Neat math tricks

My brother taught me two neat math tricks yesterday. To add a series of numbers in sequential order, such as 1+2+3+4+5+6+7 (we'll stick with cases that end in an odd number, to start), simply take the highest number, and split it into two integers as close together as possible. In other words, for 5, split it into 2 and 3, for 7, into 3 and 4, and so on and so forth. Then take the higher of the two numbers and multiply it by that same high odd number again, and you have the answer. In our example, 7 becomes 3 and 4, so we take 4 and multiply by 7 to get 28, which is the sum of 1+2+3+4+5+6+7. Works every time.

But what about even numbers? Ah, well, for those, split the highest number in half. 6, for instance, splits into three and three. Then vary them by half an integer, so you have 2.5 and 3.5, and multiply the higher number by the original high even number. 6 times 3.5 is 21 (3x6 = 18 + [1/2 x 6 = 3] = 21). But this gets unwieldy, so let's turn back to the first trick we learned. Remember how we split 7 into 3 and 4, and used the 4 to multiply? Well, if you use the 3 to multiply by 7, then you get 21--our desired answer. So all you have to do is pick the odd number just higher than the even one you want and use the *lower* of the two numbers to multiply by the odd number to get your answer.

Some of you figured this out ages ago, I'm sure. I just never thought about it before, and now that I know how, I just had to share. *g*