INTERSECTING STICKS/LINES MULTIPLICATION TRICK

As many of you probably know, there are a myriad of ways on coming up on techniques in multiplication. This time, I would like to share one of my favorites – the intersecting sticks/lines multiplication trick which I first learned not so many years ago.

Now, the very premise of this technique is by drawing lines or sticks (vertical and horizontal) corresponding to the digits used in the algorithm. What is needed is to make count of the intersection points of these lines to formulate the answer. For this article, we would just first focus on two-digit to two-digit number multiplications, since this technique is most appreciated in such types of problems.

SAMPLE PROBLEM: Find the product of 36 and 26.

Solution:

First, focus on 36. As seen in the image, draw three vertical lines on the left side to represent 3 and six vertical lines on the right side to represent 6.

int1

Now, focus on 26. As seen in the image, draw two horizontal lines on the upper portion intersecting the earlier drawn lines to represent 2, and six horizontal lines on the bottom part to represent 6.

int2

And now, the main part of the algorithm, focus first on the bottom part as seen in the image in the right. Notice that the encircled part has 36 points of intersection. On a separate sheet of paper, write down “6” and take note of the remaining “3”. We’ll use it for the next step.

int3Now, for the second step, we focus on the two encircled parts as portrayed in the image. On the lower part, we can see that there are 18 intersection points, while on the upper part there are 12 intersection points. That hence gives us 18 + 12 = 30. Now, remember the “3” we had in the previous step? Add it to this. Thus we have 30 + 3 = 33. Write down the digit “3” in front of the “6” you wrote earlier and take note of the remaining “3” again. As a recap, you shall now have “36” on your paper.

int4

For the final step, focus on the remaining part of the diagram (the encircled part). This has 6 intersection points. Now add the “3” we set aside from the previous step. Hence, have 6 + 3 = 9. Write “9” down on your paper in front of “36”. You now have “936” on your paper, which shall be your final answer.

int5

Indeed, by checking through a calculator, 36 x 26 = 936 !

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