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Area Model Division – Definition, Examples, Facts

Jessica Kaminski

reviewed by Jo-ann Caballes

Updated on March 10, 2026

Area model division is a way to solve division problems by drawing rectangles and splitting big numbers into smaller, easier parts using simple answers along the way.

This guide will cover what the division area model is, how to do division with the area model, and the method’s benefits. We’ll also share practice test problems and engaging worksheets so you can continue your learning.

What is an area model for division?

The area model is a method of teaching division that breaks up the equation. It can be used with decimals and whole numbers to divide non-integer numbers.

Definition of the division area model

The area model of division is a method for performing division. It involves both visuals and incorporates multiplication and subtraction. First, you create a rectangle. Let’s use the example of 215 ÷ 5. You’d place 215 inside your box, and 5 on the left of your box.

Rather than trying to solve this large sum in one go, you can use multiplication and subtraction. Think about multiples of 5:

• 1 x 5 = 5
• 5 x 5 = 25
• 10 x 5 = 50

Use these multiples of 5 to subtract from 215 and create additional blocks in your rectangle. So we know 10 x 5 is 50, and we can take that away from 215 4 times, so you multiply them together. This becomes your first block in your rectangle, with 40 at the top.

Now, we have 15 left over to divide. We know we can subtract 5 from 15 3 times and then reach 0. Put 3 at the top of your second block.

Now, you add the numbers at the top of your block to get your answer. 40 + 3 = 43. Therefore, 215 ÷ 5 = 43.

How does area model division work?

Division using the area model breaks up a complex division into smaller, more manageable parts. By taking multiples of your divisor (the number you’re dividing by) away from your dividend (the number you’re dividing), you can break down a complex equation and make it easier to solve. Because we’re taking all of these numbers away from our dividend, we still get the same result regardless.

Benefits and uses of the area model division

The benefits of dividing using area model are two-fold.

• Firstly, this model for division helps students visualize division problems. This is especially useful for kids who are visual learners or have trouble understanding the logic behind multiplication and division.
• Secondly, it helps simplify large, complex division operations by breaking them down into smaller steps. Many kids, when learning math operations, find division the most difficult to grasp. Therefore, by multiplying our divisor and then taking those multiples away from our dividend, we make the division easier to solve.

Examples of area model division

Let’s take another example of area model division. We have to divide 943 by 23.

• First, let’s work out some simple multiples of 23. We know 10 x 23 is 230, and that we can take that away from 943 multiple times
• 4 x 230 is 920, so we can subtract this from 943. This means we’ve taken 23 away from 943 40 times, so we put that at the top of our block
• Now, we only have 23 remaining, so we take that away once to get to 0
• Finally, we add the number of times we’ve taken away 23 from 943. 40 + 1 = 41
• Therefore, 943 ÷ 23 = 41.

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Steps in area model division

There are some simple steps you take to use the divide with area model:

• Draw a rectangle and write your dividend in the center, then your divisor to the left of the rectangle
• Identify multiples of your divisor that can be taken away from your dividend, and subtract them
• Continue doing this until you’re left with 0
• Count up the number of times you’ve taken away your divisor from your dividend, and you’ll get the answer to your division equation

Properties and characteristics of the area model division

There are some properties and characteristics of the area division model that make it both useful and unique:

• It makes division visual. By turning numbers into rectangles and sections, your child can actually see how the divisor fits into the dividend, which is especially helpful for visual learners.
• It breaks big problems into smaller steps. Instead of solving everything at once, students subtract manageable chunks, making complex division feel less overwhelming.
• It connects to multiplication and subtraction. Since the model relies on partial products and repeated subtraction, it strengthens skills children already know.
• It builds a real understanding of the topic. Rather than memorizing steps, kids learn why division works. 

Comparing the area model division with other division models

Area model division is different from other models. Many division models can divide faster, such as the area model long division, but this model for division focuses on simplifying the calculation. It’s a great method for younger kids, or kids who aren’t confident in division, to solve equations.

Applying the area model division in a real-life context

You can apply the division area model to a number of real-life problems, including:

• Sharing a large number of sweets between friends
• Splitting a large bill between people

Deriving equations using the area model division

To derive equations using the area model to divide, we use other operations. Deriving an equation means to answer it using what you know about the numbers or equation. Because we know the multiples of our divisors, we can derive the equation with them.

Area model division with remainders

Area model division can also be done with remainders, and you don’t need to change your steps.

Let’s use the area model division examples of 294 ÷ 5. We know 5 x 10 = 50, and 5 x 50 = 250. This means we take 5 away from 294 25 times and are left with 44. 5 x 8 = 40, so we’re now left with 4, and we can’t take 5 away from that again. Therefore, 294 ÷ 5 = 58 with the remainder of 4.

Area model for dividing decimal numbers

The area model can also be used to divide decimal numbers, and it works the same way as with whole numbers. The only difference is that you need to pay attention to place value.

If the divisor is a decimal, you need to first make it a whole number by multiplying both numbers by 10, 100, or 1,000, depending on how many decimal places there are. This will help you keep the division balanced. 

Let’s look at an example, and divide 4.8 ÷ 0.6.

• First, make the divisor a whole number. Multiply both numbers by 10. You will get (10x 4.8) ÷ (10 x 0.6) = 48 ÷ 6
• Now use the area model just like with whole numbers. Ask how many times 6 fits into 48? 6 × 8 = 48

So, the answer is 8.

Dividing with area model with decimals helps your child see how place value shifts and makes decimal division more visual and easier to understand.

Practice problems on area model division

Put your knowledge to the test with our solved area model division problems!

Practice problem 1

Solve 482 ÷ 12.

Answer: 

40 with the remainder of 2.

12 x 10 = 120

We cannot take 12 away from 2, so our answer is 40 with the remainder of 2.

Practice problem 2

Solve 345 ÷ 15.

Answer: 

15 x 10 = 150

150 x 2 = 300

15 x 3 = 45

10 x 2 + 3 = 23.

Area model division worksheet

For some more practice, make sure to have a look at our division area model worksheet PDFs and other related worksheets to see how the theory works in practice. 

• Area model multiplication worksheets
• Division worksheets
• Long division worksheets
• Division with remainders worksheets

Frequently asked questions on division with the area model

What is area model division?

Area model division is a strategy that helps you break division problems into smaller steps using a visual rectangle. Students subtract multiples of the divisor from the dividend in parts, rather than all at once. This method helps to connect division to multiplication and improve the understanding of place value.

What are the benefits of area model division?

The biggest benefit is that area model division helps children visualize how division works by breaking problems into smaller, manageable steps. It simplifies large or complex calculations and strengthens multiplication skills.

What are some examples of area model division?

Area model division can be used in everyday situations, like dividing sweets equally among friends or splitting a restaurant bill. It also works for classroom problems, such as dividing large numbers into smaller groups. These real-life examples help children see how division applies beyond math worksheets.

What are the steps in area model division?

The steps in the area model division are the following:

• Draw a rectangle and write your divisor to the left and your dividend in the middle
• Use multiples of your divisor to subtract from the dividend
• Keep going until you reach 0 or you have a remainder

Jessica Kaminski

91 articles

Jessica is a seasoned math tutor with over a decade of experience in the field. With a BSc and Master’s degree in Mathematics, she enjoys nurturing math geniuses, regardless of their age, grade, and skills. Apart from tutoring, Jessica blogs at Brighterly. She also has experience in child psychology, homeschooling and curriculum consultation for schools and EdTech websites.