by Jason Marshall
Today we're turning our attention to using everything we've learned so far to help you solve math problems faster than you ever thought was possible. In this article you’ll learn two tips to help you add quickly…all in your head! Next week we'll build on these tips to learn another way to do some fast addition in your head.
Tip #1: Find Pairs of Numbers that Add to 10
Here is perhaps the single most useful quick and dirty tip to help you calculate quickly: When adding a list of numbers, look for pairs of numbers that add to ten. Here’s what I mean:
1 + 9,
2 + 8,
3 + 7,
4 + 6,
5 + 5.
All of those pairs add to ten.
So, when you’re adding groups of numbers, look for these special pairs. If you’ve got one or more pairs, it’s easy to add them up—as easy as 10 + 10 = 20.
How to Do It
Here’s an example: Let’s say you need to add the numbers 1, 3, 5, 7, and 9. You could run through the numbers in order, adding them up one-by-one; something like:
1 + 3 = 4, then
4 + 5 = 9, then
9 + 7 = 16, and finally
16 + 9 = 25.
But that’s a lot to keep track of. Remember the commutative property of addition? You don't have to add these numbers in the order they're given to you. Instead, if you start by pairing up numbers that add to ten—in this case 3 and 7, and 9 and 1—that leaves you with an easy problem. You just have to add the two 10s to the remaining number 5 that didn’t pair with anything:
10 + 10 + 5 = 25
When adding a list of numbers, look for pairs or groups of numbers that add to ten.
Tip #2: Find Groups of Numbers that Add to 10
The second tip is really an addendum to the first. Say you need to add a series of numbers like 47, 14, 21, and 32. Let’s look for pairs of numbers in the ones place that add up to 10. That's the 7 from 47, the 4 from 14, the 1 from 21, and the 2 from 32. Hmm, no two numbers here add up to 10. Are we out of luck?
No, look at the numbers again: 7, 4, 1, and 2. Three of those numbers do add up to ten:
7 + 1 + 2 = 10
That brings us to the second quick and dirty tip: Don’t restrict yourself to grouping pairs of numbers—sometimes looking at groups of three (or even more) can help.
How to Do It
Let’s look at how to solve the example problem from before in a little more detail: 47 + 14 + 21 + 32. First, notice that each term in the problem can be written as:
47 = 40 + 7,
14 = 10 + 4,
21 = 20 + 1, and
32 = 30 + 2.
Then, let’s use this to rewrite the original problem:
Now, as we discussed during the episode on the commutative property of addition, you can add these numbers in any order you like. So, let’s gather the numbers that add up to 10 and rearrange the terms as:
The three numbers in the first term add to 10 and the four numbers in the second term add to 100, so the problem becomes:
Believe it or not, eventually—after a bit of practice—you’ll be able to do all this in your head.
You can find several practice problems below to help you sharpen your skills. Remember, try to work them out in your head if you can. Next week we'll combine these two tips with a couple of other tricks, and continue your transformation into a calculating machine. Then, get ready, because the week after that we’re going to begin our foray into the world of fractions, decimals, and percentages.
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Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Submit your questions to email@example.com, the aforementioned Facebook page, or on Twitter. Thanks for reading, math fans!
The only way to become proficient is to practice! For these problems, add from the top down. Be sure to look for pairs or groups of numbers that add to ten. For example, in this problem
you should count in your head: 3, 13, 23. In other words, 3 + (6+4) + (9+1). Here are two practice problems with a single column of numbers to add:
Here’s a problem with two columns of numbers to add. Look for pairs that add to ten in each column.
You can find the answers to all the practice problems on the Math Dude’s Facebook page.