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 of 23 units, then we can calculate this area by taking 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 the length of 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 sq. units and one side 15 units long.

  • The rectangle can be further divided into smaller rectangles, repeatedly calculating the length of each smaller rectangle. These lengths can be added to get the required length.

      geometrically interpret a division problem 1

  • First, consider a smaller rectangle of the height of 15 units and a length of 20 units. So, the area of the rectangle would be 300 square units, and the rest of the rectangle has an area of 555 – 300 or 255 sq. unit.
      geometrically interpret a division problem 2
 

Now, we have an area of 255 sq. units for sub-division. Since 15⨉10 = 150, another rectangle of height 15 units and length 10 units can be marked. geometrically interpret a division problem 3

Finally, we have 15 ⨉ 7 = 105. So, the shaded rectangle above has a height of 15 units and length 7 units constituting an area of 105 sq. units.

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

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

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

 

Step 1:

     find the missing dimension of a rectangle 1

 

Step 2:

     find the missing dimension of a rectangle 2

Thus, 540 ÷ 30 = 18. Therefore, 18 rows of saplings would be there.

  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 procedure with another length of the rectangle? Yes, for example, in 555 ÷ 15, if we consider the sub-rectangle of length 5 units then the area becomes 15 ⨉ 5 or 75 sq. units and the rest of the area become 555 − 75 = 480 sq. units. The procedure can be continued in a similar way.

 
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