Let's look at the area model that you used to compute 18711.
Like the previous multiplication problems, we know that the rectangle's area is 187 and its height is 11. This problem asks us to determine its length.
The first step in this process is to create a model that represents an area of 187, using one flat, eight longs, and seven units:
Now use the flat and one of the longs to start the rectangle:
The rectangle we've built is composed of 11 tens, which, since multiplication is commutative, is equivalent to 10 elevens. Ten elevens is 110:
We have 77 left over. This 77 (composed of 7 tens and 7 ones) can be grouped in elevens as well. There are 7 of them:
The algorithm matches the model. You first subtracted 10 elevens and then subtracted 7 more elevens, for a total of 17 elevens. Thus, there are 17 elevens in 187. The length of the rectangle is 17, and the answer to the problem 18711 is 17.