Using the area model, we start with one flat, nine longs, and five units, and we wish to make a rectangle with 13 rows.
This cannot be done without first exchanging one of the longs for 10 units.
After doing this, we can arrange a 13-by-15 rectangle, so the result of the division is 15.
Using long division, 13 goes into 19 once, with a remainder of 6. Carry down the 5 for 65. Thirteen goes into 65 five times evenly. The quotient is 15.
The area model relates to long division in that it matches the long division algorithm. In long division, you first subtracted 130, or 10 13, and then subtracted 65, or 5 13, for a total result of 15. Thus, 15 13 = 195. Similarly, the area model gave you the rectangle 13 by 15, which consists of two rectangles: 10 13 and 5 13.
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