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Mental Math Tricks: Save Time, Ditch Your Calculator!

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Quick!  What’s 14682 times 5?  Or 77 times 14? Can you square 75 in three seconds flat?

No, put away the calculator.

Believe it or not, there are quick and easy ways to do these problems in your head, saving time, paper, and calculator batteries.  That’s right.  I’m about to unlock the secrets to mental math.

 

Why is Mental Math Important?

I know, I know.  I can hear you.  Leaning on the table, smirking at me, and digging around in your bag.

“I don’t know if you heard,” you say, “but we have these mysterious, new-fangled machines called calculators.”  And with that, you produce a blocky rectangle and plunk it in front of me.

In a technology-laden society like ours, why would you need mental math?

Well, here are a few great reasons.

1. It saves time, especially in situations where calculators aren’t allowed.

If you’re taking the SAT or an AP Calculus test, there are always sections where calculators aren’t allowed.  Instead of spending valuable time multiplying 1082 by 9 longhand, you can get the answer in half the time, and put your efforts elsewhere.

2. It keeps your brain sharp.

Yes, those mysterious, new-fangled calculators are beyond helpful.  But when you get too reliant on technology, you can just feel things start to…slip.  Right?  It can’t just be me.  There’s a reason people do Sudoku, and puzzles, and crosswords.  Mental math is just another brain exercise, and it’s definitely worth the effort.

3. It looks cool.

Honestly, it’s impressive and makes you feel a little bit like someone in a James Bond movie when someone wants to know what 273 x 11 is, and you can casually say the correct answer before someone’s done typing it.  It’s a little bit like an academic magic trick.

 

Anyway, now I’m off my soapbox—and you’re clearly still reading, so you’re definitely interested in learning a little bit more of the Secret World of Numbers.

Through all of these techniques, THIS is the main thing to remember.

Each trick has different rules that make it work—and you have to learn to recognize at a glance when a number (or a pair of numbers) fits those rules.

All right.  Ready?  Let’s get started!

 

Trick 1- Multiply Two-Digit Numbers by 11

You totally know how to multiply things by 10, right?  Just add a 0 to the end of the number! So easy.

But hang on. What about 11? …Especially if it’s a number like 67?  Or 81?

That seems a little more complicated…but as soon as you learn this trick, it’ll be a breeze.

Here are the steps:

  1. Look at the number you’re multiplying by 11.  (So, if you’re multiplying 36 x 11, look at 36.)
  2. Add those two digits together.  (3 + 6= 9)
  3. Stick that digit between the number from step 1.  (396)

mental math multiply two digits

Simple, right?

But hang on.  What if the number you come up with in Step 2 is something like 14? Or 18? How do you deal with something like that?

Well, it’s a little different, but not much.

Let’s try it with 86 x 11.

     1. Look at 86. (Sound familiar?)
     2. Add those two digits together. (8 + 6 = 14)

Okay.  So now you have two first digits, right?  You have the first digit from step 1 (8, from 86)…and you have the first digit from step 2. (1, from 14.)

Here’s the trick.  You’re going to add the first digits together.

     3. Add the first digits together. (8 + 1 = 9)

This is the first digit of your answer, now. After that, you go right back to the old, familiar steps.

     4. Stick the second digit from step 2 in the middle.

The middle of what, exactly?

Well, follow along closely.  Take your new first digit from step 3 (9), stick the second digit from step 2 right next to it (4), and close with the second digit from step 1 (6).

So your answer is 946.

mental math multiply two digits

 

Trick 2- Multiply Three-Digit Numbers by 11

 

So now you can multiply any 2-digit number by 11 in the blink of any eye! (Or maybe two blinks of an eye.)

But what about three-digit numbers?

The process is pretty similar to the two-digit one…but with a twist.

Remember how the first step of the two-digit process is to add your digits together? (Example: If you’re multiplying 26 times 11…… 2 + 6 = 8.)

You might think that with a 3-digit number, you’re just supposed to add all three numbers together…but that’s not the case.

Instead, think of your 3-digit number as…well, let’s think about it like two sisters looking after their little brother.

(Stay with me.)

 

Problem: Multiply 317 x 11.

So here’s where the sister thing comes in.  The number we want to focus on is 317.

 

3 is Threeresa.  She’s a sister with red hair, and she loves oatmeal cookies.

7 is Sevenie.  She’s tall and willowy with a sprinkle of freckles, and stays up late reading.

They’re both going to the park with their little brother, One.  (He’s one year old.  His parents appear to be strange namers.)

 

To properly multiply these siblings, you’ll have to split them apart first—but One can’t be left on his own.  (For heaven’s sake, he’s only a child!)

So split the number apart…but one of the sisters always has to be hanging on to One.

317

First, Threeresa holds One.  Let’s add the two of them together.  (3 + 1 = 4)

Then, Sevenie holds One. (7 + 1 = 8)

Both of those numbers get stuck in the middle…so the final number looks like this:

Threeresa, Threeresa-holding-One, Sevenie-holding-One, Sevenie.

 

Or in other words: 3, 4, 8, 7 —> 3487

 

multiply three digits mental math

 

Easy-peasy, lemon-squeezy.

 

Oof! Okay.  Let’s take a breather.

I haven’t scared you off, right?  ‘Cause I’ve got three more tricks for you to read…and trust me, they’re WAY easier to explain.

Go, get a glass of water.  Stretch.  Watch an episode of Arrested Development.  Contemplate the universe and its infinite possibilities.

Feeling better?

Let’s get back to the whole mental-math thing.

 

Trick 3 – Squaring

This one really is super-easy—to do, to remember, and to explain.

For this one, you need a two-digit number that ends in 5.  25, 55, 15, 95—whatever.  They’re all game.

A couple things to remember:

  1. The answer will always, always, always end in 25.
  2. You’ll always multiply the first digit by the next highest number.

Wondering what that means?

So if you’re squaring 25, your first step is to multiply 2 x 3.

Squaring 55? Multiply 5 x 6.

Squaring 85? Multiply 8 x 9.

See the pattern?

Then, just add 25 to the end.  Seriously.  It’s THAT easy.

 

mental math squaring

 

Trick 4 – Multiply a Big Number by 5

Whoa.  That was simple, right?  Well, here’s an equally simple one.

We’ve already talked about the well-known trick to multiply a number by 10.  (Add a zero.)

Well, what if you’re multiplying it by 5?  And I’m talking a big number—like 2486, or 18067.

Here’s a simple two-step trick that can make it easier.

  1. Divide the number by 2.
  2. Multiply it by 10.

Right?  So for 2486, divide it by 2…which gives you 1243.

Then just add a 0…and you get 12430.

Talk about snappy!

mental math

 

Trick 5 – Multiply a Big Number by 9

Here’s the last one, and it operates off of a similar concept.

Let’s say you’re multiplying 230 by 9.  Follow these steps:

  1. Multiply 230 by 10.  (2300)
  2. Subtract 230.  (2300-230= 2070)

Just add a zero, and subtract the number itself.  That’s all there is to it!

 

Conclusion

Not so smirky now, are you?  Calculator Person?

And as you learn more and more of these tricks, you’ll have an even better understanding of math…and you’ll be able to succeed in so many ways!

Now go forth—hone your mental math swords!  Take down any math problem that arises.  We’re all rooting for you. 🙂

Co-authored by Rita Khalaf

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Test Person

Dressler Parsons spent most of her childhood in an adobe house her father built in rural Arizona. Right now, she's taking so many business and art classes at Barrett, the Honors College at Arizona State University, and plans to graduate in Fall 2016 with a Bachelor of Science in Marketing, and a Bachelor of Fine Arts in Intermedia. And, handily enough, her SAT scores and grades qualified her for ASU's Presidential Scholarship (worth $24,000), as well as the AIMS tuition waiver. She is passionate about showing people their potential for a bright, beautiful future. In her free time, she cooks edible things and knits inedible ones.

Comments 12

  1. thanks in all for being bright ,but finish up the general formulae for squaring other numbers say 7,12 etc because they cant fall in trick 3, more so
    multiplication by which ever methord especially big was done on similar numbers say 5678*4539, what hapens in case we are multiplying e. 95678 *675?

  2. excellent,though im learning to discover hidden treasures of math secretes when i have grown old i needed more of this during my youthful age .allthe same they may need me in heaven when im sharp.
    let me proceed ,
    i desire to be the sharpest than you inventors of this . my challenge is somewhere one must need a small paper to jote down before calculating yet i needed to mentally give answers with out a paper and a pen.
    be blessed for this hidden knowledge .its great,its real,its sexy,its awesome.

  3. Dressler,

    Thank you for these mental math tips! I will be sure to use them in my daily life: they are very useful and efficient in lots of situations. One of your tips that I use in daily life already is multiplying by elevens, I found it on my own years ago and have been using it since. Another tip I have, which is an addon to your last tip, is multiplying by 99, 999, 9999, etc. To multiply a number by one of these, add the number of zeros equivalent to the number of 9s, and subtract by your starting number. For example: 32 * 999 = 32000 – 32, or 31968!

    1. Matthew! So exciting seeing that you use them in your daily life. I still use some myself. Helpful tricks right! 🙂

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