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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## Step 1: Example

## Step 2: First lesson: 22x22

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)

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!

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.

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.

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.

If anyone wants a more detailed explanation just let me know as I know this one was quick and dirty.

241in Step 3, not 53 x124; this only equals 6,572.Your comment has the same tone as someone saying: "Really (sic), tommiesmee? Do you think that no capitals, misspellings, and lower-case first-person-pronouns equals proper English?" Compare it with something like this:

GreatInstructable, but yourpunctuation mark should be a dot.Right nowIwas like,"Really?Do you think 53X124 equals 12,773?".I'mgoing tovote for you anyway ...ifIfind out how :).Or better still:

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 :).Instructable's Authoring Tips recommends: "Check all copy for proper language, spelling, grammar, and capitalization where needed." (Which, if I may be constructive, emihackr, you need to do with your Instructable...)

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.

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.

If they had this skill, or something similar, we could all move on with our lives and actually start to learn something.

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.

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.

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.

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.

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.

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.

(step 2 pic 3)