Think! There is always an easier way

Do you mean that you would start all over again when you lose track of the numbers? Oof, thankfully I don’t have to do that, I can just do it one go. I can look back at my steps until I reach 20-25 steps, after that I just have to go forward and don’t try to look back because that costs too much time. It does drain me a lot, I think because I see the numbers and am calculating.

I hope to know all of that one day. I really enjoy math but because of anxiety I have a hard time forcing myself to study it. Just like numbers, I can see the equations in my head and manipulate them.

Sometimes, other times I am in a better condition and don’t have to start all over again. By losing track I mean when I am unable to recall which number was in that position, I don’t have to recall the entirety while doing the calculations, but I kind of feel it when its lost and often automatically do checks after every digit I have correctly calculated.

When you start over again it becomes a lot simpler than it was the first time since some of the memory remains. I also see the numbers when I am calculating but I usually have the answer digits darken out as I calculate the other answer digits. I don’t really find it functioning with sound, but at the time I did use sound to remind myself of the numbers as I went along. It’s simply faster to see the numbers to calculate the numbers, I find, rather than saying the calculation.

I’m sure you will, you can take things at the pace you find best , perhaps have a look at a few books until one really clicks with you. I also see the equations in my head when I manipulate them. I think the only time I don’t see things visually in my head with mathematics is when I am using proofs or definitions or part of my own verbal reasoning.

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Not entirely right.
Difficult to explain though. On 25 X 36 the result forces itself. So I see 900 quicker than trying to actually do the calculation. Also the memorisation occurs when doing the calculation first. But it is not the answer that is memorised. It is the path to the answer.
What I suspect happens is, that my brain the path to the last time I did this calculation finds and then just redoes the same calculation.
What I did was 25 x 36 = 100 x 9.

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Here is how I would do 253 X 368:
In this case , since 25x36 is easy to do I split the numbers in 2:

25 | 3
36 | 8 X

The “|” is just there to show where I split the number.
Then I do the criss cross using 250, 3, 360 and 8 as the numbers.

So to drive the point home, I treat it as a 2x2, when it is actually a 3x3.

Also I do this from left to right.

So first step is 25 X 36 = 900. Actually, in my mind I call out 250 X 360 = 90,000.
Doing it this way also gives me the ballpark number.

Then comes the cross.
8 X 250 + 3 X 360

8 X 250 = 2,000 and
3 X 36 = 1,080
Total: 3,080

Add this to 90,000 gives 93,080.

Last step:
3 X 8 = 24

Add to 93,080 gives 92,104.

Then I check it with 9 or 11 proof.

On doing the above calculation, I realise I brute force the 11 proof.
1: I think “93,104 - 88,000” and immediately 5,104 comes up. No calculation. Maybe my mind does a quick 93-88, but the process is so quick that I don’t know for sure.
2: 5,104 - 4,400 = 704. Again; no calculation.
3: 704 - 660 = 44
4: 44 - 44= 0

This happens when I visualise the numbers. Only when I see both numbers, the result comes up.

Same with the numbers in the multiplication:
253 - 220 = 33
33 - 33 = 0

(actually I would stop here, since I now know that we will be multiplying with zero, so the end result needs to be zero. But for now let’s finish the 11 proof:)

368 - 330 = 36
36 - 33 = 3

3 x 0 = 0

Later today I realised this process does not always happen.
On a simple 45 - 18, nothing came up immediately.
When I raised the 18 to 20, then immediately 25 came up.
And then cascading, 27 came up as the answer.

For people who wonder why I am writing this; I am trying to find out when my brain immediately gives an answer and when not. See this thread and others.

Also because this got me thinking:

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Your brain immediately calculated the subtraction, this was not memorization. This is calculation because you probably haven’t memorized that 93,104 - 88,000 is 5104, that would be ridiculous and random. Brute forcing would be to try to do this every time with any calculation by concentrating and trying to mimic the instantaneous calculations, like the one mention above, that your brain does sometimes.

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.
Thanks for giving a lot of your time to give such a detailed description.

As I said before, all that stuff is really amazing.

I was googling for some terms that you mentioned, such as “criss-cross”, “9 proof”, and “11 proof”. I found one of your old posts here:

So, there’s even more info in that old post for anyone that’s interested.

Thanks.

Thank you for the kind words.

If you look at my posts I really always try to find shortcuts in calculations. See my other post about calculating 37^3 for an example.

However; criss cross multiplication is a general way of multiplication that just always works (that is the same as general, right :wink: ).

The 11 and 9 proofs are just for checking the answer.

Btw, I do the 11 proof different than other people.
I like to work from left to right, but there is a quicker way of doing the 11 proof that goes from right to left.

I just don’t like that way for several reasons, so I stick to my own way, which for me is just more mental calculation.

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You can easily do this by
Let me show it
52 * 45 (45 is factor of 9 and 5)
52 * 5 (multiplied by 5 , and you Know how to do
that )
260 * 9 = 2340

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Anything times 45 is simply half the original number (with two zeros). And then that number minus itself shifted one to the right.