I did exactly the same and thought "what is the big deal?" at first, but the method in the video IS superior as it is immediately obvious what 75% of 4 is without doing any extra division and multiplication steps in your head.
4% of 75? Well 1% of 75 is .75. Multiply that by 4, you get 3. 32% of 25? 10% of 25 is 2.5. Multiply that by 3, you get 7.5. 1% of 25 is .25. Multiply that by 2 you get .5. Add together you get 8.
That is exactly how I do it 99% of the time. It makes me laugh that the gen Z kids I deal with CAN NOT figure it out without resorting to their phones.
@@That_Stealth_Guy 99% of the time? Well 90% of “the time” is “the tim”. 9% of “the time” is “e”. Add together and you get “the time,” so yeah, just about all the time.
Math has always been challenging to me. The content of this video is very helpful to me as I was not taught this in elementary school like some of you have commented. At the age of 70, I continue to struggle with many mathematical concepts and appreciate this video. I'm a whiz in other subjects, but math tests used to make me cry with frustration in school. I spent 10x the amount of my study time with math as my other subjects and put forth my hardest efforts just to pass tests. Any shortcuts are valuable to me. Thank you.
Instead of swapping the % you can also multiply one side with a handy number and divide the other side with the same number to simplify it. 18% of 50 (/2,*2) = 9% of 100 = 9. 4% of 75 (/4,*4) = 1% of 300 = 3. 32% of 25 (/4,*4) = 8% of 100 = 8. 15% of 20 (/5,*5) = 3% of 100 = 3. Even 23% of 52 (*4,/4) = 92% of 13 = 100% of 13 - 8% of 13 = 13 - 1.04 = 11.96.
@@bobross7473 The percent swap is the exact same thing with a factor of 100. My take is that it does not have to be 100, it could be something more convenient.
@@cristinacu2286You meant to say 23*52/100=1196/100=11.96. If you do 23/100*52 you get 0.23*52 (if we assign multiplication and division the same prescedence and read from left to right) which doesnt help in any way.
I have considered myself a math nerd my whole life (over 70) and never realized this until my PhD son pointed it out to me a few weeks ago. Sure--seems simple ... once you KNOW it! Thx, Presh!
I’m a CPA. I graduated with my undergrad degree in 1969 (Accounting major, econ minor). The very first year, amongst other math, we had an extremely simple Business Math course… rule of 72s, transpositions divided by 9 and all that stuff. It was a one semester course.nLearned so do many tricks. This commutative function was learned in high school algebra but it was reiterated in this easy business math course.
We live in an age where people, who were taught the commutative property of multiplication in school, need to be told by the press about the commutative property of multiplication.
Used to be able to memorize times tables all the way to the triple digits, now i use a calculator to add single digits but i can also solve many calculus question in my head. Just because a skill is simple and basic does not mean everyone can or should maintain that skill
At least in the US, math education is generally terrible. It is presented as a set of seemingly arbitrary and arcane formulas and rules that have absolutely no connection with anything in the real world. Kids don’t learn it, they just temporarily memorize enough to pass the test and move on. Then as adults, in the years and decades to follow, they discover that there is actually a lot of real world application for that knowledge they discarded. If they even remember having learned it in the first place. You can’t entirely blame them, though. It would be hard to make a subject more boring than math *as taught in school.*
@@kenrickman6697 I'm convinced the problem is that math teachers are mostly people who love math and find it rewarding for its own sake. While people who love the application go on to do other things than teaching math. If you find math easy and you love doing it, you probably shouldn't be teaching it. Which is kind of a sad paradox.
i think its not so much a trick as it is an understanding of sufficient depth of what x% of y means. as u showed its literally just x/100*y which u can write any way u want that makes it ez for u to calculate: like y/100*x or yx/100. from my experience its that people dont exactly understand that 4% means 4 out of 100 ect.
@@underscore5673 I think you hit it. The reclassification of the problem as basic multiplication and division, and then applying all the tricks you have about multiplying and dividing by 100.
Yes, absolutely correct. These equations can be solved doing quick math without switching, and as is demonstrated, it's not always easy using this switch method nor does everyone know percentages or division, but they do know multiplication and decimals (better). It's just as easy to work it out with this method without switching, than it is with the first method, especially when the numbers aren't easily divisible or the percentages aren't obvious.
When I went to school in the seventies, we were taught what "x% of y" actually implied and how to calculate it with the formula xy/100. We also knew that xy=yx. I would definitely grab a calculator now to get some percentage. The problem are those who know the right keys in the calculator to get the result, but have no idea what they're doing or why.
This reminds me of what someone said about maths that made me laugh. Most people from the past knew algorithms and could get the right answer, but don't know why. Later schools discussed math theory, so many people were getting the wrong answer but they knew why it was wrong. Today many use calculators, but without them they can neither get the right answer or know why.
An easy "trick" that only works for a handful of numbers that are either multiple of 10 or 25 ain't much of a trick, that's just an obvious shortcut. Internet blows out for this means no one takes a proper look at their math. Okay, that'd be faster for "37% of 20%", what about "33% of 39" or "21% of 44"?
On harder percent problems, you sometimes have to break up the percentage or the number into sum or difference of nicer ones, then use distributive property...: So, for 21% of 44, we can see 21% = 20% + 1%, so that: 21% of 44 = (20% + 1%) * 44 = (20% of 44) + (1% of 44) = 2 * (10% of 44) + (1% of 44) = 2 * (4.4) + 0.44 = 8.8 + 0.44 = 9.24 With practice, this can be done mentally (if one doens't have paper-and-pencil). The hardest part, for me, is holding the numbers in my head and adding CAREFULLY so as to line up the place-values!
Have you ever head Arthur Benjamin Franklin, he is also one of the human calculators with a few ted talks. He has written a book titled secrets of mental maths which is full of exercises to develop sufficient speed in mental mathematics. I would recommend this book if you are interested in mental maths.
33% is roughly 1/3 1/3 of 39 = 13 That's a good estimate Actually 1/3 is 33.33 So 13 - 0.13=12.87 that's the exact answer It consumed half a minute to figure this out but still doable in head.
I never learned this in school, but knew it anyway...if the number is less than 100, put a decimal point in front of it and multiply by the other number. Example: 5% of 63 = 5 x .63 = 4.5. If it's more than 100, divide the number by 100 and multiple. Example: 7% of 130 = 7 x 1.30 = 9.1
I did the thumbnail example by dividing 100 by 4 to get 25, then dividing 75 by that to get 3. That took only 5 seconds or so, but simply switching the numbers and taking 75% of 4 is even faster. I'll have to remember that. I think that I learned it at some point long ago, but obviously forgot it.
1:33 I figured it was 9 within seconds without using a calculator. I turned the 18% into an easier percentage 20%. 20% of 50 is 10. I need 18% which is 2% from 20%. 2% is 1/10 of 20%, which got me 1. 10-1=9 Sometimes, there are multiple ways to solve a problem. Though some may be more complicated than others.
Yes, absolutely correct. These equations can be solved doing quick math without switching, and as is demonstrated, it's not always easy using this switch method nor does everyone know percentages or division, but they do know multiplication and decimals (better). It's just as easy to work it out with this method without switching, than it is with the first method, especially when the numbers aren't easily divisible or the percentages aren't obvious.
Nice trick. Great video too, I just love math. However the old trick of dropping the percept sign and moving the decimal two spaces is easy enough to do in my head.
One of the things I've thought about... If I went back in time and got to meet the great mathematicians of the ancient world, either hand them a math textbook or just give them a brief overview of our number system and notation. Imagine what Archimedes or Euclid could have done if they had our notation??
I literally knew this ever since i was taufght about percentage in school back in 7th grade. My teacher was explaining about percentages like how % means out of 100. He gave us some problems to solve and while solving the problem i realised that we could exchange the % of the first number with he second number, i.e. x% of y=y% of x. After this, I tried it and saw that the answers were correct, so I asked my Maths teacher to see if I was correct and he seemed quite surprised upon realising that x% of y=y% of x. I still feel proud for finding this out especially after watching this video and fiinding out that 99% dont know this trick.
Sitting through so many simple examples gave me the worst memories of infant school maths class but thanks for redeeming it with that bit of history. Watching an expert with an abacus is amazing, though. The boast was always that the fastest of them could outpace a calculator. You'd still see an abacus in some of the shops when I was growing up, and we learnt how to use them in school: a pretty solid way to visualise arithmetic. But whatever one thinks about the skill needed, the abacus definitely doesn't print receipts, so...
Here is a cool trick that gets us close to 23% of 52. 23% is very close to 3/13. Then 3/13 * 52 is very nice because we can simply the fractions and get 3 * 4 = 12. By knowing decimal approximations for just a few fractions, mental arithmetic can be surprisingly easy (sometimes).
@@SportsShowcase003 It is close, but not exact. The decimal approximation is 0.2307... Knowing the approximation meant that I could estimate a value of 12 quickly, but did not get me to the exact answer of 11.96.
Actually, I did the 'trick' first, as it was simpler - 23% of 52 -> 52% of 23. 52% is close to 50%. 50% (1/2) of 23 is 11.5, so 52% is probably "about 12, give or take a bit". And sure enough, 11.96. Interestingly, using your way, I'd've probably said 23% is close to 25%, and 1/4 of 52 = 13, so the answer is probably somewhere between 12 and 13, and my estimate would've actually been worse.
@@matthewryan9323 Nice. Maybe the easiest way is to find 25% of 52 and then subtract 2% of 52. That would work and be pretty quick. However, planning all of that pre-work before actually solving the problem probably defeats the purpose of a shortcut.
@@jeffreyvetrano5836 Yeah. It's something that might be more helpful if you're just trying to get a reasonable estimate, if the numbers work out 'nicer' one way for you than the other, swap 'em.
Years ago, I worked out an easy conversion for Centigrade to Fahrenheit that isn't too difficult to do in your head. I am wondering if this procedure is well known. The procedure is to double C, subtract 1/10 of the doubled amount and add 32. Example: C=100: 2C=200 2C-(2C/10)=180 2C-(2C/10)+32=212 This works for the following reason: F=C(9/5)+32 But: C(9/5) = 9C/5 9C/5 = 18C/10 18C/10 = (20C-2C)/10 (20C-2C)/10 = (20C/10)-(2C/10) = 2C-(2C/10) Therefore: C(9/5) = 2C-(2C/10) And: F=2C-(2C/10)+32
Alternative way 18% of 50 10% of 50 is 5 obviously Because 10%x10=100% So 5+5 =10 And since it's not 20% but 18 we need to remove 2% which is tenth of 20% so now 10-1 =9
I do it just as well without this trick. Simple multiplication of the parts, often ignoring tens values (zeroes or decimals); add them together; then consider reasonableness. Examples: - 18% of 50: multiply 1 times 5, and remember 5; then do 8x5 for 4; add them for 9 then consider whether it's reasonable. - 4% of 75: 4x7 for 28; 4x5 for 2 (ignoring the zero); reasonableness tells me it'll be a low number, less than 4 because 75 is less than 100, so 28 becomes 2.8 and 2 becomes .2 and the answer is 3. Again, the key is to ignore the true values (in factors or multiples of ten). - 32% of 25: 3x25=75, and 2x25=5; A glance tells me the answer is about a third of 25, so working with 75 and 5 gives me 8. - 15% of 20: 1x2 and 5x2 gives me a 2 and a 1, so the answer is clearly 3. So easy. Alternatively, seeing this one as 10% for the 1 plus 50% fir the 5 (again, ignoring the tens value) gives me 2+1, for 3. - 23% of 52: At first glance, I notice that the answer will be just under 13 (because 23% is just under 25%, and if it were a quarter, the answer would be 13), so I have my reasonableness already worked out. Next, 2x52 gives me 104, and 3x52 gives me 156; Now I simply add them, being mindful of the tens: 104+15.6=119.6. I should say this is similar to how I multiply any two-digit number by any 2-digit number in my head almost instantly. I just see the answer with little or no thought.
@4:55, for 23% of 52, the trick doesn’t really help you. Sure, you can switch it to 52% of 23, then find half of 23 and 1% of 23 the way you did. But you can also skip the swapping trick altogether, realize that 23% is 25% minus 2%, determine that one-fourth of 52 is 13 (as anyone who has ever played cards knows), then determine that 1% of 52 is 0.52, double that is 1.04, and 13 minus 1.04 is 11.96. You’ve reached the same answer, with math which is equivalent to what was used in the video, without having to mess around with the swapping “trick”, thus saving some time and effort.
This "trick" is actually about which number I multiply by the other one more kindly and easily during multiplication, which is commutative. I prefer to multiply the larger number by the smaller one, or an "irregular" number by a more "regular" number (=e.g. a number ending in 0 or 5, an even number with as many divisors as possible, etc.).
You actually do learn this trick if you learn foundations of math. Once you understand how numbers interact there are all kinds of shortcuts available. Too bad most people think math is boring.
Something related that's kinda interesting, so percentages are a fraction right, n% being n/100. We can find the specific percentage of any number just by changing it so that the denominator is the number we want the percentage of, the numerator becomes the percentage we're looking for. Going back to 18% of 50, 18% is the same as 18/100, which is also 9/50. We get the percentage we were looking for with 9 being the numerator and both the denominator and numerator ends up 50% of the size they were in the original fraction. Of course this works with other fractions as well. 15% of 20: 15/100 = 3/20 Both are 20% of the size they were in the original fraction. 4% of 75: 4/100 = 1/25 = 3/75 Both are 75% of the size they were in the original fraction. 52% of 23: 52/100 = 1196/2300 = 11.96/23 Both are 23% of the size they were in the original fraction. Though of course it's not as elegant with certain numbers, tho you can always get there by multiplying both with the number you want the percentage of and then dividing them by 100. I feel like I had something else I wanted to add but forgot, but yeah this kinda made me understand how switching the percentage and the number we want the percentage of makes sense.
Personally I just multiply y by x and divide the answer by 100. It's a little more brain work, but consider your example: 23 × 52 = (23 × 10 × 5) + (23 × 2) = (230 × 5) + 46 = 1150 + 46 = 1196 1196 ÷ 100 = 11,96 That's how I compute it off the top of my head. Additionally 23 × 50 could be further simplified down as (20 × 10 × 5) + (3 × 10 × 5) = (200 × 5) + (30 × 5) = 1000 + 150 = 1150 However unless I deal with thousands upon thousands and desire accuracy, I find simplifying time consuming. Anyroad, head calculation took me about than 20 seconds, that's fast enough for me. Much easier to do than roots for example.
There is another way to do this in your head To find 10% divide by 10 To find 1% divide by 100 Then you can add or subtract to find different percentages (eg 4% is 1% x4) So say you are trying to find 18% of 50 First find 20% 50÷10x2=10 Then find 2% 50÷100x2=1 Then take away 1 from 10 (20%-2%=18%) to get 9
If you mix decimalisation with fractions that might be mental arithmetic but it is a mental way of doing things - the easiest was is to multiply the two numbers and then adjust for the decimal point - 80% of 80 8x8 is 64
easier is to just go to 1% or 10% or any easy number just select matching for easy divide 5%=x/20 20%=x/5 25%=x/4 50%=x/2 depends, and use addition there is 1% from 52=0.52 x 23 or just change to 0.5x23 + 0.02x23=11.5+0.46 4% from 75, so 1% is 0.75 x4 is just 3
To be fair, most of those examples are easy to calculate even without this "trick", but it's still very good to know. WHY DIDN'T WE LEARN THIS IN SCHOOL. I remember an enthusiastic maths professor mentioning how we can easily remember certain formulas. It was incredibly helpful, but of course not part of the standard curriculum. Why can't we make things easier.
A trick I learned is multiplying the number by the percentage and dividing by 100. ex: 4% of 75 ->75 times 4 divided by 100 = 3 23% of 52 -> 52 times 23 divided by 100 = 11.96 Most of the time you’ll need a calculator to do this but everyone has one on their phone, right?
As a math teacher, the problem with this is that kids don’t know their percent-fraction equivalencies so this would make NO sense to teach as a strategy. It’s a perfectly fine strategy for people who DO know those equivalencies, but what makes more sense to teach is converting percents to decimals correctly 100% of the time, and then multiplying. Especially since secondary students in most US states are required to use a calculator on their standardized tests.
The best way to improve mathematics is to use the Base Twelve system, which has twice as many even factors as Base Ten, namely 2,3,4 and 6! We decided on twelve months in a year, for example, possibly because there are 12 "moons" in a year which then allows us to divide the year into 4 seasons each made up of 90 days each (plus change). Everyone thinks to count on their fingers when growing up as in 5 on each hand, however if you leave off your two thumbs you now have four fingers, each with three segments which add up to a total of twelve on each hand! The Dozenal Society in Great Britain has already designed a system which takes advantage of this by using numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, X, E (the last three named dek, el and doh (long o) to get to twelve, then start over with dudek, dudek unu, dudek du, etc. We already use dozens all over the world, so why not make the math this much easier?
"Of" simply means "multiplied by". You don't need to worry about the decimal place for now because you know it's going to be in single digits. Another way of multiplying something by five is thinking of halving (ie "0.5") and moving the dp one place to the right. Either way, any product containing some form of 18 and 5 is going to contain 9 and possibly some zeros - in this case none.
Thanks for the extra history. When I do tipping here with a tax rate of 9 percent, and I want to give a 20% tip on the pre-tax amount, I just multiply the bill before tax by 3 and divide by ten for the tip and tax. Thus a 100 dollar bill will be 109 with tax so 3x100 /10 = 30. Total cash given is 130 with a 21 dollar tip. No I don't tip on the tax. Tax is a tip to the city! :D...but as an aside, all the new computers are set up to tip on the total....that is a whole nuther thing going on!.
Here's the long explanation: I use the 10% and 1% Rule, then work my way up -- however, my math is slightly different from what was given here for the question of: 4% of 75. I know that 10% of 75 is 7.5, however, I just step down one more decimal space to 1%. So, I then know 1% of 75 is .75. Since .75 + .75 = 1.5, I then know that 1.5 + 1.5 = 3. That kind of math I can quickly do within a few seconds in my head; I can think this way far faster than I can in explaining it here. However, once you get the hang of this way of finding the answer, you too can begin to do it quickly this way without a pen/pencil & paper. However, I am betting that most of the people who watched this video already knew the answer and use a similar or unique version that helps them solve the answer, and I am then only 'speaking to the choir.' Perhaps like many of you, you too may the one often asked to calculate the tips and sales discounts for your partner/wife Like I do for mine. Anyway, that how I've been doing it for years in my head... not perfect, but it works.
When I was 12 I lived in France. Geometry and algebra were part of my curriculum. Four years later I returned to the US where my classmates were just beginning algebra.
1:00 Most of of us can figure it out in our heads,. At least most of us watching this channel. Figuring out a percentage of any number that is divisible by five is so trivial as to be ludicrous
The commutitive property of multiplication isn't enough here. You have "x / 100 * y". You gave to commute the division and multiplication first. And if you do that just stop at (x * y) / 100 and start simplifying the fraction before multiplying what remains.
Presh - the thing I learned along these lines a long time ago that makes it even easier (in my mind) is to always see the "of" as multiplication and essentially ignore the percentage by moving the decimal two places either in the math or in the answer - whichever makes it easier. I see "50% of 18" as 0.5 x 18. Same thing you are explaining, but the step is automatic.
When Fibonacci introduced Arabic numerals to Italy it was rejected at first, until the bankers started using them. It still took a long time for others to adopt them.
The OP was making an interesting connection with what was said at the end of the video, about how it took society some time to accept Arabic numerals instead of Roman numerals. No reason to berate them, just a fun little tidbit. One which was news to me and greatly appreciated!
1:39 I have another way, just divide something by 100 to get 1% of it and then multiply it by the number of pencentage you want, only multiply by the number, not including the percentage thingy.
When i was un School, my teacher taught me lots of tricks. Now, as a private teacher, i also teach these tricks. :) I love that math is getting viral around social media ❤
We now live in a time controlled bu gagets. Children are no longer thaught to think but are only learning to press buttons. I am 76 years old and did my schooling in Malta back in the 1950's and early 1960's. percentages and decimals were all thaught without gagets then. I t took time but you learned to tyink and solve any problem. All you needed to say is that that it is a simple fraction to solve. I'm on a comtuter so I'll use a (/) for a fraction. 4%of 75 = 75/100 X4 = 3. or simply 75/100= 3/4 x4 = 3. There is no trick here but only knoweledge.
Yeah, the percentage sign quite literally means divide by 100 in this. Since the rest is multiplication, it doesn't matter when you divide by 100, as multiplication and division are of the same order. 15% of 20 is therefore also equal to (15×20)%.
I was gonna ask if I was the only person who thought it was easy enough to multiply the percentage (x) times the number (y), then divide the result by 100. This is how I would solve it, and I assume this is the standard way to do so, assuming you don't have nice numbers to play with (such as 25% of 4), which basically equates to using a mental reference sheet you've been taught your whole life. I'm glad you demonstrated grouping, as this is what I would do if I had to mentally multiply larger numbers in this way. I don't know. I suppose I just don't see the issue or how this helps unless the numbers are neat, as I would be using grouping to simplify the multiplication in the first place. Though it is a nice thing to know, especially with the explanation!
(As a mathematician by training) this is straight from "The Department of Stating the Bleedin' Obvious" at the University of Embarrassing Lectures". BTW, I love most of your videos.
@ 5:35. 50% + 2% That’s exactly the way I usually do it. Though sometimes it does help to write part of it down somewhere. But usually writing it down just takes more time.
That is an interesting trick. They way I used solve these types of problems is to relate it something easily solvable. So looking at 4% of 75, it is easy to know 4% of 100, which 4 and that 75 is 3/4 of 100 so the answer is also 3/4 of 4 which is 3. Not quite as clean as the trick you showed, but nonetheless makes solving it in your head much easier. Another approach would be to change the percent to something easily knowable such as 1% of 75, which is .75 and it is easy to double that to 1.5 and easy to double that again to 3, which is easier than trying to figure out 4 x .75.
Where the numbers are more complex, where either can't easily be broken down to a fraction, I simply multiply the numbers, then shift the decimal 2 places. Have done so since the 70s.
Just do x*y and then divide by 100....4% of 75 is 4*75/100. 4*75=4*70+4*5=280+20=300. 300/100=3. Likewise 23% of 52 is 23*52/100. 23*52=23*50+23*2=20*50+3*50+23*2=1000+150+46=1196. 1196/100=11.96. Easy to do in your head.
You're not going to be asked to do 23% of 52. The point is to trick someone with a problem such as 4% of 75, since 75% = 3/4 and the 4 of the denominator divides into 4.
@@robertveith6383 watch the video at 5:00 to be asked to do 23% of 52. No, the point is not to trick someone, it is to realize that x% of y is the same as y% of x. Did you watch the video at all?
I just multiply the numbers. To find 15% of 20, I did 15 times 20, which equals 300. Since the answer needs to be under 20, I simplified 300 to 3. So, the final answer is 3. I figured all this out in my head in just a few seconds. Its a simple way of doing it.
I've always just taken 1% of the number and multiplied back. 23% of 52 = 23 * .52 = 11.96 with no need to juggle numbers. I do like the method in this video, but it seems to work best when the percentages are obvious when flipped. IE. What is 18% of 50. Otherwise, I might just stick with my typical method.
en mi caso para hacer porcentajes en mi cabeza sin papel a mano o calculadora aprovechaba que es facil dividir por 10 o por 100 cualquier numero entero, ´´moviendo´´ los puntos decimales por ejemplo, o ´´quitando´´ ceros. y luego ajustando con multiplicaciones faciles esos numeros. Para los Ejemplos del video serian como, 18% de 50, lo suelo hacer primero como, 50 / 100 = 0.5 que es igual a 1/2, y esto multiplicado por 18 es (1/2) * 18 = 9 * "uso 100 para dividirlo porque asi se cuanto es el 1% de 50 y asi luego multiplicar por 18 para saber cuanto es el 18% de 50.'' y para el 4% de 75 seria como, 75 / 100 = 0.75 o 3/4, y eso por 4 sale como (3/4) * 4 = 3 ** "lo de pasar un decimal a fraccion no lo hago siempre, otras veces solo hago la multiplicacion como multiples sumas, 0.75 * 4 = 3 si lo haces con sumas." me sirve mayormente para calcular descuentos en las tiendas, ejemplos: si el objeto vale 350 y le hacen descuento del 20%, saco el 20% de 350 asi, 350 / 10 = 35 y luego 35 * 2 = 70, el 20% de 350 es 70 o tambien podria decir que por cada 100 saco 20, siendo 300 entonces son 60 y del 50 son 10 mas, osea 70 es el 20% de 350, pero el otro calculo me confirma ese valor. y luego siendo que es un descuento significa que ese porcentaje se le reduce al precio final, siendo este igual a 350 - 70 = 280. *** "usar 10 aqui hace que sepa cuanto es el 10% de 350, y luego multiplicar por 2 me da el 20% de 350, mejor que dividir por 100 y luego multiplicar por 20." **** "obviamente esto solo lo aplico para porcentajes no taaan claros o obvios como 10%, 20%, 25%, 50%, 75%, 100%, pero aun en esos casos ayudan a aclarar." ***** "mi intencion con estos metodos es limitar los calculos necesarios a divisiones, multiplicaciones y sumas de rangos pequeños y faciles para calcular sin papel." AUNQUE, si que me quedare el truco de este video jeje. ese truco ayuda a encontrar casos de los porcentajes faciles de calcular, en los que antes no lo parecian.
I have an amazing trick for changing a percentage to a decimal, and vice versa. The percentage sign is one of the most amazing signs in math. It works like magic. % image that your pencil or pen can turn into a magic wand. If you remove the line in the middle of a percentage sign you are “LEFT” with 2 zeros. Removing the line means that you must move the remaining 2 zeros to the left. Tap your pencil to the left twice. Period. You have magically created a decimal from a percentage. For a decimal to percentage. Place your pencil on the dot. Now use its magic, from this spot, to pick up 2 zeros, tap twice to the right. Now place your 2 zeros one high and one low, lay down the wand, between your 2 zeros. Also a % sign is literally l00, just written in a different way.
4% of 100 is 4. 4% of 75 is 3/4 of that, or 3. And for the first problem, although I get the trick of swapping the percentage sign, it's just as simple: 18% of 100 is 18. 18% of 50 is 1/2 that, or 9. Third problem: 32% of 100 is 32. 1/4 of 32 is 8.
I have a question for all. Please comment your answer after thinking briefly. How many organs in our body help us in sensing the world around us ? [ Note - By sensing means 5 basic senses ]
And here i thought that it was the even easier method of multiplying the two numbers and dividing by 100. 4 x 75 over 100 is 3. Or 4 x .75. No dividing, even quicker.
For your easy example it isn't necessary to know the trick. I calculated them within seconds, knowing that e.g. 75 is 3/4 of 100 and 4% of 100 is 4, therefore 4% of 75 is 3/4 of 4, which is 3. Or as 20 is a fifth of 100, 15% of 100 is 15 and a fifth of 15 is 3, 15% of 20 is 3.
My approach was different in the 18% of 50. I thought of it as 9% of 100, which is 9. This works only if the 2nd number can easily be multiplied to get 100. I had the answer in a second or two. But I did not know about this trick. With the 23% of 52 I used the original to compute. 10% of 52 is easy, multiply by 2 to get 10,4. Add 3 times 1% = 3 . 0,52 = 1,56. 10,4 + 1,56 can be easily added in the mind to get the correct answer of 11,96. Turning the percentages around as 52% pf 23 does not make the calculation necessarily easier.
The percentage calculation is full of pitfalls. if you ask someone how much money you will have from 100 dollars, if you first increase it by 10% and then decrease it by 10%? The answer is almost always that it doesn't change. In fact, the following task is almost "unsolvable": A salt solution contains 2% salt and weighs 1 kg. I dilute it with enough water to reduce the salt content to 1%. What will be the weight of the salt solution after this? Anyone who wants to be a banker or a chemist must know how to calculate percentages.
Alternate title: *People% of 99 don't know this secret math trick*
LOL genius
❤
Listen here, you little shi-!
Nice 👍👍
Good one!
Convert 4% to 4/100 and rearrange the numbers to get an easier calculation: 4 x 75 is 300, then divide that by 100 to get 3.
I did exactly the same and thought "what is the big deal?" at first, but the method in the video IS superior as it is immediately obvious what 75% of 4 is without doing any extra division and multiplication steps in your head.
@CajunCatguy Still easy. 77 x 5 is 385. Divide that by 100 for 3.85.
Or just do the multiplication and move the decimal 2 places to the left.
very helpful add decimal
The way I did it was 4% is 4/100 is 1/25 and it's easy to see from these nice round numbers that 75/25 is 3.
4% of 75?
Well 1% of 75 is .75. Multiply that by 4, you get 3.
32% of 25?
10% of 25 is 2.5. Multiply that by 3, you get 7.5.
1% of 25 is .25. Multiply that by 2 you get .5.
Add together you get 8.
That is exactly how I do it 99% of the time. It makes me laugh that the gen Z kids I deal with CAN NOT figure it out without resorting to their phones.
I usually do it that way too, super easy and makes everything alot better
@@That_Stealth_Guy 99% of the time?
Well 90% of “the time” is “the tim”.
9% of “the time” is “e”.
Add together and you get “the time,” so yeah, just about all the time.
@@That_Stealth_GuyYou mean time% of the 99 😂😂
Yeah. Or 75*4=300. Divide by 100 and you get 3.
Math has always been challenging to me. The content of this video is very helpful to me as I was not taught this in elementary school like some of you have commented. At the age of 70, I continue to struggle with many mathematical concepts and appreciate this video. I'm a whiz in other subjects, but math tests used to make me cry with frustration in school. I spent 10x the amount of my study time with math as my other subjects and put forth my hardest efforts just to pass tests. Any shortcuts are valuable to me. Thank you.
Instead of swapping the % you can also multiply one side with a handy number and divide the other side with the same number to simplify it.
18% of 50 (/2,*2) = 9% of 100 = 9. 4% of 75 (/4,*4) = 1% of 300 = 3. 32% of 25 (/4,*4) = 8% of 100 = 8. 15% of 20 (/5,*5) = 3% of 100 = 3.
Even 23% of 52 (*4,/4) = 92% of 13 = 100% of 13 - 8% of 13 = 13 - 1.04 = 11.96.
This takes much longer but it could still work for a problem that’s harder than these types
@@bobross7473 The percent swap is the exact same thing with a factor of 100. My take is that it does not have to be 100, it could be something more convenient.
Just do 23/100 * 52= 1196/100=11.96
@@cristinacu2286You meant to say 23*52/100=1196/100=11.96. If you do 23/100*52 you get 0.23*52 (if we assign multiplication and division the same prescedence and read from left to right) which doesnt help in any way.
@@AnthonyBerlin yeah i meant (23/100)*52
For more complicated things because x% of y is the same as (x/100) * y you can simply multiply x and y and divide by 100. Usually much easier.
I agree, that's how I do it, much simpler. The method shown here is OK with easy numbers, but what about 37% of 19, for example?
I have considered myself a math nerd my whole life (over 70) and never realized this until my PhD son pointed it out to me a few weeks ago. Sure--seems simple ... once you KNOW it! Thx, Presh!
I was lucky I went to school in the 60 and 70’s. We were taught this at age 8 or so. Never forget these basics.
I’m a CPA. I graduated with my undergrad degree in 1969 (Accounting major, econ minor). The very first year, amongst other math, we had an extremely simple Business Math course… rule of 72s, transpositions divided by 9 and all that stuff. It was a one semester course.nLearned so do many tricks. This commutative function was learned in high school algebra but it was reiterated in this easy business math course.
We live in an age where people, who were taught the commutative property of multiplication in school, need to be told by the press about the commutative property of multiplication.
I'm pretty sure every age is an age where people need to practice a skill they learned to keep that skill.
Exactly! @@joostvanrens
Used to be able to memorize times tables all the way to the triple digits, now i use a calculator to add single digits but i can also solve many calculus question in my head. Just because a skill is simple and basic does not mean everyone can or should maintain that skill
At least in the US, math education is generally terrible. It is presented as a set of seemingly arbitrary and arcane formulas and rules that have absolutely no connection with anything in the real world. Kids don’t learn it, they just temporarily memorize enough to pass the test and move on.
Then as adults, in the years and decades to follow, they discover that there is actually a lot of real world application for that knowledge they discarded. If they even remember having learned it in the first place. You can’t entirely blame them, though. It would be hard to make a subject more boring than math *as taught in school.*
@@kenrickman6697 I'm convinced the problem is that math teachers are mostly people who love math and find it rewarding for its own sake. While people who love the application go on to do other things than teaching math.
If you find math easy and you love doing it, you probably shouldn't be teaching it. Which is kind of a sad paradox.
i think its not so much a trick as it is an understanding of sufficient depth of what x% of y means. as u showed its literally just x/100*y which u can write any way u want that makes it ez for u to calculate: like y/100*x or yx/100.
from my experience its that people dont exactly understand that 4% means 4 out of 100 ect.
@@underscore5673 I think you hit it. The reclassification of the problem as basic multiplication and division, and then applying all the tricks you have about multiplying and dividing by 100.
@@froglady7491 YESSS
I just multiply them and put the decimal point in the most logical spot.
Yes, absolutely correct.
These equations can be solved doing quick math without switching, and as is demonstrated, it's not always easy using this switch method nor does everyone know percentages or division, but they do know multiplication and decimals (better). It's just as easy to work it out with this method without switching, than it is with the first method, especially when the numbers aren't easily divisible or the percentages aren't obvious.
When I went to school in the seventies, we were taught what "x% of y" actually implied and how to calculate it with the formula xy/100. We also knew that xy=yx. I would definitely grab a calculator now to get some percentage. The problem are those who know the right keys in the calculator to get the result, but have no idea what they're doing or why.
This reminds me of what someone said about maths that made me laugh. Most people from the past knew algorithms and could get the right answer, but don't know why. Later schools discussed math theory, so many people were getting the wrong answer but they knew why it was wrong. Today many use calculators, but without them they can neither get the right answer or know why.
@@tomq6491 What about those of us who get the right answer *and* know why?
@@jursamaj They are the true mathematicians.
An easy "trick" that only works for a handful of numbers that are either multiple of 10 or 25 ain't much of a trick, that's just an obvious shortcut. Internet blows out for this means no one takes a proper look at their math. Okay, that'd be faster for "37% of 20%", what about "33% of 39" or "21% of 44"?
Exactly what I thought ...
On harder percent problems, you sometimes have to break up the percentage or the number into sum or difference of nicer ones, then use distributive property...:
So, for 21% of 44, we can see 21% = 20% + 1%, so that:
21% of 44 = (20% + 1%) * 44
= (20% of 44) + (1% of 44)
= 2 * (10% of 44) + (1% of 44)
= 2 * (4.4) + 0.44
= 8.8 + 0.44
= 9.24
With practice, this can be done mentally (if one doens't have paper-and-pencil). The hardest part, for me, is holding the numbers in my head and adding CAREFULLY so as to line up the place-values!
The real trick is that percentages are just multiplication so as long as you can do two digit multiplication in your head you'll be fine.
Have you ever head Arthur Benjamin Franklin, he is also one of the human calculators with a few ted talks.
He has written a book titled secrets of mental maths which is full of exercises to develop sufficient speed in mental mathematics. I would recommend this book if you are interested in mental maths.
33% is roughly 1/3
1/3 of 39 = 13
That's a good estimate
Actually 1/3 is 33.33
So 13 - 0.13=12.87 that's the exact answer
It consumed half a minute to figure this out but still doable in head.
I never learned this in school, but knew it anyway...if the number is less than 100, put a decimal point in front of it and multiply by the other number. Example: 5% of 63 = 5 x .63 = 4.5. If it's more than 100, divide the number by 100 and multiple. Example: 7% of 130 = 7 x 1.30 = 9.1
Haven't watched the vid yet but I'm betting its about reversing percentages. 4% of 75 is 75% of 4 - so 3.
Edit: yep
I figured it would be 1/25 of 75 = 3. So I figured the trick would be if x% is the same as 1/y then y% is the same as 1/x.
Working out 1% is simple and then multiplied by the result equals the percentage. What’s so difficult about that? 4% of 75 (1% .75. .75 x4 =3
Another problem with this trick is that it is only applicable if in x% of y, y
I think it does work for your example. 1000% of 25 is 10 x100% ..100% of 25 is 25...10 x25 is 250.,,...right answer.
25% of 1000 = 1000/100 =10 x 25 -= 250. Look at how I excplained it
Approx. 8 billion% of 99 people don’t know this secret math trick.
Try making numbers in titles like 98.7% or something like that to make it seem more interesting.
Agree on that. It's kinda the same feel effect as 9.99$ thing
Oh yeah, because those numbers are made up anyway haha
Made me laugh ;)
Where did that 99% come up from anyway? Where's the data?
@@cpsof it's kinda like they say "source: I made it up"
I did the thumbnail example by dividing 100 by 4 to get 25, then dividing 75 by that to get 3. That took only 5 seconds or so, but simply switching the numbers and taking 75% of 4 is even faster. I'll have to remember that. I think that I learned it at some point long ago, but obviously forgot it.
1:33 I figured it was 9 within seconds without using a calculator.
I turned the 18% into an easier percentage 20%.
20% of 50 is 10.
I need 18% which is 2% from 20%. 2% is 1/10 of 20%, which got me 1.
10-1=9
Sometimes, there are multiple ways to solve a problem. Though some may be more complicated than others.
Without watching the video. 1% of 75 is .75, multiply that by 4 and you get 3. Thank you for coming to my ted talk.
I ALWAYS do it that way, is more easy
Yes, absolutely correct.
These equations can be solved doing quick math without switching, and as is demonstrated, it's not always easy using this switch method nor does everyone know percentages or division, but they do know multiplication and decimals (better). It's just as easy to work it out with this method without switching, than it is with the first method, especially when the numbers aren't easily divisible or the percentages aren't obvious.
Stunning
Nice trick.
Great video too, I just love math.
However the old trick of dropping the percept sign and moving the decimal two spaces is easy enough to do in my head.
One of the things I've thought about...
If I went back in time and got to meet the great mathematicians of the ancient world, either hand them a math textbook or just give them a brief overview of our number system and notation. Imagine what Archimedes or Euclid could have done if they had our notation??
I literally knew this ever since i was taufght about percentage in school back in 7th grade. My teacher was explaining about percentages like how % means out of 100. He gave us some problems to solve and while solving the problem i realised that we could exchange the % of the first number with he second number, i.e. x% of y=y% of x. After this, I tried it and saw that the answers were correct, so I asked my Maths teacher to see if I was correct and he seemed quite surprised upon realising that x% of y=y% of x. I still feel proud for finding this out especially after watching this video and fiinding out that 99% dont know this trick.
I got the first one straight away by reversing. The second one that's on the thumbnail, I did by going 4%=1/25, and 1/25 × 75 = 3.
It just clicked for me when looking, I neglected the percent (like the video).
I am lost with 1/25x75=3 oh dear I need some help
@@HRH.Wholly-Royal So, 1/25 × 75 = 75/25 = 3. I wish I could show that better, but plain text is a thing, so just see 1/25 as a fraction.
Sitting through so many simple examples gave me the worst memories of infant school maths class but thanks for redeeming it with that bit of history.
Watching an expert with an abacus is amazing, though. The boast was always that the fastest of them could outpace a calculator. You'd still see an abacus in some of the shops when I was growing up, and we learnt how to use them in school: a pretty solid way to visualise arithmetic.
But whatever one thinks about the skill needed, the abacus definitely doesn't print receipts, so...
Here is a cool trick that gets us close to 23% of 52. 23% is very close to 3/13. Then 3/13 * 52 is very nice because we can simply the fractions and get 3 * 4 = 12. By knowing decimal approximations for just a few fractions, mental arithmetic can be surprisingly easy (sometimes).
how is 23%= 3/13 ?
@@SportsShowcase003 It is close, but not exact. The decimal approximation is 0.2307... Knowing the approximation meant that I could estimate a value of 12 quickly, but did not get me to the exact answer of 11.96.
Actually, I did the 'trick' first, as it was simpler - 23% of 52 -> 52% of 23. 52% is close to 50%. 50% (1/2) of 23 is 11.5, so 52% is probably "about 12, give or take a bit". And sure enough, 11.96. Interestingly, using your way, I'd've probably said 23% is close to 25%, and 1/4 of 52 = 13, so the answer is probably somewhere between 12 and 13, and my estimate would've actually been worse.
@@matthewryan9323 Nice. Maybe the easiest way is to find 25% of 52 and then subtract 2% of 52. That would work and be pretty quick. However, planning all of that pre-work before actually solving the problem probably defeats the purpose of a shortcut.
@@jeffreyvetrano5836 Yeah. It's something that might be more helpful if you're just trying to get a reasonable estimate, if the numbers work out 'nicer' one way for you than the other, swap 'em.
Years ago, I worked out an easy conversion for Centigrade to Fahrenheit that isn't too difficult to do in your head. I am wondering if this procedure is well known.
The procedure is to double C, subtract 1/10 of the doubled amount and add 32.
Example:
C=100:
2C=200
2C-(2C/10)=180
2C-(2C/10)+32=212
This works for the following reason:
F=C(9/5)+32
But:
C(9/5) = 9C/5
9C/5 = 18C/10
18C/10 = (20C-2C)/10
(20C-2C)/10 = (20C/10)-(2C/10) = 2C-(2C/10)
Therefore:
C(9/5) = 2C-(2C/10)
And:
F=2C-(2C/10)+32
Alternative way
18% of 50
10% of 50 is 5 obviously
Because 10%x10=100%
So 5+5
=10
And since it's not 20% but 18 we need to remove 2% which is tenth of 20% so now
10-1 =9
It's easier to do half (50%) of 18 = 9.
Way way faster.
Base 10. Therefore 50 equates to 1/2. Half of 18.
I do it just as well without this trick. Simple multiplication of the parts, often ignoring tens values (zeroes or decimals); add them together; then consider reasonableness. Examples:
- 18% of 50: multiply 1 times 5, and remember 5; then do 8x5 for 4; add them for 9 then consider whether it's reasonable.
- 4% of 75: 4x7 for 28; 4x5 for 2 (ignoring the zero); reasonableness tells me it'll be a low number, less than 4 because 75 is less than 100, so 28 becomes 2.8 and 2 becomes .2 and the answer is 3. Again, the key is to ignore the true values (in factors or multiples of ten).
- 32% of 25: 3x25=75, and 2x25=5; A glance tells me the answer is about a third of 25, so working with 75 and 5 gives me 8.
- 15% of 20: 1x2 and 5x2 gives me a 2 and a 1, so the answer is clearly 3. So easy. Alternatively, seeing this one as 10% for the 1 plus 50% fir the 5 (again, ignoring the tens value) gives me 2+1, for 3.
- 23% of 52: At first glance, I notice that the answer will be just under 13 (because 23% is just under 25%, and if it were a quarter, the answer would be 13), so I have my reasonableness already worked out. Next, 2x52 gives me 104, and 3x52 gives me 156; Now I simply add them, being mindful of the tens: 104+15.6=119.6.
I should say this is similar to how I multiply any two-digit number by any 2-digit number in my head almost instantly. I just see the answer with little or no thought.
0:02 Captions : Hey this is Press Tow Walker 💀
Fortunately, it is also written on the screen in the graphics.
@4:55, for 23% of 52, the trick doesn’t really help you. Sure, you can switch it to 52% of 23, then find half of 23 and 1% of 23 the way you did. But you can also skip the swapping trick altogether, realize that 23% is 25% minus 2%, determine that one-fourth of 52 is 13 (as anyone who has ever played cards knows), then determine that 1% of 52 is 0.52, double that is 1.04, and 13 minus 1.04 is 11.96. You’ve reached the same answer, with math which is equivalent to what was used in the video, without having to mess around with the swapping “trick”, thus saving some time and effort.
@@eternaldarkness3139i mean depends, it’s easier to add in my head rather than subtract
I mean, this trick only works in neat, tidy, cases like this. But... What's 27% of 86? 86% of 27 isn't any easier.
(27*86)/100
@@Pabs1234 Still not "easy" to do quickly in your head, especially in a time when we all carry calculators with us at all times.
@@brianstraight9308 tell that to igcse 2025 takers
Well, that doesn’t make it nearly as fun, does it?
25% of 86 = 86/4 = 21.5
2% of 86 = 2(86*0.1) = 1.72
27% of 86 = 21.5 + 1.72 = 23.22
For me this is pretty quick to do in my head.
5:30 yeah but you can literally do the same thing with the original question.
23% is 20% + 3%
23% of 52 = 52/5 + 3*(0.52) = 10.4 + 1.56 = 11.96
This "trick" is actually about which number I multiply by the other one more kindly and easily during multiplication, which is commutative. I prefer to multiply the larger number by the smaller one, or an "irregular" number by a more "regular" number (=e.g. a number ending in 0 or 5, an even number with as many divisors as possible, etc.).
The reason this blew so many peoples minds, is that we forget 18% of 50 is equal to 0.04 * 50, multiplication is interchangeable
You actually do learn this trick if you learn foundations of math. Once you understand how numbers interact there are all kinds of shortcuts available. Too bad most people think math is boring.
Something related that's kinda interesting, so percentages are a fraction right, n% being n/100.
We can find the specific percentage of any number just by changing it so that the denominator is the number we want the percentage of, the numerator becomes the percentage we're looking for.
Going back to 18% of 50, 18% is the same as 18/100, which is also 9/50. We get the percentage we were looking for with 9 being the numerator and both the denominator and numerator ends up 50% of the size they were in the original fraction.
Of course this works with other fractions as well.
15% of 20: 15/100 = 3/20
Both are 20% of the size they were in the original fraction.
4% of 75: 4/100 = 1/25 = 3/75
Both are 75% of the size they were in the original fraction.
52% of 23: 52/100 = 1196/2300 = 11.96/23
Both are 23% of the size they were in the original fraction.
Though of course it's not as elegant with certain numbers, tho you can always get there by multiplying both with the number you want the percentage of and then dividing them by 100.
I feel like I had something else I wanted to add but forgot, but yeah this kinda made me understand how switching the percentage and the number we want the percentage of makes sense.
Personally I just multiply y by x and divide the answer by 100. It's a little more brain work, but consider your example:
23 × 52 = (23 × 10 × 5) + (23 × 2) = (230 × 5) + 46 = 1150 + 46 = 1196
1196 ÷ 100 = 11,96
That's how I compute it off the top of my head.
Additionally 23 × 50 could be further simplified down as
(20 × 10 × 5) + (3 × 10 × 5) = (200 × 5) + (30 × 5) = 1000 + 150 = 1150
However unless I deal with thousands upon thousands and desire accuracy, I find simplifying time consuming.
Anyroad, head calculation took me about than 20 seconds, that's fast enough for me. Much easier to do than roots for example.
There is another way to do this in your head
To find 10% divide by 10
To find 1% divide by 100
Then you can add or subtract to find different percentages (eg 4% is 1% x4)
So say you are trying to find 18% of 50
First find 20%
50÷10x2=10
Then find 2%
50÷100x2=1
Then take away 1 from 10 (20%-2%=18%) to get 9
If you mix decimalisation with fractions that might be mental arithmetic but it is a mental way of doing things - the easiest was is to multiply the two numbers and then adjust for the decimal point - 80% of 80 8x8 is 64
Thanks so much for this dividing technique!
Can also do: 23 * 52 / 100 = (20*50=1000) + (20*2=40) + (3*50=150) + (3*2=6) / 100 = 1196 / 100 = 11.96 ... idk if it's faster or easier, but it's also an option.
easier is to just go to 1% or 10% or any easy number just select matching for easy divide 5%=x/20 20%=x/5 25%=x/4 50%=x/2 depends, and use addition
there is 1% from 52=0.52 x 23 or just change to 0.5x23 + 0.02x23=11.5+0.46
4% from 75, so 1% is 0.75 x4 is just 3
To be fair, most of those examples are easy to calculate even without this "trick", but it's still very good to know. WHY DIDN'T WE LEARN THIS IN SCHOOL. I remember an enthusiastic maths professor mentioning how we can easily remember certain formulas. It was incredibly helpful, but of course not part of the standard curriculum. Why can't we make things easier.
A trick I learned is multiplying the number by the percentage and dividing by 100. ex: 4% of 75 ->75 times 4 divided by 100 = 3 23% of 52 -> 52 times 23 divided by 100 = 11.96 Most of the time you’ll need a calculator to do this but everyone has one on their phone, right?
As a math teacher, the problem with this is that kids don’t know their percent-fraction equivalencies so this would make NO sense to teach as a strategy. It’s a perfectly fine strategy for people who DO know those equivalencies, but what makes more sense to teach is converting percents to decimals correctly 100% of the time, and then multiplying. Especially since secondary students in most US states are required to use a calculator on their standardized tests.
the historical perspective after the math stuff was great, thanks so much for adding that!
Hi, Mr. Talwalkar. Here is a hard problem most people can't solve: suppose 0
4√3
@@MOODY_Shorts Great! How did you come up with the answer?
Super tip - sure solved my dilemma with percentages! Thanks for taking the time to make the video!
The best way to improve mathematics is to use the Base Twelve system, which has twice as many even factors as Base Ten, namely 2,3,4 and 6! We decided on twelve months in a year, for example, possibly because there are 12 "moons" in a year which then allows us to divide the year into 4 seasons each made up of 90 days each (plus change).
Everyone thinks to count on their fingers when growing up as in 5 on each hand, however if you leave off your two thumbs you now have four fingers, each with three segments which add up to a total of twelve on each hand!
The Dozenal Society in Great Britain has already designed a system which takes advantage of this by using numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, X, E (the last three named dek, el and doh (long o) to get to twelve, then start over with dudek, dudek unu, dudek du, etc.
We already use dozens all over the world, so why not make the math this much easier?
"Of" simply means "multiplied by". You don't need to worry about the decimal place for now because you know it's going to be in single digits. Another way of multiplying something by five is thinking of halving (ie "0.5") and moving the dp one place to the right. Either way, any product containing some form of 18 and 5 is going to contain 9 and possibly some zeros - in this case none.
Thanks for the extra history. When I do tipping here with a tax rate of 9 percent, and I want to give a 20% tip on the pre-tax amount, I just multiply the bill before tax by 3 and divide by ten for the tip and tax. Thus a 100 dollar bill will be 109 with tax so 3x100 /10 = 30. Total cash given is 130 with a 21 dollar tip. No I don't tip on the tax. Tax is a tip to the city! :D...but as an aside, all the new computers are set up to tip on the total....that is a whole nuther thing going on!.
Convert the percentage to a decimal by moving the decimal point two times to the left. 4% becomes .04.
Multiply .04 by 75.
Here's the long explanation: I use the 10% and 1% Rule, then work my way up -- however, my math is slightly different from what was given here for the question of: 4% of 75. I know that 10% of 75 is 7.5, however, I just step down one more decimal space to 1%. So, I then know 1% of 75 is .75. Since .75 + .75 = 1.5, I then know that 1.5 + 1.5 = 3. That kind of math I can quickly do within a few seconds in my head; I can think this way far faster than I can in explaining it here. However, once you get the hang of this way of finding the answer, you too can begin to do it quickly this way without a pen/pencil & paper. However, I am betting that most of the people who watched this video already knew the answer and use a similar or unique version that helps them solve the answer, and I am then only 'speaking to the choir.' Perhaps like many of you, you too may the one often asked to calculate the tips and sales discounts for your partner/wife Like I do for mine. Anyway, that how I've been doing it for years in my head... not perfect, but it works.
When I was 12 I lived in France. Geometry and algebra were part of my curriculum. Four years later I returned to the US where my classmates were just beginning algebra.
1:00 Most of of us can figure it out in our heads,. At least most of us watching this channel. Figuring out a percentage of any number that is divisible by five is so trivial as to be ludicrous
The commutitive property of multiplication isn't enough here. You have "x / 100 * y". You gave to commute the division and multiplication first.
And if you do that just stop at (x * y) / 100 and start simplifying the fraction before multiplying what remains.
Presh - the thing I learned along these lines a long time ago that makes it even easier (in my mind) is to always see the "of" as multiplication and essentially ignore the percentage by moving the decimal two places either in the math or in the answer - whichever makes it easier. I see "50% of 18" as 0.5 x 18. Same thing you are explaining, but the step is automatic.
When Fibonacci introduced Arabic numerals to Italy it was rejected at first, until the bankers started using them. It still took a long time for others to adopt them.
My cat puked on the carpet.
How is that relevant? Well, it's as relevant as your comment, so ..
The OP was making an interesting connection with what was said at the end of the video, about how it took society some time to accept Arabic numerals instead of Roman numerals. No reason to berate them, just a fun little tidbit. One which was news to me and greatly appreciated!
@@Kyrelel did you watch the video, sober?
1:39 I have another way, just divide something by 100 to get 1% of it and then multiply it by the number of pencentage you want, only multiply by the number, not including the percentage thingy.
When i was un School, my teacher taught me lots of tricks. Now, as a private teacher, i also teach these tricks. :) I love that math is getting viral around social media ❤
100% of Gen X can do math.. 👍🏻
We now live in a time controlled bu gagets. Children are no longer thaught to think but are only learning to press buttons. I am 76 years old and did my schooling in Malta back in the 1950's and early 1960's. percentages and decimals were all thaught without gagets then. I t took time but you learned to tyink and solve any problem. All you needed to say is that that it is a simple fraction to solve. I'm on a comtuter so I'll use a (/) for a fraction. 4%of 75 = 75/100 X4 = 3. or simply 75/100= 3/4 x4 = 3. There is no trick here but only knoweledge.
All of those years doing multiplication using decimals in my head...
OR you can just multiply the numbers and move the decimal point two spaces.
That's WAY easier.
I've been doing this automatically in my head since grade 5. That's probably why I had such a hard time in math.
Yeah, the percentage sign quite literally means divide by 100 in this. Since the rest is multiplication, it doesn't matter when you divide by 100, as multiplication and division are of the same order. 15% of 20 is therefore also equal to (15×20)%.
I was gonna ask if I was the only person who thought it was easy enough to multiply the percentage (x) times the number (y), then divide the result by 100. This is how I would solve it, and I assume this is the standard way to do so, assuming you don't have nice numbers to play with (such as 25% of 4), which basically equates to using a mental reference sheet you've been taught your whole life. I'm glad you demonstrated grouping, as this is what I would do if I had to mentally multiply larger numbers in this way.
I don't know. I suppose I just don't see the issue or how this helps unless the numbers are neat, as I would be using grouping to simplify the multiplication in the first place. Though it is a nice thing to know, especially with the explanation!
Uhm, faster is moving the decimal 2 places for one percent & multiply to get the percentage... E.g. 4% of 75, 1%=0.75, 0.75*4=1.5.
PRRCENT means /100. OF means multiply. 4/100 x 75/1.
= 4x75/100 = 300/100 =3.
(As a mathematician by training) this is straight from "The Department of Stating the Bleedin' Obvious" at the University of Embarrassing Lectures".
BTW, I love most of your videos.
@ 5:35.
50% + 2%
That’s exactly the way I usually do it. Though sometimes it does help to write part of it down somewhere. But usually writing it down just takes more time.
That is an interesting trick. They way I used solve these types of problems is to relate it something easily solvable. So looking at 4% of 75, it is easy to know 4% of 100, which 4 and that 75 is 3/4 of 100 so the answer is also 3/4 of 4 which is 3. Not quite as clean as the trick you showed, but nonetheless makes solving it in your head much easier. Another approach would be to change the percent to something easily knowable such as 1% of 75, which is .75 and it is easy to double that to 1.5 and easy to double that again to 3, which is easier than trying to figure out 4 x .75.
I just multiply in my head and it’s no problem.
I'm glad people are learning this useful teq.
Where the numbers are more complex, where either can't easily be broken down to a fraction, I simply multiply the numbers, then shift the decimal 2 places. Have done so since the 70s.
4% = 1/25. Divide 75 by 25 gives 3. The reversing is a good hack.
I’m a math teacher and was never aware of this trick, but I went to writing this out and it made sense quickly, thanks
Just do x*y and then divide by 100....4% of 75 is 4*75/100. 4*75=4*70+4*5=280+20=300. 300/100=3. Likewise 23% of 52 is 23*52/100. 23*52=23*50+23*2=20*50+3*50+23*2=1000+150+46=1196. 1196/100=11.96. Easy to do in your head.
You're not going to be asked to do 23% of 52. The point is to trick someone with a problem such as 4% of 75, since 75% = 3/4 and the 4 of the denominator divides into 4.
@@robertveith6383 watch the video at 5:00 to be asked to do 23% of 52. No, the point is not to trick someone, it is to realize that x% of y is the same as y% of x. Did you watch the video at all?
I just multiply the numbers. To find 15% of 20, I did 15 times 20, which equals 300. Since the answer needs to be under 20, I simplified 300 to 3. So, the final answer is 3. I figured all this out in my head in just a few seconds. Its a simple way of doing it.
Bruh, This was taught for us in elementary school 🤦🏻. But anyways, thanks for reminding it!
If this remedial math question stumps too many people then the dumbing of America is complete.
I've always just taken 1% of the number and multiplied back. 23% of 52 = 23 * .52 = 11.96 with no need to juggle numbers. I do like the method in this video, but it seems to work best when the percentages are obvious when flipped. IE. What is 18% of 50. Otherwise, I might just stick with my typical method.
en mi caso para hacer porcentajes en mi cabeza sin papel a mano o calculadora
aprovechaba que es facil dividir por 10 o por 100 cualquier numero entero,
´´moviendo´´ los puntos decimales por ejemplo, o ´´quitando´´ ceros.
y luego ajustando con multiplicaciones faciles esos numeros.
Para los Ejemplos del video serian como,
18% de 50, lo suelo hacer primero como, 50 / 100 = 0.5 que es igual a 1/2,
y esto multiplicado por 18 es (1/2) * 18 = 9
* "uso 100 para dividirlo porque asi se cuanto es el 1% de 50 y asi luego
multiplicar por 18 para saber cuanto es el 18% de 50.''
y para el 4% de 75 seria como, 75 / 100 = 0.75 o 3/4, y eso por 4 sale como (3/4) * 4 = 3
** "lo de pasar un decimal a fraccion no lo hago siempre, otras veces solo hago la
multiplicacion como multiples sumas, 0.75 * 4 = 3 si lo haces con sumas."
me sirve mayormente para calcular descuentos en las tiendas, ejemplos:
si el objeto vale 350 y le hacen descuento del 20%, saco el 20% de 350 asi, 350 / 10 = 35
y luego 35 * 2 = 70, el 20% de 350 es 70
o tambien podria decir que por cada 100 saco 20, siendo 300 entonces son 60 y del 50 son
10 mas, osea 70 es el 20% de 350, pero el otro calculo me confirma ese valor.
y luego siendo que es un descuento significa que ese porcentaje se le reduce al precio final,
siendo este igual a 350 - 70 = 280.
*** "usar 10 aqui hace que sepa cuanto es el 10% de 350, y luego multiplicar por 2 me da el 20%
de 350, mejor que dividir por 100 y luego multiplicar por 20."
**** "obviamente esto solo lo aplico para porcentajes no taaan claros o obvios como 10%, 20%,
25%, 50%, 75%, 100%, pero aun en esos casos ayudan a aclarar."
***** "mi intencion con estos metodos es limitar los calculos necesarios a divisiones, multiplicaciones
y sumas de rangos pequeños y faciles para calcular sin papel."
AUNQUE, si que me quedare el truco de este video jeje.
ese truco ayuda a encontrar casos de los porcentajes faciles de calcular, en los que antes no lo parecian.
I have an amazing trick for changing a percentage to a decimal, and vice versa. The percentage sign is one of the most amazing signs in math. It works like magic. % image that your pencil or pen can turn into a magic wand. If you remove the line in the middle of a percentage sign you are “LEFT” with 2 zeros. Removing the line means that you must move the remaining 2 zeros to the left. Tap your pencil to the left twice. Period. You have magically created a decimal from a percentage. For a decimal to percentage. Place your pencil on the dot. Now use its magic, from this spot, to pick up 2 zeros, tap twice to the right. Now place your 2 zeros one high and one low, lay down the wand, between your 2 zeros.
Also a % sign is literally l00, just written in a different way.
4% of 100 is 4. 4% of 75 is 3/4 of that, or 3.
And for the first problem, although I get the trick of swapping the percentage sign, it's just as simple: 18% of 100 is 18. 18% of 50 is 1/2 that, or 9.
Third problem: 32% of 100 is 32. 1/4 of 32 is 8.
I have a question for all. Please comment your answer after thinking briefly.
How many organs in our body help us in sensing the world around us ? [ Note - By sensing means 5 basic senses ]
I learned this trick a couple years ago. It is very useful. I have used it enough times that my brain pretty much does it automatically
This is insane bro. This will help me in my percent unit in school so much
And here i thought that it was the even easier method of multiplying the two numbers and dividing by 100.
4 x 75 over 100 is 3.
Or 4 x .75.
No dividing, even quicker.
good , I usually in my head multiple the % with the number and divide by 100, so 4% of 75 becomes 4x75/100 =3
Yes that’s what I said!
@@ChocoLate-t6v You can also divide 75 by 100 and multiple it by 4, same thing.
100/X=y
Z/y=≈the answer
X=X%
Z=the number you are calculating the percentage of
(I don’t use variables much)
Nice math trick, this will definitely come in handy for my math studies
For your easy example it isn't necessary to know the trick. I calculated them within seconds, knowing that e.g. 75 is 3/4 of 100 and 4% of 100 is 4, therefore 4% of 75 is 3/4 of 4, which is 3.
Or as 20 is a fifth of 100, 15% of 100 is 15 and a fifth of 15 is 3, 15% of 20 is 3.
My approach was different in the 18% of 50. I thought of it as 9% of 100, which is 9. This works only if the 2nd number can easily be multiplied to get 100. I had the answer in a second or two. But I did not know about this trick. With the 23% of 52 I used the original to compute. 10% of 52 is easy, multiply by 2 to get 10,4. Add 3 times 1% = 3 . 0,52 = 1,56. 10,4 + 1,56 can be easily added in the mind to get the correct answer of 11,96. Turning the percentages around as 52% pf 23 does not make the calculation necessarily easier.
In the mid seveties my physics teacher insisted that the slide rule was faster than those new fangled calculators.
My mental heuristic is to first find 1% =0.75 ( 3/4), 2% =1..5 (1 1/2), 4% = 3. Finding 1% first is a simple way into many % calcs.
The percentage calculation is full of pitfalls. if you ask someone how much money you will have from 100 dollars, if you first increase it by 10% and then decrease it by 10%?
The answer is almost always that it doesn't change.
In fact, the following task is almost "unsolvable": A salt solution contains 2% salt and weighs 1 kg. I dilute it with enough water to reduce the salt content to 1%. What will be the weight of the salt solution after this?
Anyone who wants to be a banker or a chemist must know how to calculate percentages.
This is not a trick, it is just straight forward mathematics; clearly people don't know or understand basic mathematics.