Ancient Chinese were one of the biggest inventors, we all know about black powder, paper, etc. all Chinese. But did you know about chinese way of multiplying?

Here's how, its fast 'n' easy and it works with equations from 1x1 to 3856x2955, etc. Just about anything!

These is a technique I found very useful in Mathematics to do large multiplication without burning our brains so thats why I decided to post it in the Back to school contest:

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thanks, now we can go on!

### Supplies:

## Step 1: Example

Here's an example of just a simple multiplicatn, 2x2. these is kind of what your multiplicatins will look like, but don't worry just yet, we'r gonna find out what those drawings mean and how are they done.

## Step 2: First Lesson: 22x22

Here we see just four crossed lines that probably wont mean much to you, but thats the harder thing, the lines! (It looks kinda easy hah)

Heres how its done:

First: write down your multiplication.

Second: draw the lines according to the numbers in the multiplication. (see 2nd picture for explanation)

Third: Divide the lines in sectors and sum the points in each sector, then sum each sector's numbers to get the answer. (see 3rd picture for explanatin)

## Step 3: Coming More Complicate! 53x241

The square represents the intersections between the digits of the first number with the second number (e.g. in the above the first column is made up of the intersection of the 5 from the first number and the 2 from the second number) Think of each set of lines as a single unit. The square is broken up into columns from left to right. The first column will consist of the just the corner. In the example below, that is the intersection between the lines from 5 from the first number and the lines for 2 from the other. The next column will consist of the next set of intersections you come across going from left to right

Treat the sums of the intersections as two digit numbers with a leading zero if the number is less than 10. The first digit of the sum lines up with the last digit from the number above it. That makes the sums from above be: 10 26 17 03 _____ 12773Here's an example of a more complicated multiplication just to show you how easy can these be done.

Here, it involves a lot more digits so the sum is a bit more complicate than with just 1 digit per sector!

Thnks for reading!

Hope it helps!

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## 59 Discussions

7 years ago on Introduction

Just stumbled across this instructable, tho a bit puzzling, helped me understand how a abacus works... there's a video on youtube which made it a bit clearer for me.

1.

stands for theEach linein the problem.numbers2. Starting from the

leftthe first number is. Now5fromdraw FIVE LINES2 o'clock to 8 o'clock3. The next number is

- so3after leaving adraw THREE LINESin the same directionspace4. the next part of the equation is

2 4 1.+Draw TWO linesgap++FOUR linesgap+standing for each number at right angles in the other direction.ONE line(11 o'clock to 5 o'clock)(Making sure to begin from the

- seems to be aleft bottom corner)left to right method5. The totals

are figured out by10, 26, 17, 3at eachplacing a DOTof theintersecting lineyou've just drawn.gridGroup each group of dots by the corners of the grid. ie north east west south (

Emihack hasNBgrouping each intersection.)drawn an orange lineNow

for each corner group. (That's whereadd up those dotscomes from)10, 26, 17 and 3Next add up

keeping them in their columns of10, 26, 17 and 3- just like abacus.1000's, 100's, 10's and 1'sI guess this method's pretty cool since one needn't memorise the time table and stick to adding which is a lot easier to calculate. Is it faster than the usual way? Definitely!

8 years ago on Introduction

@paperrhino

I think you're overthinking the process of how this works too much. This is almost identical to how you would multiply by hand, only this method saves the mental work of remembering the multiplication tables and makes it easier because you only have to count intersections.

For example, say you have the 22x22 example in step 2. When you're multiplying by hand, you would first take the 2 and multiply it by 22. Thus we have 44. This means we have 4 tens and 4 ones, analogous to 4 intersections on the very right column and 4 tens in the middle column.

Next you take the second 2 and multiply it by 22. The second two is in the tens place, so it's really doing 20 x 22 (When doing this by hand, this is basically the "shifting over" of the product of 2x22). Continuing our calculations, 20 x 22 = 440, so you would have 4 tens and 4 hundreds and 0 ones added by the second 2. analogous to the bottom 4 intersections in the middle column and the 4 intersections on the very left column.

Total the results, so that 4 hundreds, 8 tens (4 tens + 4 tens) and 4 ones (4 ones+ 0 ones). That gives us the answer of 484.

Hope this helps in understanding how this works.

8 years ago on Step 3

wtf ? where the 10 come from ? why its divided like that ? what about the 26 and 17 ?, and the 3 ? I mean the 2 x 2 was simple and I though I got it, by looking at the 22 x 22 I think I still got it, but now I'm lost. You need to explain more

Reply 8 years ago on Step 3

I agree that the explanation is inadequate for getting from the lines to the answer. I played around with it some and I believe I have figured out how it works. The square represents the intersections between the digits of the first number with the second number (e.g. in the above the first column is made up of the intersection of the 5 from the first number and the 2 from the second number). Think of each set of lines as a single unit. The square is broken up into columns from left to right. The first column will consist of the just the corner. In the example above, that is the intersection between the lines from 5 from the first number and the lines for 2 from the other. The next column will consist of the next set of intersections you come across going from left to right. Make sure to include no more then one intersection on the lines representing a given number per column. In other words, the intersection between lines from a given digit will only appear once per column. I have not done the proof, but I believe you will always have (1 - (number of digits in first number + number of digits in second number)) columns. In the example above, the first number has two digits and the second has three to there should be (1 - (2 + 3)) = 4 columns, which it indeed does have. Thus, to check yourself make sure you have the correct number of columns and make sure to include the intersection between a digit's lines only once per column. The next trick which does not have adequate explanation is to treat the sums of the intersections as two digit numbers with a leading zero if the number is less than 10. The first digit of the sum lines up with the last digit from the number above it. That makes the sums from above be: 10 26 17 03 _____ 12773

Reply 8 years ago on Introduction

Sorry for my bad explanations, im not really good at that. But i think that your explanation is really good an would like to include it on my instructable, i just need to ask you if you give me the permission?

Reply 8 years ago on Introduction

First and last sectros have 1 set of crossed lines, seconth and penultimate sectors have 2 sets of crossed lines,ett. etc. tell me if u still dont get it.

8 years ago on Step 3

wow, honestly this not back to school its flash back to how stupid my math teachers have been over the years. this is so simple and easy. im 21 and i've almost aways been bad in math and failed i studied so hard never went out just so i could pass school. this would have saved me so much time. another really good thing for math is juggling, if you guys like math try it, i'm a professional circus artist and juggling is my maine discipline and it really works your brain. my good friend is her degree on how juggling can make your brain think and grow due to the eye cordination that is the basis to thinking, exp wen you don't know the answer to a question you use looking around to different points to help your brain think. its really cool. thanks for the instructables ill go do some math equations

3 years ago

very nice

3 years ago on Introduction

Play games to learn Chinese is a very good way, but you need to play the game before, I suggest you learn simple Chinese, it is easy to learn simple Chinese,you can sign-up with any of the online courses like http://www.hanbridgemandarin.com/course/chinese-language-course , it provides one-to-one Chinese teaching service on the internet to students, the teachers are from China. But some are free, but some change a minimal amount. As long as you dedicate time to practice, an online course is as good as a classroom one. The community always helps.The best way to learn or test is to learn with an intention to solve a problem.

3 years ago

Suppose it is 76*98

Now first multiply 7*9then 6*9&8*7(cross multiplication) and finally 6*8 and add

This seems confusing at first but if u get to know it will same much time as adding is easier than multiplying

3 years ago

Suppose it is 76*98

Now first multiply 7*9then 6*9&8*7(cross multiplication) and finally 6*8 and add

This seems confusing at first but if u get to know it will same much time as adding is easier than multiplying

3 years ago

Ok nice one but can be simplifie

4 years ago on Introduction

'scuse me but this isn't making much sense - the pictures are unexplanitory, and the text at the bottom doesn't help

Reply 3 years ago on Introduction

I've figured it out - only works with most mathmatical multiplications - some don't work

4 years ago on Introduction

i can any one explain how do if we use more then 3digits ?

like if i need to multiply 1234*5674

4 years ago on Introduction

how many lines do you suposd know to put

4 years ago on Introduction

4 years ago on Introduction

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4 years ago on Step 3

I'll take the hit, and say that my brain has been hard-wired the Western way, but wouldn't take less time, just to line it up and multiply? Surely if you used flash cards as a child, this problem would take less time to figure out the Western way than it would just drawing out the lines.

4 years ago on Introduction

Watch this - it'll explain everything:

https://www.facebook.com/video.php?v=817396358300020