Easy Multiplication Trick you will Actually Use
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- Опубліковано 29 вер 2024
- This multiplication trick is so easy - but you probably don't know it...because it doesn't get taught.
That's OK - youtube and tecmath has your back - with this, the easiest multiplication trick you were EVER taught in school!
Here is THE mental multiplication lesson playlist - progressing you through your mental multiplication.
• Tecmath's mental multi...
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Where were you when I was in school? Silly question I know, I'm now goin' on 82 yo. lol
He was a twinkle in a young boy's eye
GOD bless you Sir!
I'm only 67
70 here !!
Wow..
Another use of FOIL. The way it works is basically writing the number as 10 + x. Then you multiply it, and get
(10 + x)(10 + y)= 100 + 10(x + y) + xy. The reason you just add to the original number is the 100 at the beginning. Factoring it out, you get
10(x + y + 10) + xy, which is basically what you do in the video.
THIS makes me all warm and fuzzy!
Thanks mate I was wondering why this works
Ah yes, the ALGEBRA way
I have a 3 step method. I multiply to the nearest 10th and either subtract or add as needed. As an example, your first math problem, I multiply 10 x 17 . Then 4 X 17. Then add the answers.
if you multiply large numbers well (definitely not me ;-;) then its faster i guess
@@grieferoncamera4600 I'm used to the way I do it. But I need to see the math problem. My memory is terrible.
Yo I came BAKC to tell u thank u so much for helping me since 4th to 11th grade I don’t know what I would’ve done without your channel
This was fun. I learned a new multiplication short cut! Thanks🤗💚
Thanks. More to come.
Thanks. More to come.
Thanks. More to come.
Thanks. More to come.
This simplification and other tecniques should be taught along with the basic methods in every day shooling.
honestly life saver because, the way I was taught in high school was so complex now knowing this I had to look at it more simple.
Your channel is a national treasure.
Maths is easy when you're willing to learn and have a good teacher. Sadly for me I had neither when I started high school.
with the 21x14 and similar it seems really tricky to remember to count to that 11 thingy
I'd rather use the separation method where i multiply the numbers individually as they are, for example
21x14 = 20x10 + 20x4 + 1x10 + 1x4 = 200+80+10+4
you multiply the 20 with the 10, then the 20 with the 4, then proceed to multiply the 1 with 10 and lastly the 1 with 4
basically 21x14 = (20+1)x(10+4)
In this particular example doing it like that:
10x14 + 10x14 + 1x14
is actually easier.
@@pokretny I would dare to say 2x14x10 + 1x14 is even easier, by separating 20 in 2x10, I can multiply 2*14 and then add the zero. It is basically the same thing you did, but I think easier.
you can do it as (20+1)x14 = 280 + 14 = 294
I love all of these options so much more than the vid and seem even easier to understand than the way I had to do it, thank you all and please come with more easy options if there is! These comments are basically the easy math hacks I was looking for when clicking the video!
00:00, holy moly. You got a new mic since 2013. I werent prepared for that sexy voice
You make math easy. Love your channel!
Thanks
Thanks
Easy?! He teaches too fast and doesn't slow down and revise
Thank you! These are REALLY helpful tricks!
So now simple math is becoming instantaneous. Like a gut reaction to seeing expressions. Love this content.
Just found your channel, Brilliant! Today, 50yo, and I finally found out I can enjoy maths! Thanks so much, keep up the cool vids.
You're good. I say that as someone who flunked Algebra 6 times. Luckily, @ 71, as far as I know, I still haven't encountered an algebra problem in real life. I still can't believe they thought it was something we should "practice" and get good at. If I ever have an algebra problem, I'll deal with it on an ad hoc basis.
I just watched your reverso trick for getting some percentages calculated in your head, and now this excellent multiplication trick---BTW, I got them all right. Very cool trick.
I'm subscribed as of now.
GREAT video and great channel, in general. I've watched quite a bit of your stuff in the past and just came back to it a day or so ago.
I've been studying this book called, "Rapid Math Tricks and Tips" by Edward H. Julius.
The hardest thing for me right now is dividing by 2 twice to divide by 4. Usually it's easy; but gets WAY complicated in my head (it's mental math), to do things that end in odd numbers; because they wind up with decimals that tack on extra digits that you have to keep track of.
For instance, divide 54 by 4. Still not so easy; but not nearly as complicated as 55. Divide 54 by 2 = 27... Divide again by 2... keeping in mind that 26 divided is 13; I know that I need 13 + 1/2 or 13.5 to add back up to 27, once 13.5 is doubled. So final answer is 13.5.
I can pretty much keep that straight in my head; but then when you do ODD numbers, and try to take the LOWER odd number rounded down from .5 - dividing any odd number by an even number gives another odd number and then you have to do it again!
So I realized that rather than rounding DOWN to rest at another odd number at step 2, which when divided by 2 will give me both more steps and more digits to have to remember in sequence; I'll just round up to rest at an EVEN one at step 2, and then SUBTRACT half of .5 to arrive at the answer of of the original odd number divided by 4. Always landing me at an answer plus .75 tacked on at the end of the final step.
So for instance, take 95/4. Divided by 2, I think 'divide 94 and add .5 to the answer and double it to check that I'll arrive back at the original original 95 at step 2', and then dividing again by 2. The first part of the answer is 47 +.5 = 47.5... (47 doubled is 94 + .5 doubled is 1 more, or 94 + 1 = back to your original number you started with of, 95. So now, I have to not only divide the 47 in order to get 3 digits; but convert the the last 2 of the 3 digits behind the decimal by dividing them by 2 and remembering THAT! - or .5/2=.25, as well breaking the division of the decimal into 2 pieces and then recombining in the last part of step 3! That's IF I take the lower number. So I make it easy on myself; and rather than dropping down to 47, taking half of that and then adding .25 to that number + another .5; I'll simply round UP .5 to 48, take half of THAT for step 2, which is 24 MINUS .5 (doubled) gives back the Step 2 answer of 47.5. THIS is the point that rounding up or down is a critical decision to make. Rounding down brings you to another odd number 47, you'll divide that to get (much more difficult) brings you to 47 rounded down again to 46 or 23 + .5 + .25 or 23.75. (23 doubled back is 46 and .75 doubled back is 1.5, so 46 +1.5 brings you back to your 47.5)
Rounding down is such a much more difficult process; that I actually messed up when first trying to describe it to you!
But I'd much RATHER round up at stage 2 where I have 47.5 - to 48. SUPER SIMPLE TO CALCULATE THAT... 24; then just reduce by .25 (which came from from the .5 that was added to the 47, which gave you at step 2, the original 47.5 - to arrive at the same 23.75 that you got by the longer and more painful process of rounding down to to 47 from 47.5 at step 2.
So the original problem reads, divide 95 by 4 OR use method of dividing by 2 twice, which will give you, 23.75. Rounding down has more steps and more strings of digits to try and remember, and it's split up by a decimal which is easiest; (still difficult using 4 digits) to split up left and right of the decimal and do calculations separately; and then to recombine later after all's said and done. Whereas rounding up, gives you an easy even number to play with and you just have to remember to subtract half of .5 or 2.5 from the intermediate answer at step 3. Which keeps you from having to deal with remembering decimal numbers 2 more times.
This is a great memory and visualization exercise; but HELL ON TRYING TO DO IT FAST! This bogs me WAY down and I tend to make mistakes.
I'd love to find a better way to approaching dividing an odd number by 4.
Any suggestions?
this helps so much for doing long multiplication in my head. thank youuu!
This is just another thought process for this. Split the numbers into easy math.
7x8=56
56+56=112
112+112=224
224+14=238.
Each of those calculations are easily done in your head. I turned 17 into 16 because it's an even number and I just added the last 14 at the end. Basically you're just doubling easy middle school multiplication. Not saying this is better, but could be another direction for others to understand.
These tricks help me to understand math a little better.
Trying to encourage my kids to use your methods.
"Thats a great trick right?" Is iconic at this point
From Steve. I learned a lot from you. Thank you very much. Cool
Couldn't figure out the third one had to let the video play so smart💯😎
Thanks for the amazing video
Loved you every videos ❤️
Best math teacher ever.
Great math teachers make it look easy. Well done.
Excellent! 👏🏻👏🏻👏🏻
Nice. Thanks for this. It's been quite some time since I last saw your video.
Ah. Check some of the newer ones out. And welcome back!
@@tecmath thanks man. Sure will
love you bro that helped so much
So clever thank you
You honestly do sound like Bruce the shark from Finding Nemo LOL. Awesome trick thank you! Practicing now!
This comment is for you to feel all fuzzy and warm inside. wish you the best wishes man.
This is really interesting. Do you have a rigorous proof for this method?
Thanks mate!
Awesome man, You're awesome
Do more using odd numbers.
Nice Videos... thanks
This guy is Amazing
This is a very good and helpful channel. In this case the examples (each having at least 1 ten) weren't so difficult my usual way (e.g, 21x10, then add 21x4 ), so not much speed difference, but i'll try it with other examples..
thanks
Your the best
Long story short, the FOIL Method:
F=first
O=outer
I=inner
L=last
14x17=?
10x10=100
10x 7= 70
10x 4= 40
4 x 7= 28
-------
14x17=238
dude this is perfect
really handy
and yes guys no cap no clickbait
its really handy
srew your calculator if you have this
Can you do the same thing with the number 99? Such as 99 × 25.
Why does this trick work? And what are the limits to it?
I have an easier way to add 15x 18 divide 18 x 2 and then 15 multiplied by 2 and the multiply 9 x30
Subscribing to your channel makes me smarter already, lol!
Sheer genius!
Yo thanks so much!!!!!
hi is this applicable only in two digit number having number 1 digit in both numbers?
Vedic maths👍🏻👍🏻
mind blown
Bloody smart arse! Is this based on Ayervadic maths?
nick loves you
OK. I got 3 out of 3. No problem. If I change the last one to 31 x 14 I get the right answer. But if I change it to 31 x 64 ((64+21)*10)+(21*4) I get the wrong answer. Ditto for 21 x 64 ((64+11)*10)+(11*4). What am I missing?
Why didn’t our math teachers teach us this back in the day? They wanted us to do it the long way.
because this way doesn't encourage any understanding
You da bomb!
Nothing more confusing for a kid than getting marked down in a test. even though the answer was right, I had used the wrong way of working it out.
Aaargh why can't I make this work for 34 x 31???
Try doing it like so move the 1 from 31 to other side then count in your head 30 times 35 that equals 1050 if that was hard also move the 0.
3 times 350 should be easier. Then count 1 times 4 and add it to 1050 and there 1054 you got your answer
Since neither number contains a 1 in the tens place, we will have to find the distance from 10 for both of them. 34-10=24 and 31-10=21. For the first part of the method we add 24 from the left side to 31 on the left which gives us 55 and then put a zero on the end, giving us 550. For the second part of the method we multiply 24*21=504. Adding 550 and 504=1054. However, Morgur's method is probably easier, since it let's you work with round numbers. Much easier than having to do 24*21 as a step.
So does this only work with teens? How would it work for 20s, or say a 10s x 30s?
Him: Solve this in 3 seconds.
My brain: Don't even bother.
Me too
Fax
Good for you.
😂😂
To me this seems fairly difficult to do still. I always just simplify the equations looking for the easiest way to do so. For 21 x 14 that means first calculating 20 x 14, which is 280, and then simply adding another 14 to get 294. For the 15 x 18 I just calculate 15 x 20, which is 300, and then deduct 2 x 15, which is 30, to get to 270. Now the last one seems to be the most tricky, but it really isn't. Just start with 10 x 16, which is 160, and then add 48 (3 x 16), which accumulates to 208.
28 tens plus 1 ten plus 4... so 294
15*18=180+90=270 how is this? You should use common sense and apply..
My method: 21 x 14: multiply 2x14 = 28, therefore 20 x 14= 280. Then add one more 14 = 294. Easy!
I definitely use that for numbers that are close to a multiple of 10, such as with 21 and 14. But for 17 and 14 I'd rather use this method than 20x14 - 3x14.
@@InsatiableMonkey Breaking up a single number is the standard way to do it, but is harder to mental math for most people.
the best way
Thanks !
Thank you 😊
After 12 years you still upload. What a legend.
I feel so lucky i found this legend when I'm still in school. You really did made me LOVE math. Thank you SO much! I feel like I'll owe you forever.
That’s straight from the soul. Full on!
@@ohm1945 i hate you
@Elisya 78
Thanks,… I think.
I suppose any sort of acknowledgment is good acknowledgment.
Peace Elysa 78
What yr r u in?
for one's with a small digit, like 21 x 14, I just do 20X14 then add another 14. If it was 19X14 then it's 20x14 - 14. You method is nice for the "middle sized" digits.
That is a good way of doing it. Thanks!
Yeah I did 15x18 as 15x20-30 to get the 270
That is the way my brain works too. Seems easier.
@@BigAlCapwn That’s a good method. Other way of showing this is transforming the 15 into a 10 + 5, leaving you with:
18(10 + 5)
Multiply every member of the parenthesis, 5 is basically 10/2, so you can calculate 10 first by ading a 0 to 18, and getting half of that for 5
180 + 180/2 = 180 + 90 = 270
21x14=2.1x140. So 2x140=280 then as +0.1 = 1/10th add 14 to 280 which is 294.
This is amazing I forgot I subbed to this channel
Thanks mate. Hope you liked the trick.
@@tecmath it was great
It's annoying videos you're subscribed to don't get recommended to you.
@@Onmysheet ikr
@@Onmysheet just turn on notifications
Absolutely superb. Why was I not shown this in school. You’re awesome!
Math has always been like a fun puzzle to me (I’m 71) so this is really great. Don’t remember how I stumbled across your channel the other day but I’m sure glad I did.
When I took Freshman Algebra in 1963, I had had no Algebra or Geometry in Grade School, as in 8th Grade we were still doing Basic Math. Half the HS class took Basic Math and we were only required one yr of Math to graduate, No summer school prep class, no after school tutoring, no bookstores full of math help books especially on how to solve word problems (Kumon Math, Painless Math). My parents hadn't gone to HS so they couldn't help. I made a "D" for the year & was told I couldn't repeat the class, even by just using my Study Hall period the next yr and not changing the grade. No, No, I was now in the Secretary/ Home Ec tract. Thankfully, there is a world of help today to learn math.
Absolutely fantastic videos! Love learning something new or a new way of doing things through them. What would you do for something like 52*26 though? Many thanks.
Yes that's my question as well...was trying to do 47x26 and got a completely different answer, then i tried doing your 52x26 and again got a different answer....HELP tecmath!!!
Same concept just a little different,
First 52 + 6 = 58
58 x 20 = 1160
Difference between 52 and 20 is 32
32 x 6 = 192
1160 + 192 = 1352
I'm enjoying these. We're trying to get a 3rd grade student interested in math using your methods.
Is he interested?
An explanation of why this works, using algebra:
(There is a better version using geometry, but it's hard to draw in YT comments; if you want to find it, draw a rectangle with sides of 10 + 7 and 10 + 4 and rearrange the resulting small rectangles).
14 x 17 = (10 + 4) × 17
= (10 × 17) + (4 × 17)
= (10 × 17) + (4 × (10 + 7))
= (10 × 17) + (10 × 4) + (7 × 4)
= (10 × (17 + 4)) + (7 × 4)
= 210 + 28
= 238
The thing you want to see here is that the rearranging depends on those 10's being the same, but they don't specifically have to be 10's, that's just what makes the multiplication easiest.
To build on this, here's an example (I'm using the same units digits so it's easy to see the parallels, but it works with any units digits):
34 × 37 = (30 + 4) × 37
= (30 × 37) + (4 × 37)
= (30 × 37) + (4 × (30 + 7))
= (30 × 37) + (30 × 4) + (7 × 4)
= (30 × (37 + 4)) + (7 × 4)
= (30 × 41) + (4 × 7)
= 1230 + 28
= 1258
This is easiest when both numbers have the same 10's digit, but not necessary, like the last example in the video. For example, if you want to do 53 × 49, you can do:
((49 + 13) × 40) + (13 × 9)
= 2480 + 117
= 2597
Your "units digit" for 53 here is 13. You can also get fancy and think of 49 as 50 with a "units digit" of -1 and use the trick just like I did with the 30's but with 50 instead of 30:
[(53 + (-1)) × 50] + [3 × (-1)]
= (52 × 50) + (-3)
= 2600 - 3
= 2597
If you're okay with negative numbers this is often going to be easier than using "units digits" that are actually two digits.
Not a bad trick, I have to say. It's a smart rearrangment to make multiplication easier by always doing as much of it as possible by a multiple of 10. Thanks TecMath :-)
Multiply 10 x 14 mentally, double it then add 14 to it. Fast and easy.
For my trick, I always used the tens trick, just take 17 by 10 plus HALF of 17 by 10 minus 17, so 17*10 + 0.5*17*10 -17 = 17*14, it seems complex by the eye but when you actually do it it's quick and simple
I'm getting this the way you explained 10x14= 140 double 280 plus 14= 294 can you elaborate on this Thanks!
@@TributeHurrikane It’s easy to multiply by 10 mentally. In the arithmetic problem 21 x14, I choose to multiply 10 x 14 two separate times and sum the two because it’s fast and easy. It’s also easy to add 14 to the result. It goes like this, 10 x 14 =140 x 2 = 280 + 14 = 294. This works well with most problems similar to this one. Multiplying by 15 could be done by multiplying by 10 first then taking half of that answer and adding to the first answer. For example, 15 x 25 = 10 x 25 = 250 + 125 = 375. Best of luck.
@@ba0700 Thanks that make sense math was not one of my favorite subjects.
You know what's magic? Your VOICE. So easy and pleasant to listen to. You look really great on the radio, as they would say back in the day.
Thanks. I have a great head for radio!
@Strat Abuser It means he looks good on the radio. The amplifier might be up to high on the Strat.
@Strat Abuser You are so lucky to have a Strat - wish I did!
I always thought it meant it was saying the person was a bit ugly... that is - they have a great head for radio - in that you can't see them!
@@tecmath That's exactly what it means-in addition to having a great radio voice. And yes, I, too, look fabulous on the radio!
Whenever I multiply 25×36, I get 540, whereas the answer should be 900.
Why so??????
Patience. Future videos will deal with these types of questions.
Try ( 20x 36) +( 5x36) i.e. 25 x 36
720 + 180
900
If only you were my maths teacher at school…maths would’ve been a lot easier and more enjoyable…thanks! 😎
You were probably taught FOIL and regrouping in school which allows you to DERIVE these tricks. He isn't really teaching fundamentals, but a limited-use trick derived from fundamentals without mentioning how they were derived. I don't mind teaching these exist, but I'd pause to let people know they exist and maybe give a few examples of degrees of usage rather than dwell on something that calculators make trivial.
@@lapurdy71 Fair enough....but doesn’t really matter. If the penny drops....aim achieved!
Yes, but even he is our elementary school math teacher, he still has to follow board of education teaching guidelines, and can't teach math tricks like these during regular math classes.
This is really weird for me to watch because when I was in 5th grade this is the way I figured out on my own how to do multiplication... I was never taught to do it this way I just used common sense. That was many moons ago and now I am 60 years old , So this is nothing new to me. I quit school in 1977 and I am a better person for it... They were slowing me down.
You also invented the wheel right?
tectmath has break the career of our math teachers, btw thank you so much for this video!
thank you so much for these! I just started college and wanted to do some deep research and tutoring on math, this channel is AMAZING! God bless you and keep up the good work!!
I tried 14 x 21= 250 +4....=254....what is the trick here? So if it is 21....i have to use 11...? And if it is 41 I have to use 31?
Yes - you're not just taking the last digit, you're subtracting ten from the whole number
We learned the slow dumb way and still can’t multiply without a calculator
That's because math is a b#### unless you have your basic multiplication table memorized (up to 10^2) once you have that table memorized and know a few tricks like the tens trick it becomes tremendously easier, all you gotta do to memorize that table is write it down a few times without copying anything, including calculator, and eventually you'll memorize it
also if the number haves like one or two numbers diference from a tens part like 19×21 you multiply the first one that is 19 by 10 so 190 and multiply by the tens part of the other one so 21 without the 1 and its 190×2=380 and you add 19 to 380 and 380+19=399 so 19×21=399
Fantastic tricks as usual, you’re so shrewd my friend, also, your videos are informative with clarity and fascinating, that I love the video so much, excellent work!
Thanks mate.
I actually found the third one to be easier, at least for me, if l did it this way... 21 X 14: 2 X 14 = 28, add 0, 280, then add 1 X 14, or just 14 = 294 ;)
Another example would be 35 X 13: 3 X 13 = 39 add 0, 390, plus (5 X 13) 65 = 455
Thank you for teaching me this it’s making my timestables so much easier 😊
Hi Mr techMath my solution 14x10=140; 14x7=98; 140+98=238 simplest ways.
Now they teach math in schools that are "easier", but also don't work with any complex math, this is even easier and works with complex math.
I must be doing something wrong here...
Q1: 13 * 27
(3+27) * 10 = 300
3*7 = 21
300+21 = 321
But the correct answer is: 351
Help!!!
Love this series though! You have a mellifluous Aussie accent!
Me too, while I multiply 25×36, it gives me 540, while the answer should be 900....
Have patience. New videos will deal with this.
@@tecmath it would be good to at least know when or when you can not rely on the fantastic method you described otherwise we won't have confidence to us it. Be good to set the terms of use.
Damn! I gotta sub to this channel. This is very helpful knowledge.
I knew amazing content coming up.....that’s why I subscribed to your channel. Good work
Thanks.
@@tecmath 👍
At school we had to memorize the multiplication table not just to 10 but up to 20. Since I wasn't very good at memorizing I figured out precisely this trick so I could calculate the answers on the fly.
Isn't it all fun⁉️
Thank you for the tips and tricks! But for my own issues, I'll still do the long form. Maybe not in my head, but definitely on paper if available, or on a calculator. Please keep this good stuff coming.
This is the third video from this channel that I whatch, but honestly, I can barely understand what he is saying.
This is the problem I've always had in school.
Everybody else(in the comments) always understands, and I'm still left confused as the teacher continues.
I'm convinced I have a learning disability. 😐
This was my problem is school. For some reason numbers just confuse me. If I don’t write it down I forget the previous numbers.
All I did in those first 3 sec was panic but this video helped
I see the same look of panic when I ask a student even simple questions. Math teachers seem to do that!
I didn’t understand what you meant by how far the third problem was from ten until you showed it in process. Now that you explained it, I need three more problems to know if I learned it.
Thank you. I’m dyscalculic and struggle with keeping any numbers in my head, so tricks like this do help because it shows me what is going on with the numbers-that, I can do: comprehend. It’s the calculating that fumbles.
Last one was way to complicated. 20x14=280+14=294.
In the last example there is the consideration of how far the 10’s are above 10, resulting in the addition of 11 and 14. Might one just add the number on the right and the one’s column on the left, and simply replace the numeral in the 100’s column with the numeral in the 10’s column of the number on the left? This saves addition “of the 11 and 14” by just operating the procedure as before, and doing this replacement instead...
..still testing, I see if the 14 were 19, it would advance the 100’s to 3, which would require a rule to consider the 9 differently...so...yeah,, the investigation continues...
21 x 19
Is 21+ 9 = 300
11 * 9 = 99
Ans 399
I don’t know how to do for example 21*22 I tried it with 11 and 12 as the gap between 10 and I was way off