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)
<br> 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.<br> <br> 1. <em><strong>Each line</strong></em> stands for the <em><strong>numbers</strong></em> in the problem.<br> 2. Starting from the<strong> left</strong> the first number is <em><strong>5</strong></em>. Now <em><strong>draw FIVE LINES</strong></em> from <em><strong>2 o'clock to 8 o'clock</strong></em><br> 3. The next number is<em><strong> 3</strong></em> - so <em><strong>draw THREE LINES</strong></em> after leaving a <em><strong>space</strong></em> in the same direction<br> 4. the next part of the equation is<em><strong> 2 4 1.</strong></em> <em><strong>Draw TWO lines</strong></em> + <strong>gap</strong> + <em><strong>FOUR lines</strong></em> + <strong>gap</strong> + <em><strong>ONE line</strong></em> standing for each number at right angles in the other direction. <em><strong>(11 o'clock to 5 o'clock)</strong></em><br> <br> (Making sure to begin from the <em><strong>left bottom corner</strong></em> - seems to be a<em><strong> left to right method</strong></em>)<br> <br> 5. The totals<em><strong> 10, 26, 17, 3 </strong></em>are figured out by <em><strong>placing a DOT</strong></em> at each<em><strong> intersecting line</strong></em> of the<em><strong> grid </strong></em>you've just drawn.<br> <br> Group each group of dots by the corners of the grid. ie north east west south (<em><strong>NB </strong></em>Emihack has <em><strong>drawn an orange line</strong></em> grouping each intersection.)<br> <br> Now <em><strong>add up those dots</strong></em> for each corner group. (That's where <em><strong>10, 26, 17 and 3</strong></em> comes from)<br> <br> Next add up <em><strong>10, 26, 17 and 3</strong></em> keeping them in their columns of<em><strong> 1000's, 100's, 10's and 1's</strong></em> - just like abacus.<br> <br> I 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!<br>
@paperrhino<br><br>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. <br><br>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. <br><br>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 &quot;shifting over&quot; 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.<br><br>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.<br><br>Hope this helps in understanding how this works.
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
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
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?
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.
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
<p>very nice</p>
<p>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 <a href="http://www.hanbridgemandarin.com/course/chinese-language-course" rel="nofollow">http://www.hanbridgemandarin.com/course/chinese-language-course</a> , 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.</p>
Suppose it is 76*98<br>Now first multiply 7*9then 6*9&amp;8*7(cross multiplication) and finally 6*8 and add<br>This seems confusing at first but if u get to know it will same much time as adding is easier than multiplying
Suppose it is 76*98<br>Now first multiply 7*9then 6*9&amp;8*7(cross multiplication) and finally 6*8 and add<br>This seems confusing at first but if u get to know it will same much time as adding is easier than multiplying
Ok nice one but can be simplifie
<p>'scuse me but this isn't making much sense - the pictures are unexplanitory, and the text at the bottom doesn't help</p>
<p>I've figured it out - only works with most mathmatical multiplications - some don't work </p>
<p>i can any one explain how do if we use more then 3digits ?</p><p>like if i need to multiply 1234*5674</p>
<p>how many lines do you suposd know to put</p>
<p>if you want to learn Chanies then join us its free course. we provide you our best quality.our teachers are highly Qualified they teach you in this way you can learn fast.</p><p>http://preply.com/en/chinese-by-skype</p>
<p>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. </p>
<p>Watch this - it'll explain everything:</p><p>https://www.facebook.com/video.php?v=817396358300020</p>
<p>Wow, this is an amazing method. It is a lot more fun than basic long multiplication.</p><p>Here are some additional problems for people to practice with: <a href="http://stemsheets.com/math/multiplication-worksheet-horizontal" rel="nofollow">Practice Worksheet</a></p>
Hey im trying to figure this out as i am pretty bad at multiplicating so whe you got the ten did you times it by the two separate lines in that same sector ....explain to me like you would a little kid :)
<p>This video might be better..... Better explanations, in my opinion, and showing step by step. It might help to actually see it done. </p><p>http://sfglobe.com/?id=14460&amp;src=share_fb_new_14460</p>
<p>the Method of solving is good for two digits</p><p>but how about for three?</p>
<p>Yes. Try a different explanation instead though..... I found a video, then I found this through it (recommended automatically). I would never understand the explanation on this page, had I not watched the other person explain first. And yes, it does go into three digits too. </p><p>http://sfglobe.com/?id=14460&amp;src=share_fb_new_14460</p>
<p>Hi,</p><p>Thanks for sharing this awesome trick. But i can't get answer for 23x32 by using this method. www.classiblogger.com</p>
<p>holy crap, that's fast multiplication! you can even do it in your head!</p>
Hi Everyone, <br> Personally I don't think this method is any easier as it leaves you counting every intersection. For instance the product 99x99 has nine intersections for each of the 4 place values. The standard algorithm on the other hand reduces this product into 4 partial sums, all of which are easily calculated by single digit multiplication. Of course everyone is entitled to their own opinion. <br> Now, the reason this works is for the same reason the standard algorithm works which is the place value process. The diagonals, from lower left to upper right, each represent a specific place value so 1's, 10's, 100's, etc. So this is why we can simply count them and record the sums appropriately. <br> If anyone wants a more detailed explanation just let me know as I know this one was quick and dirty.
Errr.. I think tommiesmee is trying to tell you that 53x124 = 6,572
tommiesmee transcribed the numbers incorrectly: he should have written 241 rather than 124.
great instructable, but you punctuation mark should be a dot. right now i was like 'realy? do you think 53X124 equals 12,773?'. i'm gonna vote for you anyways... if i find out how :)
Er, no. emihackr's punctuation should be a comma as it is a &quot;thousands separator&quot;: unless you're proposing that 53 x 124 = 12.773 (i.e. just over a dozen). In any case emihackr wrote 53 x <strong>241</strong> in Step 3, not 53 x <strong>124</strong>; this only equals 6,572.<br> <br> Your comment has the same tone as someone saying: &quot;Really (sic), tommiesmee? Do you think that no capitals, misspellings, and lower-case first-person-pronouns equals proper English?&quot; Compare it with something like this:<br> <em><strong>G</strong>reat <strong>I</strong>nstructable, but you<strong>r</strong> punctuation mark should be a dot. <strong>R</strong>ight now <strong>I</strong> was like, <strong>&quot;R</strong>eally? <strong>D</strong>o you think 53<strong> X </strong>124 equals 12,773?<strong>&quot;</strong>. <strong>I</strong>'m <strong>going to</strong> vote for you anywa<strong>y ...</strong> if <strong>I</strong> find out how :)<strong>. </strong></em><br> Or better still:<br> <em>Great Instructable, but your punctuation mark should be a dot. 53 X 241 equals 12.773 rather than 12,773. I'm going to vote for you anyway ... if I find out how :).</em><br> <br> Instructable's Authoring Tips recommends: &quot;Check all copy for proper language, spelling, grammar, and capitalization where needed.&quot; (Which, if I may be constructive, emihackr, you need to do with your Instructable...)
sorry and thanks
you're welcome, ow and one question: how about 5,4 X 3?? =D i'm just kidding, but could anyone explain me how i'm supposed to vote? instructables has some weird contest customs i believe.
there will be a period of time when you can vote
wow, It&Acirc;&acute;s a funny way to make kids like maths!! <br>
This is actually an abacus implemented on paper. We don't teach this for the same reason we don't teach people how to use an abacus. It's more important for people to learn the math than how to operate a device.
I disagree. We don't teach the abacus because Americans dislike learning from other cultures. &quot;It would be beneath us to use something from China to teach our children.&quot;<br><br>And, if we taught the abacus early on, you would eventually not need the device, and children would learn how to do mental math fairly easy.<br><br>I teach Algebra 1 and Geometry in High School, and I can't get my kids to understand abstract math, because they get hung up on simple multiplication.<br>If they had this skill, or something similar, we could all move on with our lives and actually start to learn something.
Your are kidding, right? Ever since the start of the Age of Exploration, Western culture in general and America in particular has been way, way, way more ready to study, learn from and borrow from other cultures.<br> <br> By contrast, even though Western learning and technology were freely available to anyone over the centuries, almost all the other major cultures arrogantly rejected Western science, technology and cultural elements. Many continue to do so.<br> <br> The Chinese, in particular, were violently xenophobic and utterly contemptuous of anything non-Chinese. The Manchu dynasty went to bizarre lengths to suppress Western learning and the adoption of Western technology. The Japanese initially adopted a similar attitude but once they were humiliated by a British/French flotilla, they became obsessed with learning and copying everything possible. As a result, Japan is today a wealthy nation.<br> <br> The reason that your students can't perform basic multiplication is because ever since the 70s, the education establishment has devalued rote learning of fundamentals. They got this idea that calculator could replace just having the value of 7x6 stuck in memory.<br> <br> Education today is centered around avoiding accountability by deemphasizing any skill that can be easily measured. It's easy to measure whether students know their times tables so its easy to hold educators accountable if the children don't know them. To avoid that, educators develop convoluted theories to explain why children don't need to know their times tables.<br> <br> In any case, Westerns used to uses abaci in the form of counting tables and similar devices (as well as techniques such as casting out nines.) The use of such tools in schools was traditional frowned on because it became clear that students learned just how to carry out the algorithm and not how all the math fit together. Richard Feynman talked about running into an abaci salesman in Brazil and realizing that the guy had absolutely no mathematical intuition at all.&nbsp;<br> <br> We have the same problem today with calculators where students can't tell that an answer that is a couple of orders of magnitude off is incorrect.&nbsp;<br> <br> <br>
dude just make a video explaining clearly what all that mess is about.
When I saw the picture &quot;multiply like the chinese&quot; I thought you ment like having babies. lol
hahahahaha Lol. no, it's ancient chinese multiplication method.
I dont get it. The explanaition is not clear enough.
Does it matter how many sectors you use?
what do you mean?? please be more specific and i'll be glad to answer your question.
I actually think I understand it now, after looking at it for awhile. It's a little confusing, but I believe I figured it out.
toonth (2nth)<br>(step 2 pic 3)
Nice instructable, I have never heard of this way of multiplication.

About This Instructable




Bio: Interested in all kind of projects, mainly electronics but other stuff too! I try t publish everything I make, eventhough this is not always possible ... More »
More by Emiliano Valencia:CNC Wall Mounted Desk DIY Modular Guitar Amp! TinyDice: Professional PCBs at home 
Add instructable to: