3 Tips for Subtracting Quickly
When can addition speed up subtraction? What’s the most important trick for doing some lightning quick mental minus-ing? And what’s the fastest way to check your work? Keep on reading to find out!
Jason Marshall, PhD
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3 Tips for Subtracting Quickly
While addition may be the undisputed belle of the arithmetic ball, subtraction is a close runner-up. After all, as inverses of one another, these two operations are intimately related: add and then subtract any number from any other number, and the net result is no change whatsoever.
As you might suspect given this special relationship, many of the best tricks for performing lightning-fast mental subtraction are closely related to the mental addition tricks we recently talked about. What are these tricks? And how can you use them to become a mental subtraction maestro? Those are exactly the questions we’ll be answering today..
Tip 1: Add, Then Subtract
Do you ever add when you’re supposed to subtract? I know, it sounds like a crazy thing to do, but believe it or not, I do it all the time. Because one of the best ways to speed up mental subtraction is to add…then subtract. Here’s how it works:
Let’s say you’re trying to subtract 94 from 212. Instead of writing the number 94 below the number 212, starting the slow and painful process of borrowing and whatnot, here’s what I do: I take into account that 94 is only 6 away from 100 – which is great, because it’s really easy to subtract 100. In other words, I realize that the problem 212 – 94 is the same as the problem 212 – 100 + 6.
Once it’s written this way, you can pretty much see that the answer must be 118 (since 212 – 100 = 112, and 112 + 6 = 118) without doing any work at all. The key to it all is to remember to look for help from your old friend addition before starting any subtraction.
And lest you think this technique only helps when subtracting a number that’s close to 100 (or any other number that ends in zero), let’s take a minute to think about subtracting a number like 77 from 212. In this case, I’d argue that it’s still helpful to toss a bit of addition into the mix.
Why? Well, since 77 = 100 – 23, we can turn the problem 212 – 77 into the problem 212 – 100 + 23. Of course, this is just 112 + 23, or 135—pretty easy!
Tip 2: Split Tough Problems Up
The basic idea we’ve used in this first tip—to split a number up into two (or more) easier-to-work-with numbers—is useful in a more general sense. Which leads us to our second, and possibly most powerful, tip: break numbers up into smaller numbers to make solving problems easier.
Break numbers up into smaller numbers to make solving problems easier.
For example, to solve the problem 1,276 – 857, start by thinking of it as two separate problems:
- 200 – 800 = 400
- 76 – 57 = 19
To find the answer to the original problem, all you have to do is add the answers to these two sub-problems. So, 400 + 19 = 419.
What exactly have we done here? We’ve simply noted that 1,276 = 1,200 + 76, and that 857 = 800 + 57. And then we’ve used this to rewrite (hopefully all in our head) 1,276 – 857 = 1,200 + 76 – 800 – 57. Rearranging the terms a bit, we arrive right back at our method of combining the two sub-problems: (1,200 – 800) + (76 – 57).
In the end, it all adds up (or rather, subtracts down) to the same thing. But how you look at the problem—and in particular, how you break it up into easier parts to work with—can make a tough mental problem much, much easier to solve.
Tip 3: Swiftly Check Your Work
Our final tip to help you master mental subtraction isn’t about making you faster, but instead about making you more accurate (an equally important aspect of your new skill!) This tip is going to sound completely obvious once I say it, but nonetheless, it’s extremely useful because it’s easy, and it works.
Here goes: after you finish a subtraction problem, you should always add the result back to the number you were subtracting to make sure you get the original number back. See, it’s obvious, right? And although it sounds like a lot of extra work, it’s usually pretty quick to do, since addition is fairly fast.
For example, we just found that the answer to 1,276 – 857 must be 419. But is that true? We can check simply by adding 419 to 857 to make sure we get back the original number, 1,276.
To do so, we can mentally break the numbers up into easier-to-add pieces to find that 419 + 857 = 400 + 800 + 19 + 57. You’d then note that 19 = 20 – 1 and 57 = 60 – 3, to very quickly find that 400 + 800 + 19 + 57 = 1,200 + 20 – 1 + 60 – 3 = 1,276. So, it turns out we were right!
While it might be hard to believe, after a bit of practice all of these mental arithmetic tricks will start to become second nature to you, and you’ll begin using them without even realizing it. But don’t just take my word for it—give it a go, try putting them into practice yourself, and soon you’ll see that it’s true.
Wrap Up
Okay, that’s all the math we have time for today.
For more fun with math, please check out my book, The Math Dude’s Quick and Dirty Guide to Algebra. And remember to become a fan of The Math Dude on Facebook, where you’ll find lots of great math posted throughout the week. If you’re on Twitter, please follow me there, too.
Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!
Subtraction watch image courtesy of Shutterstock.
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About the Author
Jason Marshall is the author of The Math Dude’s Quick and Dirty Guide to Algebra. He provides clear explanations of math terms and principles, and his simple tricks for solving basic algebra problems will have even the most math-phobic person looking forward to working out whatever math problem comes their way.