# How do you use area models to divide 217 div 31?

Oct 24, 2016

See below

$\textcolor{w h i t e}{\text{XXX}} 217 \div 31 = \textcolor{g r e e n}{7}$

#### Explanation:

Draw a rectangle; place the dividend inside the rectangle (as an area to be divided) and the divisor outside to the left of the rectangle.

Pick a number such that the number times the divisor is not greater than the number inside the rectangle.
Write that number above the rectangle.

For this particular example it would have been easy to pick the final answer, but to make this example useful, I picked something much smaller).

Multiply the number above the rectangle by the divisor;
write the product under the number already in the rectangle;
subtract the product from the original number and write the difference under the rectangle.

Since the number under the rectangle is not $0$
we will repeat this process, starting by drawing another rectangle adjacent to the first and writing the difference from the previous step inside it.

Again we pick a number which when multiplied by the divisor is not greater than the number in the rectangle.
(For demonstration purposes I picked $2$)
Multiply this number by the divisor; subtract their product from the number in the rectangle; and write the difference under the rectangle.

Since the difference was not $0$
repeat this entire process again.

Finally we have reached a point where the difference under the rectangle is $0$
and
the result of the division is the sum of the number above the rectangle:
$\textcolor{w h i t e}{\text{XXX}} 4 + 2 + 1 = 7$