# Math Tricks: Simple Strategies Teachers Don’t Want You to Know, Part 2

If you have MUCH better things to do in your life than figure out mathematical calculations, then you’ll be glad that you stumbled upon this article. We’re going to show you how you can save so much time (well, maybe a few seconds) by using simple, fun math shortcuts.

In an earlier post, we offered techniques to simplify multiplying by 5 and 25. In this post, we will explore a couple of amazing tricks with other numbers that will come in handy.

Multiplying By 11:

When multiplying a one-digit number by 11, most of us can instantly produce the correct answer. But what about two-digit numbers? Can you solve these equations just as easily? Try this:

45 x 11 = ?

Step #1: Take the target number (45), and Add the two digits together (4 + 5 = 9).

Step #2: Then insert your insert your answer (9) between the two numbers: 495. And there’s your answer!

Let’s try another: 52 x 11 = ?

5 + 2 = 7

Answer: 572

Easy, right?

Do the two digits add up to more than 10? No problem. It just requires one extra step:

68 x 11 = ?

Here’s the snag: 6 + 8 = 14

It won’t work if you try to place the 14 between the 6 and the 8. Instead, simply carry the one and add it to the lead number (6 + 1 = 7). Then insert the 4 in the middle, and finish the technique as described above:

68 x 11 = 748

The Power of Doubling

Complicated equations can be made simpler when broken down into smaller parts. With the power of doubling, it’s possible to solve multiplication problems quicker, easier, and in your head. Let’s try a few using the number “23.”

Multiply by 4 = Double and double again: 4 x 23 = ?

Doubling 23 is 46. Double it again and you get 92.

Multiply by 8 = Simply double your answer one more time: 8 x 23 = ?

Double 92 and you get 184.

Multiply by 16 = Double one more time: 16 x 23 = ?

Double 184 and you get 368

If you are brave, you can continue with 32, 64, 128, and beyond!

Divisibility Rules:

So, you’ve just robbed a bank with two of your pals. You get to your hideaway to divvy up your heist. After counting, you arrive at the number \$4,587. Mugsy looks over at you and asks, “Well, boss, is the total sum cleanly divisible by 3?” You turn to Mugsy and ask, “Huh?” He replies with, “Can you split the loot evenly by threesies?”

Can you quickly answer Mugsy? You will be able to after reading this:

Add up all the digits (4 + 5 + 8 + 7 = 24). Is the sum (24) divisible by 3? If yes, then the original number (4,587) is also divisible by 3. In this case, yes; 24 is cleanly divisible by 3, so you and Mugsy won’t have to worry about duking it out over a remaining dollar.

But what if there are 6 of you?

Just as simple. First, make sure the original number (4,587) is even (if it’s not, then the number is not divisible by 6). Then, employ the same trick that you used for 3s (Is the sum of the numbers divisible by 3?). If the original number is even and the sum of the added numbers is divisible by 3, then the original number is divisible by 6. In the example of \$4,587, the number is not even, so it is not divisible by 6.

But what if there are 9 of you?

First of all, never rob a bank with 9 people. Someone is bound to squeal. But let’s say that you decided not to heed this advice, and you packed into a van with 8 of your closest conspirators and knocked off the First National State Bank. You hauled away the same amount we’ve been using: \$4,587 (quite a heist!). Is that number divisible by 9?

Try this: Add up all the digits. If your total sum is divisible by 9, then the original number is also divisible by 9. If the sum is not divisible by 9, then the original number is not divisible by 9.

4 + 5 + 8 + 7 = 24. Divisible by 9? I’m afraid not. Someone will need to duck into a 7-Eleven and get some change.

And now that you know these math tricks, it will be so much easier for you and your pal Mugsy to calculate how many more months you have until you’re up for parole!