This works because finding the percentage of a number is just multiplication, and multiplication is commutative.

This dude just casually shows up in my recommends and absolutely teaches me to understand this. Incredible YT this is what you should be promoting.

Back in school i learnt this way: 28% x 75 = 28 / 100 x 75 = 28 / 4 x 3 (simplify by dividing common factors) = 7 x 3 (simplify again) = 21 Video method, 28% x 75 = 28 x 75% = 28 x 3 / 4 = 7 x 3 = 21 (Faster mental calculation because everyone knows 75% = 3 / 4) I was part of the generation of students who were banned from using calculators in school (especially in math class), so our go-to rule was always divide before multiply to keep numbers small. Till today its faster for me to do 28 / 4 x 3 than to do 28 x 75 regardless of how we shift the decimals.

Even easier is to know that 3/4 is half of the number plus half of the half. Half of 28 is 14; half of 14 is 7; so the answer is 14+7=21. You only carry small numbers in your head.

This has always been my issue with math, everything makes sense, until the last step, then it becomes magic.

These are the kinds of math vids i need as an adult, to shore up weak spots in the useful day to day operations that come up. Thanks!

I got it quite quickly in my head with (30*75-2*75)/100. But this is a nice trick to keep in mind for certain numbers like 75 20 25 and so on.

You can also do things with multiples of 10% and 1% both easy to figure at a glance. 10% of 75 is 7.5 1% of 75 is 0.75 (3 x 10%) - (2 x 1%) = 28% (3 x 7.5) - (2 x 0.75) 22.5 - 1.5 = 21 It's more manageable to calculate 7.5 x 3 in your head and 0.75 x 2 then thinking about 0.28 x 75.

How is 15 yr old me not enjoying this? I'm 30 and have recently needed this in my life. Thank you. Saved.

This works due to 2 properties. The commutative and the associative property. It’s probably easier to understand with the commutative. Here’s both quickly. 28% of 75 = .28 x 75 First, you need to be aware that we’re actually dealing with 3 numbers - not just 2. The actual problem is 28 x .01 x 75 … The "28 x .01” part is the same as "28 divided by 100” , it makes the “.28” part of the original problem. Now, you’re done. Lol. Let’s look at the 2 properties. Commutative property states that when adding or multiplying, the ORDER of the numbers does not matter. 1 x 2 x 3 = 3 x 2 x 1 …. Still with me? Let’s look at our 3 number problem from above. That means that 28 x .01 x 75 = 75 x .01 x 28. Do you see? I just flip flopped the numbers! Now look at the 3 numbers after I flip flopped them: 75 x .01 x 28 …. Wait a sec! That’s the same as .75 x 28 ! That’s why our teacher was able to write .75 x 28 on the board! Ta Da!! Commutative Property. Associative property states that when adding or multiplying, the GROUPING of the numbers does not matter. How do we tell if numbers are GROUPED together? By seeing if they have parentheses around them. ( 1 x 2 ) x 3 = 1 x ( 2 x 3 ) Do you see? All I did was group the 1st two numbers on the left and then I grouped the middle and last number on the right. The answer is still 6. You see? Kinda cool huh? No matter how you group 2 out of the 3 numbers, the answer will always be 6. Now let's look at your favorite 3 number problem from above: 28 x .01 x 75 …. Let’s group them and see what happens! First, let’s group the first two numbers: (28 x .01) x 75 …. That equals .28 x 75 , our original problem. Now, let’s group the 2nd and 3rd numbers: 28 x (.01 x 75) … Wait! That equals 28 x .75 ! It’s the same thing the teacher wrote on the board! (He just switched the order and wrote .75 x 28 instead of 28 x .75) Ta Da!! Associative Property! You’re done. BONUS: In the end, the answer will be the same no matter if you use the Commutative Property OR the Associative Property. Both of them are extremely similar - one deals with the order of numbers (Commutative) while the other is the grouping of numbers (Associative).

I’m 30 and I literally forgot how to do math and all that we learned in school. So simple yet so hard 😂

I wish I had a math tutor like you

This man doesnt breathe oxygen, oxygen slides itself into him to be breathed

Beautiful as sunlight❤ Thanks KEEP IT GOING

KZfaq is the best place to learn online.

As @swarley2500 said in their comment, "This works because finding the percentage of a number is just multiplication, and multiplication is commutative." Realize that the % sign is commutative because it is simply (1/100), so: 28% of 75 = 28*(1/100)*75 = 28*75*(1/100) = 28*75% = 75% of 28 Thank again to @swarley2500's comment for the amazing insight!

Up to this day, i still can't solve math problems like this.

No whiteboards were hurt during the filming of this math.

Thank you for your incredible work,sir.😊

yeah I use this technique a lot. another thing I do is if it ask for 50%, jist divide it by 2. 25% is also equal to divide by 4. I could give more examples but it's funner to find them yourself.

Another approach easy to do in your head: 28% is close to 30%. 30% is 3 x 10%. 10% of 75 is 7.5. So 3 x 7.5 is 22.5. Then you have to subtract those extra 2% from 22.5 to get to 28%. 1% of 75 is 0.75. Times that by 2 and you get 1.5. Subtract that 1.5 from 22.5 and you get the answer = 21. You can do that in your head far faster than you can type it out or read it. Someone asked so do 27% of 76. OK. Using the preceding, I get 30% of 76 is 22.8. Then subtracting 3 x 1% (0.76 x 3, or 2.28) I get 20.52. This is even easier, since if 30% is 22.8, then 3% must be one tenth of that -- an obvious 2.28. Takes just a few seconds to do in your head. Something to keep in mind is the relationship between subtraction and division and between addition and multiplication. Division is subtracting multiples and addition is adding multiples (e.g., 2x4 is the same as adding 2 four times, or adding 4 twice).

He picks 75 because 75% is 3/4. What if it’s not 75?

This is what I want in my KZfaq Algo. Thank you, sir!

This is beautiful, thank you for the info

Damn, watching this with no volume is like me looking at my teacher while not paying attention 😂

I'm here smirking and nodding my head like I know what just happened.

I generally just break it down by 10 and 1 percent. It's easy to figure out 10 percent, just move the decimal. In this case 7.5 would be 10 percent of 75, multiply that by 3, you get 22.5 Then to make it 28 percent, instead of 30, move the decimal again for 1 percent. Making it .75. then 2 of those makes 1.5, minus that from our 22.5 we got earlier, and now you get 21. I swear reading it like that sounds harder than it actually is lol

Easy to understand. I love watching your videos. Great way to re-learn things I forgot.

Or take 10% (aka move the decimal point once) do it again for 1%. Multiply 10 % by 3 and minus (2 x 1%). If it's closer to a 5% then take half the value you get from 10%. Way easier to mentally do that on the fly.

Simple. Short. Good. ❤

you don't need any tricks, just do it in mind, 8 X 75 = 600, 20 x 75 = 1500, 1500+600= 2100, then take off the last two 00= 21

Back in school I learned this way: 100% is 75. 28% is x. So we multiply across: 100•x=28•75 100•x=2100 x=21

If you teach kids this way, it's no wonder they grow up confused about associative properties and their logic is screwed. It's more important to teach why that logic works.

👁👄👁 me watching, still stumped af waiting for the ah ha moment that never comes 😢

2024 and I'm still lost in math 😂😂😂

Lost me and I now remember why math was never a happy time for me 😅

I'm not sure what the easiest method is. In my head I just broke it into three parts. First I wanted 10%, which is 7.5. I doubled that to get to 15. Then I wanted to find 80% of 7.5. 10% would be .75, which doubled is 1.5. Then I subtracted 1.5 from 7.5, leaving me with 6. Then I added 7.5 7.5 and 6, and arrived at 21 and concluded that was 28% of 75. I am sure my method probably wasn't that efficient. It took me maybe 8 to 10 seconds, which I am sure many can do much faster!

Very helpful trick to do calculations faster in exams thanks 😊

I miss chalkboards. 1980’s baby!!!!

Alternatively you can do 28/100 times 75. Divide 75 and 100 and you get 28/4 times 3. You divide 28 and 4 and get 7 times 3 and finally thats 21

50% (half) of 28 is 14, 25% (half in half) is 7, so 28 - 7 = 21. I do this way.

That chalkboard tapping may have been the sole reason I disliked math. That sound just sent me back 😳, it drives me 🤯.

21 is our answer. take two 10%'s and add them together (7.5 +7.5 = 15 which will make up our 20%) take another 10% and we'll take two 1%'s out (0.75 +0.75 = 1.5) to make up our 8% (6) and we'll add our 8% and 20% values together! (21) edit: this is the same way i calculate a 15% tip. if our bill is $11 and i want to leave a 15% tip. I take two 10%'s ($1.10) but instead i half one of those 10%'s ($0.55) for the 5% of the 15%. and then add the 5% and 10% value together ($1.65). Viola a 15% tip on a $11 bill. His method is nice but quickly you'll find it doesn't play well with the tipping scenario when you're trying to tip 15% or 20% on a bill that's an oftentimes not as nice looking as the value of "75"

Since you know 75 is really a form of times 3 and divide by 4, then 28% is really divide by 4 to get 7 then times by 3 to get 21. But if you get really uncommon two digit numbers to be calculated then you need to be able to multiple in your head two digit multiplication then drop two digits from the result to get the percentage. In real life, you never get such an easy problem to calculate. Only on exams and class work will you ever get precise results.

I've never been good at math!!! Never. But I've always appreciated how you could get to your answer in a variety of ways.

With percents ive always just taken 10% of the number. Multiplied it by whatever and then take 1% and mulitiply it by whatever. Then add both answers. So 7.5×2=15 and .75×8=6 so 15+6=21. This is in my head if I dont have a calc around.

I wish i had a math tutor like him in my high school

This man’s chalk skills are just as good as his math!

This is amazing. How have I not noticed this, or been told this before now? 😢

I'm Asian but even for me this is a Keanu Reeves "Whoa"

Now let's do 27% of 76 without the calculator.

Multiplying 0.28 by 75 is not difficult, but it relies on the individual's proficiency with their multiplication table. The second method depends on whether the person can recognize 75% as 3/4.

The KZfaq recommendations every kid needs right now. 😊

It makes so much sence

Finally. I have more reasons to use calculator. Thank you.

30% of 75 = 22.5 2% of 75 = 1.5 28 % = 22.5 - 1.5 = 21 Pretty easy if calculation is fast enough

😱 I'm a software engineer but today I realised that x% of y is equal to y% of x. It's an amazing discovery for me! You just naturally thik it now, 10% of 50 is 5 and 50% of 10 is also 5 Proving it mathematically by breaking down every part may look a little longer, but it's very simple, lets do it. x% × y =(x × 1/100) y =(x/100) y = xy/100 = yx/100 = (y/100) x = (y × 1/100) x = y% × x Hence, x% of y = y% of x

Thank you teacher! Please continue teaching maths and helping us to learn more.

Ok..... I think I need to watch this again 🤔

Or play with decimals, 75×2=150 75×8=600, then change decimal place 1.50+.60=2.10 or 21.00 which equals 28% of 75. This is easier to me because its no division and just adding and multipling.

Finally No music Easy education Useful Tricks to be better at Math Thank you for your time making videos and explain!

To calculate it in my head I round it to 30% of 75, then substract 2% of 75. I find it easier to just round up or down either the % or the number, then add or substract the difference.

You are a wonderful teacher!

I always go for the "divide by 10 and then add or substract" method. 75/10 = 7,5 75/100 = 0,75 So : (7,5x3) - (0,75x2) = 22,5 - 1,5 = 21 It looked complicated and very mechanical when I was a kid, but it just works all the time when everything else fails, so I use it without even trying any smart trick. This got me through all of the mental calculations required during all my students years, from beginning to end lol

I immediately remembered you used this technique in a previous example. Always enjoy these little tips and tricks.

This gave me warm fuzzies....I was back in high school again for a moment.

Sir you are a genius....my head is spinning 🎡

just think it as 75% of 28. Much easier to do in head. Ans: 21

I used to a love math in high school and university... so watching your videos is like therapy Thank you!

i use this all the time, the most helpful little trick in math fs

Still a pretty easy pair of divisible numbers tho but a great trick i didnt know asian dude thx

The reason it works is that this question is basically [(28/100) * 75] = [(28 * 75)/100] = [(75/100) * 28]

Pulls out phone instead....life's too precious! 💯

28% οf 75: 0,28*75 = 75*28*0,01 75% of 28: 0,75*28 = 75*28*0,01 So, basically, this trick works for any numbers 34% of 56: 0,34*56 = 56*34*0,01 56% of 34: 0,56*34 = 56*34*0,01 See?

That is genius! Never thought this was possible!

Really enjoy watching you explain things! Always felt like Math was never my strongest suit so you’re making me feel much more confident! Thank you!

This guy has the best videos I wish he was my teacher in highschool

The way I did it in my head in about 10 seconds is: I split up the 28% to 20% and 8%. I know quickly 20% of 75 is 15 (in my head: 10% of 75 = 7.5, then I double 7.5 = 15). Then, knowing 1% of 75 is 0.75, I multiple 0.75 eight times, which gives me 6. Add 15+6, and there you go.

Very nice! ❤ Just subscribed! 😊 Thank you!!!❤

Great videos, proffesor. Thanks for inspiring us!

That's how you make maths complicated

My way of solving maths is slightly different, Instead of finding 28% find the nearest round figure which is 30% that is 22.5 Now subtract 2% which is easy 1.5 Answer is 21 It might look complicated or stupid, but it is the best way for me atleast.

I was today year's old learning this, thanks ❤

If he explained a Lil slower and included why he was doing each step, that would make more sense. Feel like I'm back in high school.

Not bad. For anyone not wanting to deal with fractions, here is a trick I use for quick percentage calculations. 28 and 75 are both integers, so here is what you do. Divide them both by 10 and multiply the results. So 28 ÷ 10 = 2.8 and 75 ÷ 10 = 7.5 and 2.8 × 7.5 = 21. Simple. NOTE: The division is not ACTUALLY necessary in this trick since during any multiplication the decimal is ignored until after the addition which follows the multiplication (during multiplication involving 2 or more digit numbers). The trick can actually be done thusly: 28 * 75 = 2100, then shift the decimal the appropriate number of places to the left (in this case 2 decimal places). I thought this was obvious but it has been brought to my attention that it caused misunderstandings. I only included the division to make the intention and workings of the trick more apparent for those trying to apply it. I am sorry for any confusion, take care. :)

Some useable knowledge on a short Thank you

*HATS OFF TO THIS AMAZING MAN!* 🎩😎👍 *ALSO, THANK YOU FOR THE INFO.* 👍💫

You start with 28 but we don’t want that instead we replace the 7 with an upside down umbrella symbol that turns the 8 into a cucumber salad. That means you can multiply the sky with your new basement door leaving you with 1% of your late uncle frank. You take that 1% and decide the number 8 never existed in the space time continuum and then you have to go out because it started snowing in the living room again. I hope this helps everyone who found the first explanation complicated.

It’s not “difficult to do without a calculator” if you don’t create calculator dependency for things that can be done in your head; like this problem.

Wow!😮

I love math,n I remember this trick from 8th grade.great stuff.Salute.

Some of my teacher used to teach math without any passion which is why I was always scared of math even though I was getting good grades at it... After watching you videos my latent interest about math rose up

Re-write 0.28 as 28/100 then proceed in the same way (28 x 75)/100 🤷‍♂️ there is no need to “switch” anything

That's a neat trick. But sometimes it's not possible (you'll not always get a clean number like 75). So what I do is approximate to a clean number. For example, 28% of 75 is almost equal to 25% of 75 which is 75/4 which is almost equal to 76/4 which is 19. 19 is not that far off the correct answer which is 21. For serious accuracy, there's serious tools.

Who needs school when you have the internet, so many people googled their way to getting degrees over the years 🤣

They’re each as incomprehensible as the other.

😂😂😂😂 28% of 75 literally means 28/100 x75 , which get the same answer. But uncle unnecessarily adding 1 more step. 😅

My answer without a calculator: 28% = 30% - 2%, which means that if we figure out what 30% and 2% are, we can find the answer. To find 2%, we consider the following: 10% of 75 is 7.5, so 20% of 75 is 15 (because 20% = 2 * 10%), which means that 2% of 75 is 1.5 (because 2% = 20% / 10 = 15 / 10). To find 30%, we consider the following: 30% = 20% + 10% = 15 + 7.5 = 22.5 Since 28% = 30% - 2%, then 22.5 - 1.5 = 21, which is the correct answer. Thank you for your videos, I'm learning a lot! Your idea of putting the equation on the blackboard with a projection is very original, at least I haven't seen that anywhere else. But of course your explanations are the real meat of your videos.

Wow. That is so cool!

This tough 🔥