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.
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:
Step 2:
Thus, 540 ÷ 30 = 18. Therefore, there will be 18 rows of saplings on the farm.
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