Instructables
... using mental arithmetic tricks. I'm not going to teach you how to do long addition on paper, although I will assume you are comfortable with doing it. This Instructable is for those times when you don't have paper or a calculator handy.
 
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Step 1: Borrow ones

"From where?", I hear you cry. Essentially from nowhere- sometimes you can make an addition (or sometimes a subtraction or multiplication) easier by borrowing a one, doing the sum and putting the one back. Example:

13+29 is a bit of a pain to do in your head. If you like the previous technique you could call it thirty-twelve, but to do that precise addition is a little awkward. 13+30 is much easier, however. Borrowing ones essentially means you say "13+29 is hard- I'm going to borrow a one and add it to the 29, 13+30 is 43, then I put back the one I borrowed so the answer is 42". It sounds complicated, but with a little practise I now do all of those steps in my head much faster than just trying to add 13+29.

Borrowing ones can also work in reverse by "burying" a one you would rather ignore for the time being- for example, 13+31 can be turned into 13 + 30 = 43 and then you add the one you ignored earlier, but additions that become easier by "burying" a one are less common that those made easier by borrowing.

Pros: simple, conceptually easy
Cons: limited application, doesn't allow very large additions.
Dr Qui3 years ago
I have one of those old adding machines. :-)

In step 6, you put a 1 where a 2 should go, specifically in the 63+18 section.
PKM (author)  mettaurlover4 years ago
I suspect you're looking at the tens column of 63+18.  Remember that gets the one carried from 3+8, so it's actually 6+1+1=8.

You can do this one my other method which involves treating numbers above ten as single digits: "three plus eight is eleven", so "sixtythree plus eighteen is seventy-eleven"- in other words

63 + 18 = 70 + 11 = 81.
Actually, it was here: "63+18 might be a pain to work out in your head explicitly but a knowledge of the 9 times table will tell you that it is 7*9 + 1*9 = 9*9 = 81. For small numbers this method may not be much quicker than simple addition but certain problems may be greatly simplified." When that part should be "7*9+2*9". That's where your mistake was.

AstralninjA5 years ago
I think you typed one too many zeros in your last diagram. 50.5 = 5050
Other than that, great instructable!
PKM (author)  AstralninjA5 years ago
Well done for catching that- I was going number-blind after writing all of that :)