# How do you use area models to divide 640 div 21?

Oct 26, 2016

(see below)

#### Explanation:

Start with a rectangle and label its area as $640$ inside the rectangle.
Write $21$ as the height of one side to the left of the rectangle. Estimate a width for the rectangle such that the width times the length ($21$ in this case) in not greater than the area of the rectangle.
Write this estimate above the rectangle. Multiply this estimate for the width times the height and subtract their product from the area of the rectangle. Unfortunately, for this example, my estimate was too good for demonstration purposes. The remainder is less than the height of the rectangle and we are done with the result $640 \div 21 = 30 R 10$ or $30 \frac{10}{21}$

For demonstration purposes suppose that I had made a poor choice for my initial estimate of the width and chose $20$.
Multiplying this estimate times the height and subtracting the product would give me something like: We still have an area of $210$ unaccounted for, so we will draw another rectangle beside the first one (so the rectangles have the same height) and write-in this excess area: Again (for demonstration purposes) I will make a poor choice for the estimated width of this excess area and repeat the process: Since the excess area is still greater than the height of the rectangle,
we write this new excess area in another rectangle and repeat: Now the excess area is less than the height and we can no longer continue.
The width of the series of rectangles (which is the result of the original division) is $20 + 8 + 2 = 30$ with a remainder of $10$