How to Subtract Quickly
Quick, what’s 212 – 22? If that’s too easy for you, how about something tougher like 212 – 77? Want to learn an easy way to perform lightning fast subtraction in your head? Keep on reading to find out!
Jason Marshall, PhD
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How to Subtract Quickly
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Do you remember how you learned to subtract two numbers? You know, start by lining them up one on top of the other, then subtract the numbers in the ones column (borrowing from the tens column if you need to), then move on to subtracting the numbers in the tens column (borrowing from the hundreds column if you need to), then do the hundreds column, the thousands column, and so on until you’re done.
As you may have noticed, this process is really slow and tedious to do in your head. In other words, this method that we all learned in school isn’t exactly ideal for most of the real world mental subtraction problems we face in our daily lives. But—good news—there is a better way! So get ready to say goodbye to your Slow Subtraction Blues forever because today we’re going to learn that better way and turn you into a lightning fast mental subtraction machine!
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What Is Left-to-Right Subtraction?
The right-to-left method of subtraction that you learned in school—meaning you start from the ones column on the right and then work your way to the left—is fine and dandy for working out subtraction problems on paper. In fact, it works great for that purpose. But when it comes to working out subtraction problems in your head, it’s terrible. After all, it’s really tough (almost impossible actually) to keep track of all those carried digits mentally. Which is why you shouldn’t subtract from right-to-left in your head. Instead, as we’re about to learn, you should subtract from left-to-right.
You shouldn’t subtract from right-to-left in your head…subtract from left-to-right.
To see what I mean by left-to-right subtraction, let’s take a look at an example you’re bound to see almost everyday: getting back change from a cashier. Let’s imagine you take a trip to the farmer’s market to pick up your week’s supply of leafy green veggies. The total cost of your take is $14.63, which you pay using a $20.00 bill. How much change should you get back? Well, the right-to-left method would have you start by subtracting the 3 from $14.63 from the last 0 in $20.00. But to do that, you’re going to need to carry a bunch of digits and keep track of them all.
Instead of starting from the pennies on the right and working towards the tens of dollars on the left, the left-to-right method has us work in the other direction. In other words, it has us start with the biggest numbers—the tens of dollars—on the left. How exactly?
How to Subtract From Left-to-Right
The real trick to mastering mental subtraction is to combine this left-to-right direction of action with a little rounding trick. In the case of our farmer’s market change example, instead of saying that we spent $14.63 on veggies, the trick is to say that we actually spent $0.37 less than $15. They mean the same thing, but this different way of looking at the problem makes a world of difference. Why?
Well, if we ignore those $0.37 for a second, we can immediately do the subtraction problem: $20 – $15 = $5. So, we should get back $5 in change, right? No, of course not! Because we actually spent $0.37 less than $15. Which means that we should get back $5 + $0.37 = $5.37. Do you see how easy that was? It doesn’t even really feel like we had to do any subtraction at all! By simply rounding and keeping track of how much we rounded, we were able to subtract from left-to-right—meaning we subtracted the largest digits first—almost without thinking. Then, all we had to do was remember that we rounded in the beginning and add that amount to our answer. Easy!
To sum things up, here are the steps to carrying out lightning fast mental subtraction:
Quick and Dirty Tips for Left-to-Right Subtraction
- Round the number you’re subtracting to a convenient digit (we rounded to the nearest dollar).
- Remember how much you rounded by, and remember if you rounded up or down.
- Perform a quick mental left-to-right subtraction.
- If you rounded up, add the amount you rounded by to this result. If you rounded down, subtract it.
- Bask in the glory of your very impressive skills.
Practice Problems
As with any new skill, to get good at mental subtraction you have to practice. So, here are a few problems for you to work through. You can find my answers and explanations below.
- 77 – 26
- 132 – 34
- 2,037 – 775
- 2,037 – 1,999
Wrap Up
Okay, that’s all the math we have time for today. If you want to learn some more mental math techniques, check out these earlier Math Dude articles…
Be sure to check out my mental math audiobook called The Math Dude’s 5 Tips to Mastering Mental Math. And for even more math goodness, be sure to check out my book The Math Dude’s Quick and Dirty Guide to Algebra.
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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!
Practice Problem Solutions
- 77 – 26 This problem is probably easy enough to do in your head without thinking about it. But if you want to use our left-to-right rounding method, you could round 26 up to 30 (keeping in mind that we rounded up by 4), then subtract 77 – 30 = 47, and finally adding 4 to the answer (since we rounded up) to get 77 – 26 = 51.
- 132 – 34 To solve this problem, you could round 34 down to 30 and then go through the normal process. But we could make things even quicker if we realize that 34 is simple 2 more than 32. Which means that 132 – 34 is the same as 132 – 32 – 2, which of course is equal to 98.
- 2,037 – 775 We can round 775 up to 800 (remember that we’ve rounded up by 25), subtract 800 from 2,037 (which, with a bit of practice, you’ll be able to quickly figure out is 1,237), and then add 25 to this result to find the final answer: 2,037 – 775 = 1,237 + 25 = 1,262.
- 2,037 – 1,999 The trick here is to realize that 1,999 is just 1 less than 2,000. Which immediately tells us that 2,037 – 1,999 must be equal to 38.
The point with all of these is that a bit of quick thinking before acting along with a little simple rounding allows you to solve the problems from left-to-right. Do you see how much easier that makes things? If not, try doing the problem 2,037 – 1,999 using the old-fashioned right-to-left method—and be sure to do all of the carrying. You should find that it’s a lot more work…and it’s work that you simply don’t need to do!
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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.