Math Is Fun Forum

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

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.
So this method shortens all that by assuming you start with
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!!

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igloo myrtilles fourmis

Sylvia104

Banned

Registered: 2011-09-19

Posts: 29

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:

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Multiply 11 up to 19 (shortcut)

Hi Sylvia104;

I recognize the lion by his paw.

Nice signature but I already knew.

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

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Multiply 11 up to 19 (shortcut)

hi xhintim

welcome to the forum.

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!

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.