Schools teaches memorization. This guy just taught me how to save time while still using my brain and avoid using a calculator. I just learned something so useful in like 2 minutes meanwhile in school it takes years to learn something that you'll actually use in your life
That's so true The reason behind that is that they just teach u whats in the book that the government gives for schools so they don't teach u the exiting and easy ways to do it.
This reminds me of the time when I was multiplying numbers out loud and broke down one of the numbers to make the multiplication easier and someone at the same table was surprised you could do that. If school did a better job of explaining how basic math worked, they could easily teach simple tricks like this to speed up mental arithmetic.
Because it isn't typically useful to know how to do this. The method taught in school is slower, but more comprehensive, and teaches and understanding of what is going on (specifically the distributive law of multiplication over addition and subtraction)
@@aaronwarwick9966 Well, when youre little and first learning multiplication I dont think itll be a good Idea to teach this, but It might be a pretty good idea to teach it to students who already understand multiplication. Like teach it to an 8th grader or something.
you are being teach this at school. You learn to calculate (a+b)(a+c)=a*a+a*(b+c)+b*c with 14*12, a=10, b=4 and c=2 so that gives you 10*10+10*(4+2)+4*2=100+60+8=160+8=168. That's it
I'm 65, and a little over 10 years ago, I was diagnosed with dyscalculia, which is a math specific learning disability. If only I had known this as a child, I would have felt a lot better about not getting math! But, your explanations also make more sense than any I remember in school! Thanks!! I'm watching math without breaking out into hives!!🤔😂😂👵
Learn it by high school and a few big words, you know bigger then the 4/5 letters that are in every sentence these days, and people will think your smart/intelligent for the rest of your life. Tricky, tricky. Just be casual about it. Throw in occasional comments like “caught thinking outside the box again” or shrug your shoulders when asked how you do that. Or, offer to teach them. I’ve fooled people for 50 years. After awhile people just assume.
Using base 10: 14×12 14 is 4 more than 10. 12 is 2 more than 10. 4. 2 14×12 So, 14+2 (or 12+4) = 16 Add 0 to the end, making the number 160. Then, multiply 4 by 2, which equals 8. Finally, add 160 to 8, which equals 168. I hope this helps. :)
The more I learn about math on RU-vid in my post-college graduation life, the more I realize that our math teachers probably didn't care that much about actually teaching us.
hey there, please be kind and help.….iam now 7th grade , i fear my study a lot bcoz i mostly depend on memorization, i barely can use logic or i suckk, i am not good at other subjects except math....i love math its fun as i am killing and torturing monsters in game.… so..… is it okay if i learn these genuine knowledge besides my studies
@@emiyakiritsugu6329 let me tell you right now. It is okay to learn for fun but DO NOT SUPPLEMENT THIS FOR UNDERSTANDING OF MATHEMATICS. Tricks don’t lead you anywhere. At that point you are computing like a computer. As u get into higher level math many idiot teachers will try to get you to memorize things without explaining the reasons why they work. The same applies here. It’s okay to have fun or have this as a party trick, but unless you understand the fundamental reasons behind it, you should never use this as an alternative.
@@SortaFresh iam gonna cry 😱😨😭from your huge pressure but i dont use this trick for anything but iam bored in lockdown so i learn this bcoz i want to do this in my head otherwise i will do it in general way thank u for scolding me , it took u forever to type
Only if they follow the syllabus that they're taught! Which is why my mother got fired she never followed what they told her, as a teacher and happened to be one of the greatest not only special education but honor classes for 8th graders, she gave all students inspiration to understand learning she was very creative and everyone loves it
I have to express my gratitude to you for all that I've learned from your teaching videos. I deeply appreciate the relaxed pace and concise yet easy techniques you employ. I have suffered for years from a deep anxiety regarding math. My mind locks and my thought process borders on paralysis when it comes to calculations. Thanks to your vids, that is no longer the case. I can't express adequate thanks to you.
You are definitely not alone in feeling anxiety about math! Math, in general, gives me anxiety, but especially having to do calculations in my head and on the spot! Idk if there’s a “math equivalent” to the reading disability of dyslexia, but I can’t help wonder if there’s a similarity beyond their comparative nature in being “learning disabilities.” I have very little problem when working math problems on paper (or calculators or course), but the minute I’m asked to visualize a math problem in my head, I blank out or “lose my place” as I call it, and end up even more flustered and anxious as I search for a pencil and paper. It’s almost like the part of my brain that requires envisioning numerical symbols is missing or blocked, much like the dyslexic person’s eyes and brain do not connect when deciphering letters in order to read. Anyway, the feeling of paralysis you mentioned feeling hit the nail on the head!
Pretty cool trick. I've always used the method of splitting the multiplication into 2 easier ones and it worked fine for 30 years and counting: 15 x 13 = 15 x 10 + 15 x 3 = 150 + 45 = 195
Difference between 3years and 10minutes am kinda thinking that teachers have a secret conspiracy to torture students and not telling them the easy way thank goodness your a secret agent to come save us right? RIGHT? Lol
What the hell?! All the way through high school and 5 years at uni and I never was shown this technique?! 🤯 It's so simple and intuitive!! I'm actually kinda angry I was never shown this at school.
There are a lot of ways to multiply in your head. The one I found easiest and always stuck with me is to simplify any multiplication by adding together two easier ones. For example if you have 118×210 that is just 118x200+118x10 which is really easy to calculate.
I really struggled with maths at school, and managing to get ungraded in my maths exam, fast forward 40 years to now and I can confirm my confidence has 100% grown
Quick trick for doing a single digit times a 2-digit. I've been doing this for years so I don't have to use a calulator. Ex: 15x6, do 10x6 and 6x5 then add and get 90. The 10 is from the one in (1)5, but it is in the tens place so it acts as a ten, same with any other 2-digit. Then the 5 is from the five in 1(5) just don't multiply by ten for the number in the ones place. Multiply the 10 and 5 by 6 to get 60 and 30, then add to 90.
Lucas Games2193 There will be more to it once you go to middle school and high school. Everything won't be just multiplying numbers. But it's still a good idea to know how to do this.
This boy just learned how to math he's not suppose to know for another two years in his head. Why are you criticizing him? It seems to me as if he has a+ parents if instead of looking up dumb youtube videos he's learning maths and being passionate about them. You're getting riled up by a 9 year old.
Awesome Video! I'm going to share this with my children. I've always done this using multiples of 10. Like for 14x12, I'd calculate 14x10 and add 14x2 to get 168. Your way is easier. Thanks!
Real good method if you can remember the longer method. My method is simpler. 14 x 13 = 14x10 + 14×3 = 14×10 + 10×3 + 4×3 = 182 9×18 = 10×18 - 18 = 180 - 18 = 162 15 × 15 = 10×15 + 5×15 = 10×15 + 10×5 + 5×5 = 225 Basically break down the number on the right to be 10 or multiple thereof and multiply with on left. Work out what remains on the right, and multiply on left. If this 2nd multiply is too complicated, repeat previous simplification. I do similar for the simple numbers i cant remember, by substitute it with a number i do know and the just add. E.g i forgot 4x8 but i know 4x6=24 So 4x8 = 4×6 + 4×2 = 24+8 = 32
I have to say, I'm pleasantly impressed. At first I was skeptical of what kind of method would be presented, since the numbers were pretty low, but the method seems legit. I wasn't content however with not understanding why this works, and I think you really should explain. I deduced where this came from myself using algebra, and I'm not sure if this is how you did this but: (10 + a)(10 + b) 100 + 10a +10b + ab 10(10 + a + b) + ab Above is how I derived the method. If you notice, a and b are the second digits of each number, or what you take away if the numbers are below 10. So the first step in the videos is (10 + a) + b followed by 10 times that and adding to ab. I may be wrong, but dissatisfied by just 'doing' it I tried to find out why and this is what I found. Some may think this isn't a big deal and is just teaching kids to memorise and not think about what they are doing, however I think that understanding why this works, whilst may not concern anything of importance in Mathematics, has a beauty in its own purpose, as it demonstrates how manipulation of numbers can lead to different pathways to solutions. But only with the explanation!
what he is actually doing is writting: (a*b) = (10+X)*(10+Y) = 10*Y+10*X + X*Y + 10*10 = X*Y + 10*( [X+10] + Y ) = X*Y + 10*( a+ Y) or if you add the 10 to Y, you will get: X*Y + 10* (X+b) However I find easier to do the other way (since adding 100 is always much easier): 10* (X +Y) + X*Y + 100 So for example if you have: 14 * 15 .... X=4, Y=5: 10*(4+5) + 4*5 +100 = 190 + 20 = 210 This idea can be done in other "bases" if you call it that way... instead of writting a=10+X, b=10+Y , you can write a=100+X , b=100+Y the result will be almost the same: 10000+ XY + 100*(X+Y) base*base + XY + base*(X+Y) So in base 20 an example would be: 25*26 = 20*20 + 5*6 + 20*(5+6) = 400+30 + 220 = 650 an example containing different "bases" (1000, 300, 100 respectively): 1371* 1420 = 1000*1000 + 1000*(371+420) + 371 * 420 371*420 = 300*300 + 300*(71+120) + 71*120 71*120 = 100*100 + 100*(20-29) - 20*29 = 10000 - 900 - 580 = 8520 going up: 371*420 = 90000 + 300*191 + 8520 = 90000 + 57300 + 8520 = 155820 going up 1371*1420 = 1,000,000 + 791,000 + 155,820 = 1,946,820
Chris X Thanks very much for posting this. I'm less interested in learning arbitrary "tricks" to solve problems, and more interested in learning the real math behind the tricks. This was exactly what I was looking for. All I was taught in school growing up was to memorize patterns to solve problems, like those in the video. But you never learn WHY you're doing it. The way you've shown can be customized based on different problems and shows more of an understanding with manipulating numbers. Thanks again.
For 15x15 you might notice it’s a perfect cube, there’s an easier way of getting to correct answer for squares that end in 5 Say you have 25^2 when we have any perfect cube that end in 5 it will end in 25 always so what you want to do is just take out 5 because we got our first two digits (25) you now multiply your remaining digits (so 2) by one number above it, so 2x3=6 now you put that in front of your 25 which gives you 625 this works for any square that ends in 5 35^2= 3x4=12 add infront of 25 is 1225
@@Rose-oz6lt Ill try to explain it for you. I suggest a pen and paper because this proof is hard to explain in words. Let’s use the example of 56 x 48 = 2688 In this alternative method this would become 54 x 50 +(-18) Let’s turn turn this method into algebra Normal way of multiplying is F x G = H (Equation 1) In this alternative, you use a ‘Base’, which ill call B In this alternative method, You find the difference ( for F the difference is D and for G the difference is E) between the Base (B) and your numbers (F and G). If ‘ F=B+D and G = B + E, then B = F - D and B= G-E (Equations 2) Now we have two equations that both equal the same value, which is B, we can make them equal each other: F - D = G - E (Equation 3) Rearranging F + E = G +D (Equation 4), this equation he says in words at 2:12 to 2:25 With some more rearranging G = F + E - D Now lets bring our original equation F x G = H and lets combine with our previous equations: F x (F+E-D) = H If we Expand: F^2 + FE - FD = H. (Equation 5)Remember this equation as we will come back to it. Now using the method. The first step is to do Equation 4 so lets use F +E (In this example 56 +(-2) = 54 )The second step is to use the Base (In this example is 50) Which we know, in equations 2, is equal to F - D. Let’s multiply these together: Algebraically: (F+E) x (F-D). Expand the brackets, F^2 +FE - FD - DE = Some value (Equation 6) In this example: 54 x 50 = 2700 Now realise something? Equation 5 and Equation 6 look similar. The only difference is the Equation 6 has -DE and Equation 5 doesn’t. What is the last step? ADD DE to equation 6, thus making it equal to equation 5. That is the proof.
To all who think they learned more in this video than they ever did in school: no you didn't. You learned a faster and more efficient way of doing one math concept. Yes, it's super helpful, and I love these tricks, but you can't get to the point of doing these tricks without knowing the basics, which you do learn in school. These are meant to supplement and quicken the process, not substitute the basic concepts.
Me looking through recommended found this, clicked it, thinking to myself I can’t do multiplication, still watching, and learned I just both gained and lost Brain cells...
How does this build number sense? I am very wary of “tricks” that students learn but they have no idea how or why they work. Students need flexibility of thinking in my opinion.
here's how this works geometrically. picture a rectangle 14 high and 12 wide. take two columns off the side now it is 14 high ten wide. take the piece that's 2 wide 14 high and turn it sideways and put it on top of the other rectangle. now it is 16 high and ten wide, except the top two rows which are 14 wide. since they are 4 pieces longer than the others they stick out 4 spaces and there is two of them, so you have 16 high 10 wide plus a little piece that's 4 wide and 2 high, it's easy to see it is 168. this makes it so the "trick" actually makes sense.
I never did that but I saw my classmates always using their fingers in their 9 times tables. Say if I had 9 × 6, well I would do, 6 × 10 = 60. Then, I would take away 6 from 60. 60 - 6 = 54. And I'd have my answer, 9 × 6 = 54.
@@justinparlix5013 I always did the same. Just add something in the question to make calculation nice and easy then subtract the equal quantity from the answer. Making factors also helped me for multiplication with 2 digit nos. Like 97×99 = 97 (90+9) = 8730+873 = 9603
I absolutely love this! How long have I been searching for such a system? Years! And yet it was just a few keystrokes away. Thank you tecmath! You are AMAZING! Your website makes fundamental maths a pleasure.
Absolut brilliant - BTW this seems to be an older methodology . My Grandpa tought me this way of calculation around 40 years ago. Does anybody know its origin?
I wasn't taught exactly like this in school, but similar now that I think about it. 14x12 = (10+4) x (10+2)= （10x10）+（10x2）+（10x4）+（4x2）=（10x10) +(4+2)x10 + (4x2) = 100 + 60 + 8. I'm just so used to writing all this down as opposed to doing it in my mind; never did I think to do the "+4", "+2" thing above the numbers, either. Although it's gonna take some getting used to, you way is much faster. Thank you!
I want to thank you so much for this SIMPLE method, I suffer from mild dyslexia & im not a wizard in multiplication or division, I couldn't figure out for the life of me how I could do every other piece of math in the book in different areas yet my memory wasn't wired to deal with neither operation (im in my 2nd year of college). It was how I was trying to handle it, outgrowing lattice, & tired of the egyptian math, so again I want to thank you not just for me but for ALL OF US because there are soo many of us that feel inadequate being some kind of smart yet having issues handling these two operations. Its truly a blessing to share it regardless of the history behind it! :-)
Hello Tecmath, I figured I would post here since you have responded here before, but I was curious if you have multiplication video. I know you have one for 2 digits, for example, 24 x 12 BUT do you have one with a 3 digit x 2 digit for example 132 x 24 and how to multiply that just as fast if not faster? Thank you for your help, Mr. tecmath.
I have a nephew who hates math because he says it's too difficult. I love math because I was lucky enough to have an excellent math teacher who made learning math fun. You remind me of my math teacher. I am positive that once my nephew watches this video he won't hate math anymore. Thank you 💕
The hardest part with these is not using mental math strategies I have used that work well for these relatively simply problems that may be harder if you use larger bases. Like 9*18. That is really 10*18-1*18 or 180-18 or 162 14*13. Is 140 +14+14+14 or 182 15*15 is 150 and half again or 225 I can see how this strategy works great for harder numbers. But have trouble getting my head to not almost automatically tell me the answer and distracting me from using base 10. I'm trying to think "-1 and 18 is 17... 162. Shut up brain. Okay 170. -8 * 1 'it is 162'... 'I said shut up brain' is -8. 170-8 is 162. 'I told you'" The problem with the methods I mentioned above is that you have to find a good route every time and every combination is different. Multiplication with these base 10s I can get somewhere fast with *10, *11 (1, the second number you are multiplying plus 1, the second number you are multiplying. So if I see 11*12 I know it is 132. 11*17 is 187. 12*17 is 11*17+17 or 187+17 or 204), *15 (*10 and half again). If I can get close to any of those 3, I can add or subtract my way to the correct answer. Thanks to a lifetime of practice double digits it is almost automatic. 44*31 is 440*3+41 or 1320+44 or 1364. But bae 30. +14, +1. That sounds slow but it was pretty much 440. 1200, 1320, 1364. Took longer to type that than think it. But I assume the process for working bases beyond 10 makes that even faster, especially for numbers where you cannot easily find a mental short cut like that. Or at least not need enough practice to know how to find them fast. 44*36 for example would be a bit harder. I'd probably get to 1320 and add 220 (half of 440) to get to 1540. I'm now at *35. Add 44 to get 1584. But again, lifetime of practice thanks to my dad thinking making me practice mental math as a kid was a good way to keep me from fighting with my sister when we'd go to restaurants (must have worked because her and I used to fight like cats and dogs. But not at restaurants). Process for that in my head is I'm doing *30, *5, and *1. So 440, 1320 add 220, 1540, 1584. Takes a couple of seconds. I imagine bases would be faster with practice.
I never memorized the regular times table to begin with (my teacher use to hit me to learn it so I am traumatized). Even though I understand how to do it this way, I'm still slow at it because I have to do the lower multiplication first. Eg. 18x18 ... I have to add 18 to 8 by hand then figure out what 8x8 is then add it to the first calculation. By the time I get to 8x8 I've forgotten what 18+8 is. FML. The journey to getting better at this is most likely a long one. I hope I make it. :(
@TatTvamAsi. Pay no attention to what Ali K says. Math anxiety is a real thing but you can overcome it. Just make math a regular part of your daily studying and don't get anxious when you don't understand something right away.
If your teacher hits you you should sue the school or her individually, when she hit you I hope you asked to speak with the principal, talk to your parents about it and the right decision would be to leave the school, if they do nothing call someone, or a certain company to help you in this situation. Talk to the principal buddy hope I helped
TatTvamAsi likewise. I was taught the way u were taught. We might calculate slower but we will KNOW how to solve the answer without “remembering” math is logic and a universal language. Once u understand the basics and fundamentals, u never forget as to remembering certain shortcuts or techniques
I like the method you teached but sometimes it get me confused idk maybe the way you speak is not what I always hear or understand, btw nice video. Thanks👍👍
i think he’s done it a lot so there are some steps he goes too fast on because he assumes we understand. i found slowing the video and doing the work on paper helped me understand it better so i could do it mentally.
After 60+ years of doing it one way, I still have to remember how to do it this way, and then keep practicing it so it becomes ingrained. I'll stick with the old way, it's more fun figuring out fuel mileage in my head.
Because you are using 10 as a base. 14x17 (+4) (+7) == (14+7) x (17-7) or (17+4) x (14-4) == 21x10= 210 + (4×7) = 238 He simply "adds a 0" because doing the x10 as an extra step is futile.
Because you don't know how the trick work. In school you learn how to multiply, how it works etc... Not how to calculate faster without understand a thing.
