TITLE: Mental Math Techniques
QUESTION [8 upvotes]: What are some interesting mental math techniques that you know?
Here's one that I got from my Grandmother who got it from a book: To square a two-digit number (from $26$ to $49$), take the number minus $25$ and put that in the first two digits, and then add the square of $50$ minus the number: $$(\text{number}-25)\times100+(50-\text{number})^2$$ For example, to do $47^2$ we have $47-25=22$ for the first two digits and $(50-47)^2=9$ for the last two so we get $47^2=2209$. 
Bonus points if you include justification! For this trick, $$100(n-25)+(50-n)^2=100n-2500+2500-100n+n^2=n^2$$

REPLY [2 votes]: Of course, we have the classic trick $$9\times n=(10\times n)-n$$ which works because of distributivity. This can be generalized as follows: $$99n=100n-n$$ so for example $$99\cdot 54=5400-54=5346$$ It also helps simplify generic calculations. E.g., $$17\cdot 8=17\cdot 10-17\cdot 2=170-34=136$$