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## #1 2011-02-20 03:10:23

John E. Franklin
Star Member

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### Multiply 11 up to 19 (shortcut)

I was astounded an hour ago when
I came across this video that teaches
an easier way in most cases to
multiply any two numbers together
from 11 to 19, such as 12 times 16.

Here is an example of 12 times 16, which we know is 192,
due to its popularity in base-2 as 128 + 64.

Okay here's how it goes:

Forget one of the one's, and just add 12 + 6 for 18,
and then tack on a zero for 180.
Next do the one's digits multiplied and add that on to
the 180.  So 2 times 6 is 12, and 12 + 180 = 192.
Yes, it is correct.

If you break the 4 chiffre (digits in French) into parts
and multiply them the 4 ways you usually do, I think
you get a glimpse as to why this works.

The 1 times the 1 is 100, due to the ten's places.
This will always be true.   Then the two cross-multiplications,
the 1 times the 2 and the 1 times the 6, on diagonals, add
up to 20 + 60 or 80, so 100 + 80 is 180.
ones in the ten's place and so you get the 180.
Then the only 4th multiple to do is the two one's places and
add that on.  It is so wonderful, I am really excited I
found this video this morning!!

Here is another example:
Let's do 16 times 19.
16 + 9 = 25 so think 250 with the zero on the end.
Then add to this 6 times 9 or 54 + 250 = 304.
And my calculator says that is correct as I didn't
have that one down pat yet.

Good Day!!  Bonne Journee!!

igloo myrtilles fourmis

## #2 2011-09-20 08:07:04

Sylvia104
Member

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### Re: Multiply 11 up to 19 (shortcut)

When I do mental calculations, I normally look for shortcuts, and different calculations often require different shortcuts. For 16 × 19:

And for 12 × 16:

## #3 2011-09-21 22:32:38

bobbym

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### Re: Multiply 11 up to 19 (shortcut)

Hi Sylvia104;

#### John Bernoulli wrote:

I recognize the lion by his paw.

Nice signature but I already knew.

Hey, that signature is gone! Perhaps I imagined it.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #4 2012-02-11 19:02:01

anonimnystefy
Real Member

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### Re: Multiply 11 up to 19 (shortcut)

hi xhintim

welcome to the forum.

#### xhintim wrote:

you don't need to understand things, You just get used to it. I'll put that in my dictionary.

that's exactly how bobbym's signature goes!

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment