Fast Math Tricks - How to multiply ANY 2 digit numbers up to 100 - the fast way! 

The dislikes are from the people that try to race a calculator

Learned something new today. Can't wait to show my daughter. Thank you!

The amusing thing about this trick is that this is what we learned in elementary school when learning to multiply. This is just a simpler way of thinking about it that doesn’t really explain how it works but gets the job done.

My son LOVES math but sometimes struggles with the way it’s taught in the American classroom. I am so glad that we as parents can now find resources at our fingertips that help our kids feel confident in their abilities… and excited that they learned it in a new way 😊

You are a wonderful teacher who helped me in the way I delivered my lesson in front of the third grade without hesitation and fear with my head held high. I wish you a lot of happiness, appreciation and respect.

Before I didn’t even know how to do this method. And then I watched this video. Straight away, i got all the questions right and it takes 2 seconds!! THANK YOU

As mentioned in other videos, if you generalise this using algebra, it makes perfect sense. A two-digit number with digits ab would be expressed as (10a+b). If you multiply (10a+b) with another two-digit number (10c+d), you will get (10a+b)(10c+d) = 100ac + 10ad + 10bc + bd You can then factor this as 100(ad) + 10(ad + bc) + 1(bd) Therefore, you multiply the units (b and d) to get the units digit of the answer You multiply the first digit of one number with the second digit of the other number (a and d), and vice versa (b and c), then add together to get the 10s digit of the answer Then you multiply the 10s digit of both numbers (a and c) to get the 100s digit of the answer But what if you wanted to multiply _3_ 2-digit numbers together, such as 54 x 26 x 38, for example? Well, this would be (10a+b)(10c+d)(10f+g) - I'm deliberately avoiding the use of 'e' for obvious reasons (i.e. Euler's number). If we expand this out, we get 1000acf + 100acg + 100 adf + 10 adg + 10 bcg + 100bcf + 10bcg + 10bdf + bdg If we factor this, we can get: 1000(acf) + 100(acg + adf + bcf) + 10(adg + bcg + bdf) + 1(bdg) We can then see the following: To get the units digits, we have to multiply the units digits of each of the answers (4 x 6 x 8 = 192 - we then write 2, and carry the 19) To get the 10s units, we need to multiply the units digit of two numbers, with the 10s digit of the remaining number. This should be done three times, each time changing which number we take the 10s digits and units digits from: 4 x 6 x 3 = 72 4 x 2 x 8 = 64 5 x 6 x 8 = 240 We then add these together, 72 + 64 + 240 = 376 We then add the 19 we carried over previously, to get 395. We then put the 5 in the 10s digit, and carry the 39. For the 100s digit, this is achieved similarly to the 10s digit, except we multiply one units digit from each number, with the 10s digit of the remaining two numbers: 4 x 2 x 3 = 24 5 x 6 x 3 = 90 5 x 2 x 8 = 80 Add these together to get 194 We then add the 39 we carried over, to get 233 We then write the 3 in the for the 100s digit, and carry the 23. Finally, for the 1000s digit, we simply multiply all 3 10s digits together: 5 x 2 x 3 = 30 We then add the 23 we carried, to get 53. We should therefore, have the answer 53352. In summary, if we simply express the 3-numbers as AB x CD x FG and the result as HIJK: H = ACF I = (BCF + ADF + ACG) J = (ADG + BCG + BDF) K = BDG And, just for the sake of it, what about a 2-digit multiplied by a 3-digit number? I shall cut out the general algebraic method and go straight to it - let's use 234 x 56 for example The units digit of the answer is the product of the units digits of the two numbers (4 x 6 = 24) - the 4 is the units digit, and we carry the 2 For the 10s digit: Multiply the 10s digit of the 3-digit number, with the units digit of the 2-digit number (3 x 6 = 18) Multiply the 10s digit of the 2-digit number, with the units digit of the 3-digit number (4 x 5 = 20) Add these to get the answer 38 + 2 (carried over from the units) = 40 - digit is 0, then we carry the 4 For the 100s digit: Multiply the 100s digit of the 3-digit number, with the units digit of the 2-digit number (2 x 6 = 12) Multiply the 10s digit of both numbers (3 x 5 = 15) Add these to get the answer 27 + 4 from the 10s digit = 31 - the units is 1, and we carry the 3 The 1000s digit is the product of the 100s digit of the 3-digit number, and the 10s digit of the 2-digit number) (2 x 5 = 10) Adding the 3 we carried, we get 13 This gives us the answer 13104 In summary, for ABC x EF = GHIJ (these represent _digits_ not variables, i.e. ABC is a 3-digit number with the digits A B and C, _not_ a product of A x B x C) G = AE H = AF + BE I = BF + CE J = CF

This is brilliant! I'm very grateful for this (and I like your handwriting) :)

Absolutely awesome! Brilliant for any kind of maths related aptitude tests. Any chance for divison next please?

Great trick.. thanks for sharing it. Although I use a calculator every day in my work, I like to do as much math as possible in my head. Feels good when the calculator verifies it. Thanks for all the good teaching and learning that goes on at your channel. Thumbs up!

Thanks for this, you always upload things I need the day I have a test. Edit: I’m not being sarcastic

Cant believe I'm only just finding this! This is gonna help so much in my upcoming exam :D Thank youuuu

This is great! A whole new way to look at math! Thank you!

I love your channel, it's very very helpful! These are very genius tricks!

I really wish they taught us this in primary school. this would have helped me so much. I’m so upset i’m only finding this channel now!

Learned something newww todayy!! Thank u so much for your wonderful videoss! Can’t wait to share it with my lil siblings!!!

Thanks for helping my son, he become master please keep on teaching my son is a great fan of you. God bless you

Great video tecmath!

Thank you for sharing this technique☺️

Thanks a lot it really helped me since I’m Aussie and my teachers want me to do it a specific way! Hope you have a great day.

As always, thanks for this tricks

amazing video. I love how you explain it so clearly

Very useful math trick Thank you so much

Thanks for the math tricks, really helpful

thank you so much!

Great as usual!

Wow. Just wow. Thanks mate!

THIS WILL HELP ME A LOT ON SOLVING THE PERCENTAGE!!!!! Thank you soo much!!!!!! I wish i knew this before!!!!

I JUST LOVE YOUR MATH TRICKS

Thanks really helped me

thank you tecmath

A fantastic way of explanation

Thanks a ton.....this video is really helpful.👍

That accent makes the video even better!

You are gonna help me look like a math genius to my kids. Cheers mate 👍

Thank you so much for this super easy technique. Memorise the 'rainbow trick' and you are set to go...

I loved this trick, It's really fast and understandable.

It's a great help to do my maths test easily thank you 🙏

It's a lot harder to keep track of all the numbers in the last problem without using paper to write it down on, unlike the square root trick, lol. It took me quite a while to get the answer only using mental math (only for the last example, anyway), but then again, I am dyslexic... despite math being one of my strong suits (as well as spelling, go figure LOL). Very informative, I wish that teachers would use these kind of examples as it makes learning a lot more fun, which studies indicate strongly that students will not only have an easier time learning, but also retaining the information. Just like I still remember the old PEMDAS from the acronym used when you're given a problem with multiple equations being done in a single problem, as far as which parts of the solution are found first. (Paranthesis, Exponents, Multiplication, Division, Addition, Subtraction). I'm sure that most people here who have taken algebra still remember, "Please excuse my dear aunt Sally".

thanks, tecmath this was really helpfull to me :D

Yes i did get the answer thank you so much learned something new today!... keep it up.

I am using this for years this is amazing everyone 🎉

Thank You so much

Thank you so much sir🙏🏻 You helped me a lot ❤️

Fantastic thank you

Thanks tecmath. Mes élèves ont bien aimé cette technique pour le calcul mental

Thank you sir

The best math channel

Thank u sooooooooo much I have a math test tomorrow and I realised that I can't do two digit multiplication and this helped me so much

Nicely explain .. common rule for any 2 digit number .. that is nice

wonderful video

I like it..😁 because I suck at math, but now.. I feel like I'm a part of the Math Club. Thank you. .

Thanks

Genius work

Very helpful

Best explanation

great video!!!!!!!!!!!!

you are amazing! You are like Faci of math.

You saved my life ❤️

I don’t have kids but my nephews will be appreciating this method

So nice and easy method

thank you i feel like i will do better in solving my math problems thank you

This reminds me of foil method for multiplying things like (x+4)(x+2). Pretty neat

Best teacher

Amazing

Thats great i have never seen these kind of easi tricks before. Even i am graduated

I knew it there was something missing in the first video related to this one. Until I figured out you will need to carry the "tens digit" if ever you acquired a 2-digit number result for the right side.

Like magic and really easy to do on the fly! 10/10

very cool!

First. Love these videos. Very helpful

Hello, you are a very good teacher your videos helped me a lot, could you please make a video about trigonometric equations

Thanku sir 😇

u r a literal god

I don't know why people unlike the video this is easy and simple thx to you tec

Good videos. You should create a mental math app

Mate, do you do any one on one tutoring? Im based in Sydney, and need some help getting ready for a military pilot test Ive got coming up, and really want to nail the mental maths sides of things. Would be awesome if you could help!

sir...please upload few division tricks in order to do division as fast as possible. thankyou

You're Awrsome!!!!!

How did I not know this? I have tried to figure it out on my own but never got it. I must not be very _____. All I can say is Thank YOU.

I loved it thanx a lot friend now people will think im a genious

Dude thanks so much I greatly appreciate it remember to hit the like button on this video

Please teach compound interest

Thank u so much I have time table tomorrow and I think I will get 100/100 tysm . Oh help pretty much

Have job exams coming up, found you just in time. Great lessons, big thanks from India

hi! i got confused when i tried this set of numbers, how would you solve 89 x 77 using this method?

Also when timesing double digits with 13 26x13 2_6 2+6= 286 26x13=286

ok this is for the people that get like 12 thousand or what ever , you carry over your digits. so lets say 36 x 24 , 4 x 6 thats 24 put a 4 in the units and keep that 2. then times 3 by 4 you get 12 and and 6 x 2 you get 12 add them togther you get 26, keep the two, then 3 x 2 which is 6 add the two you got and you have 8 then put that in it and you have 864. hope i helped

Super

tecmath, what program do you sue for these videos?

Would u pls show how i have to follow for mutiplying 6549x8378.its a little bit different .pls show step by step.thnks

This reminds me of the video where he did 3 by 3 multiplication.

Yeah boy!!!!

😚😚😚😍😍😍😍thanks a loooooot

Why don't they teach us in school? You made my life much easier cause I am kinda slow in calculations like this, but this helped me a lot. I can't wait to learn more!

What is the best way to present this lesson?

bloody love this. I feel like Einstein now. Thank you very, very much mate.

dam big brain

Where have you been all my life I bro

Why not left to right?

The fastest way to multiply in your head is to: Lets say you have 12 x 52 Take the smallest/easiest number you can use to multiply with, which in this case, its 12. Now multiply 12 by the first digit (12 x 2 = 24), and remember that. Multiply 12 by the second digit now (12 x 5 = 60). Since it's in the TENs place, you add a zero to the end of that number. (60 becomes 600). Now add those two answers together (24 + 600 = 624) (It may seem like a long way to do it, but I just wanted to explain every step clearly, making it seem long to do) (Also, sadly it doesnt work half the time. If you have something like 86 x 53, then you would have to do a lot more steps that I'm not bothered to explain. And you would probably either need a sheet to write one or two numbers down if it's a sum like 86 x 53)