Mental Multiplication for 2 digit numbers.

[dgoodpasture2005]

Mental Multiplication for 2 digit numbers and beyond

1 7

| <---- this is step one... multiply the tens place times each other. =10X10

1 7 X



now we have 100. The next step will be 10X 7 either way you look at it.



17

/ <---- 10 times 7 is 70... we now have a sum of 170.

17

next step will be the same... except we will multiply with the1 in the tens place from the top of the problem diagonally and down to the right with the 7 in the ones place.



17

\ <---- 10 X 7 is 70, we now have 240, all that is left is the ones place

17





1 7

--| <----- 7X7 is 49... 240 plus 49 is 289... you have your answer.

1 7


We're doing it backwards... hope you all enjoy and understand why doing multiplication from left to right is much easier and faster than right to left. Even while adding up your sum there is no carrying over. Practice this... it's fast and effective... show it to teachers, friends, kids, anyone and everyone. Get this out, please. Mental math, bring it into our world once again. :) Do as you must with this... but please review it before you dismiss it! I didn't know where to post it... so I'll leave it here, enjoy everyone!

 

[arildno]

Sure, it is indeed effective, but hardly new. I have thought about if kids should learn at first a multiplication algorithm something akin to your approach, rather than the standard one.
say you are to multiply 23 with 45:
Then we can make a table like this:
... . 40.... 5
20... 800...100
.
.
3...120...15

It remains to sum together the 4 numbers in the centre of the table.

 

[dgoodpasture2005]

I see. Yours is exactly the same as mine, except a bit more in depth, and a few more steps. Mine takes the standard miltiplication steps and flips them backwards. All one would have to do is recognize the tens place as tens, and realize the ones only need to be multiplied one time. When going right to left, we multiply the one's too much. This is utterly unnecessary. They only need to be multiplied times each other. This is way cool, and I think we should all push in getting it out to the public in any way possible. Even if it has to be done privately. Why should we do math right to left, so much more complicated and time consuming... not to mention, it puts a hazard on the mental aspects. The ancients also did math somewhat backwards, I understand why now... we have been so blind recently.

 

[Werg22]

I think the substract and add method is more effective. Say

17x17


17x(20-3) = 17x20 - 17x3 = 340 - 51 = 289

 

[z-component]

I remember reading about Vedic Mathematics here on PF.
http://www.vedicmaths.org/Introduction/Tutorial/Tutorial.asp

Their methods include many-digit numbers with other operations.