This is the technique for solving multiplication problems that involves using lines.

We’ll all agree that Math was our most hated subject back in school; you had a hard time solving problems by hand. The growing need for smart devices have in a kind of way solved our math problem — no need to pull out some scratch paper or your handy-dandy multiplication tables. But if you’re a math nerd and still solve problems by hand, then we’ve found a method of solving multiplication problems that’s not only fun to do by hand, it’s mind blowing.

Related media: Multiply Numbers By Drawing Lines

 

Line Up

I guess you remember how to multiply digits by hand. First, placing two numbers on top of each other, then you multiply the top digits by the digit below them in the ones place, then you multiply the top digits by the digits below them in the tens place (make sure you add a 0 at the end) — you multiply the top digits by each digit below them according to their place value. Finally, you sum up the numbers you had after multiplying, and ta-da, you have your answer. Luckily, there is another way to solve multiplication problems. This one involves lines.

See how it’s done: Let’s say you want to multiply 4 by 3. Easy! You first of all draw four parallel diagonal lines from the lower left side to the upper right side. (In all of these examples, each subsequent line should be placed to the right of the last one). Next, you draw three more parallel diagonal lines perpendicular to (and intersecting) the first lines, this time draw them from the upper left side to the lower right side. Now, count the intersections. There are 12 intersecting lines, hence that’s the answer. Like we said, Easy!

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Illustration of 4 x 3

 

Draw More And More Lines

Let’s multiply 31 by 22. For the 31, draw three parallel diagonal lines from the lower left side to the upper right side, leave a space, then draw one more parallel diagonal line by the same way. Do the same for the 22 — two lines from the upper left, a space, then two more lines. The result should look like a diamond with three lines for the upper left side, two lines on the lower left side, one line on the lower right side, and two lines on the upper right side.

Next, you separate the diamond shaped lines into vertical sections. The left corner into the first section, the top and bottom corners into the second section since they vertically align, and the right corner into the third section. Now you sum up the intersections again. There are 6 intersecting lines in the leftmost section, and 8 in the middle section, and 2 in the rightmost section; hence your answer is 682. Awesome!

It gets really fun as you solve more problems. Let’s try it again with multiplying 31 by 23. It’s just a number difference, but it adds a kick to the game. This time, there are 6 intersecting lines on the left, 11 in the middle, and 3 on the right. That 11 is the new kick to the game. Just like other forms of multiplication, you’ll have to carry the one and add it to the 6 on the left side, therefore your answer is 713.

70FC5B41-2C40-4147-92A3-04B3752845BE
Illustration of 31 x 23

 

Scale Up The Lines

The method works on three-digit numbers too, but we don’t have to go all the way through the steps again. Multiply 412 by 121 using this method and count the intersections in those vertical columns again — there are 4, 9, 8, 5, and 2 in that order for a product of 49,852.

517E14C5-DF20-479D-8210-929CB13215BA
Illustration of 412 x 121

Let’s try one last teaser. Let’s multiply 246 by 305. You know what to do. Draw two lines, then four lines, then six lines. Now draw three lines, then … “zero line” … then five lines. Make sure that it sums up right, so put the “zero line” in a different color, and take note not to count any intersections of that color. So for this problem, the intersections are 6, 12, 28, 20, and 30. That’s a lot of numbers to carry over, but in the long run, the answer is 75,030. That’s math-blowing.

30715EBE-1689-48F1-BD90-245D04488C0B
Illustration of 246 x 305

 

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Written by: Nana Kwadwo, Fri, Jan 04, 2019.

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