Use anzan and other high-tech math methods

Hi John Moser,

Thanks for your suggestion!

The content specialists are busy adding new content all of the time. Currently, they're focused on adding more K12 subjects (which may include your suggestion, so I'm sure they'll consider it.)

this site helps me learn more about math

Sure, but how well can you do it?  Single-digit addition? How about keeping up with third graders?  There's a video out there of kids playing word games while paying little attention to the computations being given them, and then reciting the computation.

High school doesn't prepare you to keep up with a Japanese seven-year-old's mathematical prowess.

How fast can you perform the following computation:  2 / .04

The real question:  How did you approach it?

The answer is fifty, I got it by converting zero point zero four to the fraction one over twenty-five and then multiplying the original numerator two by the resulting reciprocal of twenty-five.

It took a whole lot less time to do it than to explain it. I spelled out the number so that a quick read of my answer would possibly not yield spoilers.

Think about these numbers:  2.00 and 0.04

The problem is merely 2 / 4.

4 isn't a factor of 2; the next digit is 0, thus 20 / 4.  We know that's 5 (multiplication table).

The 2 was two columns left; the 20 was one column left, so you get 0.5.

The answer is 50:  decimal points are meaningless and shift in the same direction in division, so just move it two columns right (200 / 4).

My point here is that you're looking at the operation as a sort of complex thing which requires an approach strategy because there's a decimal point.  People do this all the way down to addition, and will convert (6 + 7 + 4) to (5 + 5 + 7) to (10 + 7) to (17)—having carried out three additions, one subtraction, and a strategic analysis instead of only one subtraction and one addition (7-3 and 3+4).

There's no "ones place" or "tens place".  You could say that the 5 was one column left of the 4 and the decimal point was two columns left, so the 5 shifts to three columns left to give 50; that's valid, and it's required when carrying out multiplication.  Applying this prior to division happens to apply it to every operation ahead of time.

Teaching this early (instead of the Friendly Numbers thing) by digit-wise columnar addition and subtraction (Soroban and Anzan use this strategy) avoids developing the perception that math is complex and hard.

That said, division with multiple-digit numbers is…not simple.  I have never encountered any mathematical approach to division which was simple and linear.  Wikipedia doesn't suggest one exists.  Multiplication, on the other hand, can be done digit by digit—which is why we memorize single-digit multiplication tables.

There are two addition sets.  One is {(1,4),(2,3)} and the other is {(1,9),(2,8),(3,7),(4,6),(5,5)}.  Addition is rather simple, and you eventually just see (7 + 8) and immediately run 7-2 to get 15 (check the second set:  (2,8)).  That's why people get so fast at addition and subtraction in particular:  they run through single-digit isometric operations.

With addition, you can see there are no "friendly numbers" or other algorithms to reduce to easily-recognized sets such as additions of 5s and 10s; instead, you make every simple addition operation fast and easy.  Multiplication and division come down to being able to keep a lot of numbers in your head at once or using a physical register (beads, paper, a soroban, etc.).  Computing square roots is relatively-simple.

It's easy to demonstrate a single, simple algorithm for addition and subtraction, and thus convince people that there's only one correct way to add numbers (it's "correct" because attempting to use other methods only adds complexity, introduces human error, slows you down, and creates frustration).  Multiplication and division are harder to argue—and, indeed, multiple algorithms exist for human use both on paper and mentally.

Paper division has strategies like lattice division, which is just long division; or the partial quotient method, which is the only sane mental division method.

I'm trying to work out if there's an absolute lowest-effort, highest-comprehension set of basic math (and algebra) approaches; the only ones that stand out at the moment are Anzan addition and subtraction, which are far-advanced compared to how we teach introductory arithmetic in the US now.