below.

Conclusion 

The area model multiplication is a visual tool that represents multiplication problems as the area of a rectangle, making it easier to understand and solve. It helps students visualize the distributive property of multiplication and provides a step-by-step approach to multiplying multi-digit numbers.