How I keep track of my calculations

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#1 14 February, 2017 - 02:16
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Joined: 3 years 1 month ago

How I keep track of my calculations

I have a very ugly concentration in mental calculations, so to keep track of my calculations(not so hard calculations), I use a few simple tricks.
First of all, I have to explain how I do one digit times a number.
For example, 3 * 47
I visualize this as "47", all the while repeating it in my head, "four seven four seven four seven four seven"
Then I do a transition and change the first digit on the left by 3 times itself. So what I visualize now is
127 and I say "one two seven one two seven one two seven"
Then I morph the 7 by 1, changing the 2 before it
"141", "One four one". And now since I reached the end, this is my answer.

Another example:
3289 * 7
I start "3289" and pronounce it.
Then I got "21289" then "22489" then "22969" then "23023" which is my answer.

Now, for 2 digits by 2 digits multiplication, I apply the same concept.
Let's say I have to do
37*42
I first memorize 42 : "rain" in my major system.
then I visualize 37
I start by multiplying 3 by 4
12 37
Then I have to multiply 2*3
Not that the answer to that will come one digit to the right of "12"
So
126 37
Now I no longer need to visualize the 3, so I eliminate it:
126 7
Now I multiply 4 by 7, and i note that it has to go on top of 6
154 7
Next I do 2*7 and not that it has to go on the right of 4
1554
Now we're done.

Now at the moment the max I can do is 2 digits * 3 digits, but I am confident that I will be able to take this to 3 digits * 3 digits and so on.
This is the 'fast' solution I've found for my visualization problems. I've been training this for about 3 days and so far it's going well. I could not do multiplication 2 by 3 multiplications before. Now this is helping me.

What do you guys think? Is this a bad habit I am creating myself?
And do you have any visualization tricks you use?

28 February, 2017 - 06:56
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Joined: 5 years 4 months ago

I like the examples you give. They illustrate your thinking well.

Quote:

Is this a bad habit I am creating myself?

I don't think so. You have the partial answer and the numbers you still need to do both in one number in your head. As long as you remember which part is the partial answer, you are good.

However; let me give you some alternative ways of getting to the answers:
3 X 47 = 3 x (50 - 3) = 150 - 9 = 141
3289 X 7 = (3300 - 11) X 7 = 23100 - 77 = 23023
37 X 42 = 37 X 43 - 37 = 40^2 - 3^2 - 37 = 1600 - 9 -37 = 1600 - 46 = 1554

For me, this way of calculating presents less steps.

1 March, 2017 - 07:52
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Joined: 3 years 1 month ago

Hmm, so the idea would be to simplify calculations enough so that I can keep track of them?
How would you do 3253*7?
3200*7 + 53*7 ?
My problem is that I would lose track probably. Do you recommend I should use mnemonics in such a scenario?
Also, to do subtractions, do you use complementary numbers, as described by Arthur Benjamin in his book(if I remember correctly)?
I mean 23100-77 = 23100-100+33

10 March, 2017 - 07:27
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Joined: 5 years 4 months ago

Quote:

Hmm, so the idea would be to simplify calculations enough so that I can keep track of them?

Yes. If that is possible. In your next example it is not.

Quote:

How would you do 3253*7?
3200*7 + 53*7 ?

In this case it is not possible to make it simpler.
What your [b]can[/b] do is rehearse the numbers one by one.

So in your mind go like this:
7x3=21
7x2=14
7x5=35
7x3=21

Alternatively you can use the position in the number :
7x3,000 = 21,000
7x200=1,400
7x50=350
7x3=21

Try to go over the numbers a couple of times to let you mind get used to it.
Then add them together when you hear the intermediate results.

For me, this make the carry easier. Because in my mind when I hear '1 thousand 4 hundred' I add it to '21 thousand' and hear '22 thousand 4 hundred'.

Quote:

My problem is that I would lose track probably. Do you recommend I should use mnemonics in such a scenario?

You can. You can see Arthur Benjamin use this on Youtube.

Quote:

Also, to do subtractions, do you use complementary numbers, as described by Arthur Benjamin in his book(if I remember correctly)?
I mean 23100-77 = 23100-100+33

Yes. Small typo; the complement of 77 is 23 ;)

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