Window Box Multiplication

Window Box Multiplication is an alternative method for performing long multiplication. Instead of multiplying numbers within a messy column layout, the equation is performed in a simplified grid like layout. You start off by drawing a rectangle and dividing it into the number of rows and columns required (The example application performs a simple 2 digit by 3 digit equation).

[http://www.davidmgilbert.com/images/wbme/wbme1.png] Once you have divided the rectangle into the desired number of rows and columns, you then diagonally divide the squares into triangles as per the image below.

[http://www.davidmgilbert.com/images/wbme/wbme2.png] Now you need to add your numbers to the outside of the rectangle to the left and underneath. In this example, we are going to multiply 36 x 742.

[http://www.davidmgilbert.com/images/wbme/wbme3.png] Now we need to start performing some math. Multiply the number in each column by the number in the corresponding row. Place the answer as follows, tens in the top triangle of the box, units in the bottom. In the following image, you see we have multiplied 2 x 6 (12) and placed the 1 in the top triangle and the 2 in the lower triangle. Note: If the two digits being multiplied do not equal more than 10, you can leave the upper triangle blank.

[http://www.davidmgilbert.com/images/wbme/wbme4.png] Once all of the triangles are filled you can now add the numbers in the diagonal rows together and place the answer to the right and top of the triangle. Note: If the diagonal row equals more than 10, you simply place a carry-over of the tens amount (demonstrated below as a red 1).

[http://www.davidmgilbert.com/images/wbme/wbme5.png] Once all diagonal rows have been added you can now from the top left of the rectangle around to the bottom right of the rectangle read the answer. (36 x 742 = 26,712).

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