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What is Area Model Division?
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.
- 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.
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.
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.
Thus, 540 ÷ 30 = 18. Therefore, 18 rows of saplings would be there.