I have amazing magical powers. Well, not really, but that’s what many of my students seem to think when we start working together. Why do they think I have these amazing magical powers? It’s simply due to the fact that I can do relatively large math operations in my head. I promise you, it’s not magic and I can teach you the basics of my technique today and also why these techniques are useful.
What is 324*96? Don’t panic. We can figure this out. If you’re asking yourself why we should bother, that may be because your test allows you to use a calculator. If that your situation, obviously mental math is going to be less useful to you, but that doesn’t mean you should tune out. By taking the first steps in this process you’ll be able to understand the approximate value that you seek and more easily discover any data entry errors you have with the calculator.
So, back to our problem. When we look at 324*96 we see a difficult-looking problem, but to start let me ask a different question: about how much is 324*96? The answer there is a little less than 32,400 which is 324*100. That’s easy. We’re multiplying by 100, which just means adding a couple zeroes to the end of the number. But we’re looking for something a little bit better than about, so let’s move to the next stage. To get to an exact answer we can re-state our problem like this:
So, after starting with our estimation, if we can figure out the value of 324*4 we’ll be left with a straightforward subtraction problem. To do that, we’ll break down the problem again. Let’s start with 24*4. I know that 25*4 is 100, so 24*4 must be 4 less or 96. That just leaves 300*4, which is 1,200. Very quickly that gets us to 1,296.
Now we’re down to a subtraction problem: 32,400 – 1,296. Again, let’s simplify these numbers. Instead of subtracting 1,296, let’s subtract 1,300 and then add 4. 32,400 – 1,300 = 31,100. Add our 4 back in and we get our answer 31,104.
I know there are a lot of steps there, and that’s by no means an easy example, but hopefully you can see how these methods are useful. First, they give us an idea of about how big the answer is going to be. Second, they break down one big complicated problem into several smaller more manageable problems. Practice these techniques and you’ll be way on your way to your own mental math magic.