I was just helping the Firebug with his arithmetic homework, and it occurred to me that I could easily do a 45-minute presentation on arithmetic shortcuts, with a side of estimating techniques to know if your answer is in the right ballpark.
He had to do 792 x 965.
Estimation: that’s like 800 x 1000, only a little smaller. So you should expect an answer that’s less than 800,000, but not a lot less. If you get an answer that’s above 800K, you know it’s wrong. If you get an answer that’s nowhere close to 800K, you know it’s wrong.
Always estimate, because a lot of the time when you’re figuring the exact answer, you’ll get an answer that, if you think about it, can’t be right. You’ll look a lot less stupid if you can see that, even if you don’t know what the right answer really is.
Getting the exact answer: always try to turn your problem into an equivalent but simpler problem. It can’t always be done, but it’s amazing how often it can be done.
Shortcut 1: 965 is just 35 less than 1000. So your problem is now 792,000 - 792 x 35.
Shortcut 2: multiplying by 70 is easier than multiplying by 35. Double that side, cut the other in half. 792 x 35 = 396 x 70.
Shortcut 3, like shortcut 1: That’s 400x70 - 4x70 = 28,000 - 280 = 27,720.
So your answer is 792,000 - 27,720 = 764,280.
Now this is just arithmetic, which if you’re not in elementary school and being tested on it, you can do with a calculator. But these underlying lessons apply broadly to life. There are lots of opportunities to know what ballpark your answer has to be in, so use them. And there are lots of opportunities in life to turn a hard challenge into a similar but much easier one.
Yeah, I can do 45 minutes on that.
