Do you have rapid 3 column addition mental math secrets to share?

[Pen]

Ds wants ways to do addition of 3 column numbers, eg. 369 + 983, mentally, and very fast (for Sumdog).  Do you have any favorites for this sort of problem?  Are any books like Shortcut Math good on this sort of thing?

[DragonFaerie]

I don't really have any secrets.  I am fairly good at mental math, though.  The way I would add a number like the one you mentioned would be to break it down.  Add the ones to get 12.  Then add the tens to get 140.  Together, that's 152.  The hundreds are 1200.  1200 + 152 is 1352.

[Murmer]

So there are a couple of different ways based on the numbers in the problem.

For your example 369 + 983 369 rounded up 1 is 370.  980 +20 = 1000 which leave 350 then since you rounded up 1 you have to take that away from 3 which leaves 2 and the answer is 352.

It sounds complicated but is really fast in my head, just explaining it is hard.

 

Another option is the one above starting with the hundreds and adding "backwards" from the traditional algorithm.

 

Another option is for not so easy to round numbers is to find easy 10's.  IE 325+ 827  the 7 in 427 + 3 (from the 5) = 10 which leaves 2.  800+200 (from the 300) = 1000 which leave 100  and 20+20+10 (from the ones combo) is 50 so the solution is 1152.

[TracyP]

I would either do 369 + 1000 = 1369 - 17 (the estimation error on the second number) = 1352

 

or

 

add from left to right 300 + 900 = 1200 + 60 + 80 = 1340 + 9 + 3 = 1352

[ThisIsTheDay]

I think the secret is to be able to change up the order in which you mentally add numbers, based on the specific numbers given. I would do it in a different order, or different grouping, based on the numbers in front of me.  I used to challenge myself (privately, of course) to multiply large numbers in a monthly board meeting faster than the director would multiply them on her calculator.

 

[Tree Frog]

Look for books by Benjamin Arthur. The Great Courses has a dvd by him titled "The Secrets of Mental Math" that will explain several different math concepts in an interesting way.