Area model division - Definition with Examples

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What is Area Model Division?

The area of a shape is the space occupied by the shape

If a rectangle has a length equal to 32 units and a width equal to 23 units, then we can find its area by calculating the product 32 ⨉ 23. In other words, when we consider the product 32 ⨉ 23, geometrically, it can be interpreted as the area of a rectangle of length 32 units and width 23 units.


Similarly, we can geometrically interpret a division problem, say, 555 ÷ 15, as the missing dimension of a rectangle of area 555 square units and one side length 15 units.

  • We can divide this rectangle into several small rectangles. Then, we can calculate the length of each small rectangle and add them together to find the length of the large rectangle.

      geometrically interpret a division problem 1

  • First, consider a small rectangle of width 15 units and length 20 units. The area of this rectangle is 300 square units. So the area of the rest of the rectangle is 555 – 300 = 255 square units.
       geometrically interpret a division problem 2

Now, we have an area of 255 square units left. Since 15 ⨉ 10 = 150, another rectangle of width 15 units and length 10 units can be created.


We are now left with an area of 255 – 150 = 105 square units. As 15 ⨉ 7 = 105, the shaded rectangle has a width of 15 units and a length of 7 units. 

Thus, the length of the large rectangle is 20 + 10 + 7 = 37 units. Therefore, 555 ÷ 15 = 37.

Example: Catherine has 540 saplings to plant on her farm. If she plants 30 saplings in a row, how many such rows would there be?

The number of rows is given by the quotient 540 ÷ 30. Now, in the area model for division, we need to find the missing dimension of the rectangle that has an area of 540 square units and a length of 30 units.


Step 1:

     find the missing dimension of a rectangle 1


Step 2:  


Thus, 540 ÷ 30 = 18. Therefore, there will be 18 rows of saplings on the farm.

  Fun Facts

  • If the difference is greater than the divisor, the division is incomplete! If the difference is less than the divisor, then it is the REMAINDER!

  • Can you start the division procedure with a different length of the rectangle? Yes, for example, in 555 ÷ 15, if we consider a sub-rectangle of length 5 units, the area will be 15 ⨉ 5 = 75 square units, and the remaining area will be 555 − 75 = 480 square units. We can continue the procedure in a similar manner.

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