2 More Tips for Adding Quickly
What does subtraction have to do with lightning quick addition? And how can splitting numbers up into 2 or more smaller numbers make for faster addition? Keep on reading The Math Dude to find out!
Jason Marshall, PhD
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2 More Tips for Adding Quickly
Most people don’t do complex math problems every day, but pretty much everybody has to do at least a little simple addition on a daily or near-daily basis.
Tallying the money in your wallet? Addition! Figuring out the cost of that vacation you’re planning? Addition! Painfully working out how many hours of sleep you did (or didn’t) get as your baby woke you up 7 times last night? Surprise…still addition!
I figure that since we all have to do it, we may as well learn how to do it well—by which I mean accurately and quickly. Which is precisely why we took some time last week to talk about 3 tips for adding quickly.
But turns out there are a lot more than just those three tips that you can use to help you add more quickly. So today, we’re going to talk about 2 more tips that will help turn you into a super-fast, super-accurate, and super-cool number-adder-upper extraordinaire..
How to Add Quickly (the Story So Far)
In addition to the 3 tips from last week’s show, we’ve learned another thing or 2 (or 3 or 4) about adding quickly over the life of this column. So before jumping into today’s pair of time-saving tips, let’s quickly recap everything we’ve learned so far about adding numbers quickly.
Way back in our first pair of eposides on adding quickly (which were the 8th and 9th episodes of this now 245 episode-long podcast!), we learned 2 important tips:
- When adding columns of numbers, always look for pairs (or groups) of numbers that add up to 10. It’s simple to see when numbers add to 10, and adding multiple 10s together is easy – so this is a big time saver.
- To add quickly, don’t add from right-to-left as many of us were taught. Instead, start with the far-left column and work your way to the right. If you missed this one and aren’t sure what I mean, check out the episode on this tip, and the video I made describing how to use it.
And then, last week we learned these three big tips:
- Just as subvocalizing words slows you down when reading, subvocalizing numbers and operations slows you down when adding. So don’t do it.
- If you’re only interested in an estimated answer, don’t be afraid to round all the numbers you’re adding to whatever digit you want your answer to be accurate to before you do the addition. This will save you a lot of time and effort, and the result will be a good estimate.
- Look for multiple copies of the same number in any list you’re adding. If several exist, use multiplication to come up with the total for these numbers before adding this total to the rest.
Tip 1: Subtract to Add Quickly
Today’s first new tip may sound counterintuitive, but trust me – it really works. Why counterintuitive? Because the tip says that sometimes it’s best to subtract in order to add…or at least in order to add quickly. Let me explain:
Sometimes it’s best to subtract in order to add.
Let’s say you’re adding 46 + 98. You could line these numbers up and start adding the good old-fashioned way. But that’s slow, and it really isn’t necessary – especially once you realize that 98 = 100 – 2. And that, therefore, 46 + 98 is the same as 46 + 100 – 2.
How is this better? Because it’s easy to add 100 to any number (46 + 100 = 146), and it’s easy to subtract 2 from any number (146 – 2 = 144), which means that we’ve turned a somewhat difficult addition problem into an easy addition problem by throwing a bit of subtraction into the mix.
You can use this trick with other convenient numbers, too—not just those that happen to be close to 100. For example, in the problem 128 + 47, you could use the fact that 47 = 50 – 3 to turn a somewhat difficult mental addition problem (128 + 47) into a much easier problem, 128 + 50 – 3 = 178 – 3 = 175.
Tip 2: Split Numbers Up Into Smaller Numbers
Our second tip is a close cousin of the first, and it’s also very simple. The tip is to simplify addition problems by turning large numbers into little sub-addition problems made up of smaller numbers.
Why is this helpful? Because it’s almost always easier to add smaller rather than larger numbers together. And because we get to choose what those smaller numbers are, we can choose them wisely to make the problem easier.
For example, let’s go back and look at the last addition problem from the previous tip: 128 + 47. Instead of simply using the fact that 47 = 50 – 3, let’s also split the number 128 up into a couple of smaller numbers that are easy to add to other numbers—namely 128 = 100 + 25 + 3. If we put all of this splitting up and subtracting together, we can turn the problem 128 + 47 into the problem 100 + 25 + 3 + 50 – 3. The 3s cancel each other out here, and we immediately see that the answer must be 100 + 25 + 50 = 175 – without having to do nary a lick of work.
The real trick here is to learn to see potentially helpful splits like this in your head before you begin working a problem. Once you start seeing large numbers as the sum of a bunch of easily-addible smaller numbers, you’ll be able to tackle potentially difficult mental addition with ease, because you’ll have turned big problems into much tamer beasts—which, after all, are the best kind of beasts to work with.
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!
Photo of addition problem courtesy of Shutterstock.
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.