Let's say we want to do this problem: 4367*1289. Now on a piece of scratch paper draw a grid with diagonals like so. (The number of rows and columns correspond to the number of digits in the numbers being multiplied, in this case 4X4.)
Now write your numbers on the outside of the grid, as shown.
Next, cross-multiply the numbers on the outside of the grid, as shown. If the result is a single-digit number than you record it with a zero in front.
Finally, add up the numbers in the diagonals, starting at the top, right corner working down and left. Record the answer on the outside of the box by the end of the diagonal. If the answer has multiple digits, record the number ones place and carry over the remaining digits to the next diagonal.
The answer comes out to be 5,629,063. A quick check on a calculator reveals this to be correct. I like to use this system because it is simple and easy to remember. The system can be adapted to do just about any multiplication problem. Next time you find yourself facing a tough multiplication problem, you will be glad that you know how to do long multiplication!
1 comment:
your method is pretty neat, although another teacher and i had a race: long-way-stacked vs. your method. it came out pretty even. so, even though it's not any faster - i'll still show it to my gr.12 physics class :)
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