Some cool mental math tricks
I don’t want to go to sleep, and I am too tired to write, so I’m just going to post some random cool tricks I know for doing mental math.
Subtraction: do it one step at a time from the left. This is the opposite of how it’s usually taught in school, but it’s way easier to do mentally, because instead of doing the whole computation at once, you do it step by step, slowly reducing the amount of information you’re storing until you get the answer. Example: 3327 – 483. First do 3327 – 400 = 2927. Then do 2927 – 80 = 2847. Then do 2847 – 3 = 2844. As you go, all you have to do is remember the current “temporary answer” and what’s left of the thing you’re subtracting. On the other hand, if you did that the standard way, you have do do 7-3 = 4 and remember the 4. Then you have to do 2-8 = 4, and borrow a 1 from the next number. Then you have to do 2 – 4 = 8, and borrow a 1 from the next number. Then you just have a 3 that lost a 1 so it’s 2. Putting this together, you get 2844. Try it yourself with 1144 – 877!
Addition: There are lots of ways to speed up your addition. My strategy depends on what kind of thing I’m adding. The only one I’m going to describe here is grouping. The idea of this strategy is that instead of adding everything at once, you take “pieces” of some of the numbers that add up to something nice and easy to remember. So, for example, say I have to add up four paychecks, 327.44 + 89.07 + 161.53 + 491.28. Notice that 9 + 491 = 500, so you can group this as 500 + 327.44 + 80.07 + 161.53 + 0.28. Also, 320 + 80 + 100 = 500, so you can group again as 1000 + 7.44 + .07 + 61.53 + 0.28. Now, .07 + .28 + .44 = .79 (nothing special about this but it reduces the number of terms), so we have 1000 + 7.79 + 61.53, and this is pretty easy now: 1069.32.
Multiplication: This is definitely the coolest operation. There are lots of interesting multiplication tricks. Impress your friends with your ability to do quick calculations using these!
(1) Difference of squares. A really useful thing from algebra! This is the factorization x^2 – y^2 = (x + y)(x-y). So for example, 19 = 100 – 81 = 10^2 – 9^2 = (10-9)(10+9) = 1 * 19 = 19. Neat, huh? So, if you have to multiply two numbers, say 27 * 23, you might notice that these are actually 2 above and 2 below 25, so you can write that as (25 + 2)(25 – 2) = 25^2 – 2^2. Then you change your 2×2 multiplication problem into an easy subtraction: 625 – 4 = 621. Of course, this only works if you know the relevant perfect squares, so it’s easiest to use on examples like 82 * 78 or whatever.
(2) Rounding. This is an extension of the previous idea. Suppose that you have to multiply two numbers that are both close to “nice” numbers, such as 89 * 68. You can write that as (90 – 1)(70 – 2) and expand: 90 * 70 – 2 * 90 – 1 * 70 + 1 * 2 = 6300 – 180 – 70 + 2 = 6052. As before, this changes a hard multiplication problem into a less-hard subtraction problem. This trick generally works pretty well for numbers ending in 9, 8, 1, or 2. If you are rounding more than that, then the subtraction problem starts to get harder.
(3) Taking advantage of 5s. This uses the fact that numbers ending in 5 don’t gain more digits (besides the ending 0) if you multiply by 2. You can simplify any multiplication problem that’s a product of an even number and a number ending in 5 this way. For example, 26 * 75 = 13 * (2 * 75) = 13 * 150. But 13*15 is way easier than 26 * 75!
All right, now I’m really tired so I’m going to go to sleep. But one of these days I’ll explain some of my more sophisticated mental math tricks, like how to estimate complicated things quickly and accurately, or my general multiplication algorithm.
