Multiplying Using Lines

Ever wanted to know how to multiply other than using a calculator? Well we have put together a brilliant trick that is simple to learn and works every time!
We are going to use lines to calculate 21 X 32

First we look at the left part of the sum, 21.

The first digit, 2 needs to be represented in line format. How? Well we draw two lines diagonally, like so:

If it was 31 then there would have been three lines.

Ok, so now we need to draw a line for the 1 of 21:

 

So now we have the 21 part of the sum sorted out.

Next we concentrate on the 32 part of the sum.

Not surprisingly we need to draw lines in the opposite direction to the way 21 was drawn.

Let’s look at the 3 of 31:

 

 

And finally we add the lines for the 2 of 32:

 

 

Right, so we have all the work done that is necessary to calculate the answer to 21 X 32. But how do we know what to do next? Easy. Break the diagram above into three sections, the first section is the left part of the diagram, the 2nd section is the top and bottom intersection and the third is the right intersection. The diagram below should clarify this for you:

 

Looking at part one circled above, you can see 6 red dots. These dots are there when one line crosses over another one. You can see that there are 6 red dots, this makes up the first part of the answer.

Looking at section 2 there are four red dots at the top section and three red dots at the bottom section. Add them together totalling 7. This makes up the second part of our answer.

Finally, part three. There are two red dots cutting the intersection. The third part of the answer is two.

Putting all these answers together to get 672.

So our answer 21 X 32 = 672

So how did you find it?

This method will also work for larger numbers too. Try 123 X 321 and see how you fair.

So what about when the sum gets bigger? How do we tackle it?

Well let’s take an example of 42 X 37, and having drawn in all the lines we should have an image something like this:

 

Looking at part one on the left, how many red dots are there?

I count 12.

Part two, how many red lines do you see? I count 34 (don’t worry, this won’t make it any more difficult).

And finally, part three. How many red dots? 14.

so, put the numbers together, in order and you get 12, 34, 14

But, this isn’t the answer yet. We need to have only single digits in each part and to do this you add the tens part to the left hand side. The tens part, for example would be the three of 34 or the 1 of 14.

So to make these numbers be on their own its easier to work from the right to left.

Move the 1 of the 14 to the left, adding the 1 to 34 giving 35. In this movement we have just got our last digit in the answer, 4.

So now our sum looks like this:

12, 35, 4

Next, move the three of 35 across to the left, and adding it to the 12, giving:

15, 5, 4

And finally, notice that we cannot add the 1 of 15 to anything on the left hand side, so we know we have reached the end of the calculation. All we need to do now is remove the commas and we have our answer.

So 42 X 37 = 1554

And that’s how you multiply numbers using lines!



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3 Responses to “Multiplying Using Lines”

  1. I am so amazed at this method. I am a 4th grade math/science teacher and this method could help my students tremendously.

  2. i am an engineer and found this method of multipling 2 digits numbers really alluring and miracle of geometry i have never found before.

  3. do you have twitter or facebook,I want to be your fans in hurry.1$4

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