Mental Math Tricks

Mental Math Tricks: No Calculator Needed!

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

No, don’t use your calculator tricks!

Believe it or not, there are quick and easy ways to do these problems in your head, saving time, paper, and calculator batteries.

If you are someone who has a child struggling with math or simply someone who wants to improve their math, we are about to share some mental math tricks that will make your life so much easier!

Why is Mental Math Important?

In a technology-laden society like ours, why would you need simple math tricks? Why can’t you just rely on your calculator tricks?

Well, here are a few great reasons.

Mental Math Tricks Save Time

If you’re taking the SAT there sections where no calculators are 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.

Mental Math Tricks Keep 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, puzzles, and crosswords.  Mental math tricks are just another brain exercise, and it’s definitely worth the effort.

It Looks Cooler Than Your Calculator Tricks

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.

Mental math tricks you should know

Since you’re clearly still reading, that means you’re interested in learning a little bit more about the secret world of numbers. Through all of the techniques we’re going to share, 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.

Ready?  Let’s get started!

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. Consider this as a warm up to your mental math calculator.

Here are the steps:

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

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.

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

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:

The answer will always, always, always end in 25.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.

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.

Divide the number by 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!

Multiply a Big Number by 9

One of the simplest mental math tricks that you can learn is multiplying a big number by 9. This operates as a similar concept to trick no. 4.

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

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

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

Multiplying in Parts

Using your own mental math calculator, you can multiply numbers in an easier way. You just have to do it by parts:

To find the answer to 7 x 93, you just have to mentally multiply 7 x 90 and 7 x 3. By adding the results 630 + 21 = 651.

Another example would be 6 x 215. The trick would be 6 x 200, 6 x 10, and 6 x 5. 

You’ll get 1200 + 60 + 30 = 1290.

Subtract by Adding

This is one of the mental math tricks that will show you the relationship between addition and subtraction.

The principle for this trick is this: instead of subtracting, find out what number you need to add to get the other number. Quite unclear? Here’s an example.

To answer what is 10 – 6, think of the number that you have to add to 6 to make it a 10. The answer would be 4.

Add 1 to Doubles

Another one of the many interesting math tricks we’re going to share is adding 1 to doubles. This is a very simple trick that kids can learn easily. 

Basically, they just have to memorize doubles like 6 + 6, 8 + 8, etc. Once they have already memorized that, they can quickly answer what 6 + 7 is because they just have to add 1. 

Multiply Numbers That End With Zero

In multiplying numbers that end with zero, you just have to multiply the first numbers and add the zeros after. To illustrate:

200 x 600 is 2 x 6 = 12

Now that you already got the base number, just add up all the zeros you counted from 200 and 600. That would be four zeros after 12. So the answer is 120,000. Easy peasy!

Subtracting From 1000

Your mental math calculator can handle this one because this is pretty easy. In subtracting any number from 1000, subtract every number from 9 except the last that should be subtracted from 10.

Here’s an example:

1000 – 495 would be 9 – 4, 9 – 9, and 10 – 5.

The answer would be 5, 0, and 5. Combine these and you will get 505. That’s your answer to 1000 – 495.

Flipping Percentages

What is the fastest way to find a percentage of a number? Calculate a percentage in your head by turning it around.

Example:

What is 4% of 50? It’s the same thing as 50% of 4.

What if the number you are trying to find is more complicated, like 17% of 23.

23% of 17 isn’t any easier, so what would you do then?

23% is almost 25%, so you can get a rough estimate off that very fast – 4.25

But you’re 2% off. So, what’s 1% of 17? 0.17

Double it, that’s 0.34

Subtract that from 4.25 and you get 3.91.

Conclusion

Not so smirky now, are you?  Calculator Person.

And as you learn more and more of these math tricks, you’ll have an even better understanding of numbers learn how to get better at math.

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

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Todd VanDuzer

Co-Founder & CEO at Student-Tutor
Hello! My name is Todd. I help students design the life of their dreams by ensuring college, scholarship, and career success! I am a former tutor for seven years, $85,000 scholarship recipient, Huffington Post contributor, lead SAT & ACT course developer, host of a career exploration podcast for teens, and have worked with thousands of students and parents to ensure a brighter future for the next generation. I invite you to join my next webinar to learn how to save thousands + set your teenager up for college, scholarship, and career success!
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kansiime Laban
kansiime Laban
3 years ago

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?

Math trainer
Math trainer
3 years ago

Mental skills skills are really underrated. They should teach this stuff in schools.

kansiime Laban
kansiime Laban
3 years ago

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.

Rad
Rad
3 years ago

It looks so easy.Thanks a ton for the tricks.

Joss
Joss
3 years ago

Wow! wonderful

Matthew
Matthew
3 years ago

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… Read more »

Liuba
Liuba
3 years ago

I’d like to learn math faster. Thank you!

Sumi
Sumi
3 years ago

Nice experiments

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