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

##### 1 Answer

(see below)

#### Explanation:

Start with a rectangle and label its area as

Write

Estimate a width for the rectangle such that the width times the length (

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

For demonstration purposes suppose that I had made a poor choice for my initial estimate of the width and chose

Multiplying this estimate times the height and subtracting the product would give me something like:

We still have an area of

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