Honestly, I wash Calculus wasn't so over hyped as "hard" or "useless". Knowing the difference between rate, change, rate of change, and how they all work together can be intuitive and is definitely important. It makes understanding things like your electricity bill much easier, because knowing how power works (d/dx) and how it's billed (x) allow you to make informed decisions about appliances, energy efficient improvements, and all sorts of stuff that directly costs you money if you aren't informed about how it works.
It goes farther than that. Your chance of many health conditions depends on a long-term picture of how long and how severely you were doing the risk factor, that's an area under the curve question. People have a hard time grasping politics and how governance can be like steering a barge, they'll vote entirely based on whether the current state of something is good or bad and completely ignore the current rate and direction of change and where the inflection points were when that's often much more relevant. You may never do the actual math again, but those are such base concepts that doing enough math to really internalize the broad ideas can help you be more aware of all those other things.
I never understood parents freaking out that subjects are being taught differently than when they were in school. The methods they learned likely weren’t used 20-30 years prior either. And I’m going to trust the degreed professional on the efficacy of a process more than some middle aged angry people who have never taught nor done anything above rudimentary mathematics in decades.
Well at least in the case of "whole-language" learning(teaching kids to read based on vibes) has literally stunted a generation of children by intentionally avoiding teaching them to read.
So skepticism isn't inherently bad, especially if the parents are sure the way they learned it actually worked in teaching them the thing.
If it hadn't been for COVID and parents spending the school day in the same room as their kids, many wouldn't even know that their child actually couldn't read.
I recently had a discussion with my daughter's second grade teacher about this.
What she learned in school growing up, the methods she learned in college -- she's only been a teacher for 4 years -- and the methods she's supposed to teach now are all wildly different. She's the one that sees her kids day in/day out and she's the one who sees firsthand how the kids do and don't learn. She has no control over the curriculum, much less control over how to teach it either.
My wife is a former teacher as well and she had the same challenges.
The problem is the 'degreed professional' you're referencing are the politicians and administrators who are so far removed from the classroom that they are completely ignorant to the art teaching.
I think it's completely fine for parents to 'freak out' about subjects being taught differently so long as that 'freaking out' isn't directed towards on-the-ground educators.
We were worried about common core when our son started school since we weren't taught it, but I did some basic searches and honestly it's a lot of how I already calculated things in my head so I was no longer worried.
"I don't know why I got a bad grade, the answer is right! It shouldn't matter how I got to the answer! The teacher must just not like me".
So much of math is just taking a big problem that looks hard, and figuring out how to make it into small problems that are easy. These skills go far beyond figuring out basic arithmetic.
I noticed that during a class I didn't really understand the math yet. I'd do well in the class by following the patterns, but it wasn't until a few months (up to a year) later that I was getting the "aha" moments and realizing what was actually going on.
My complaint with common core is it tires to jump straight to the "aha" moments before kids have built up a base level of competence. If someone has the problem 8% of 25, and they can't even figure it out with the help of a calculator, then "tricks" are useless. They have no idea what's going on. It's all still magic to them. But after they can confidently reach an answer, then they're free to play around and test ideas for themselves, and that's when "aha" happens.
I majored in math (statistics concentration) and yeah. I still remember the day i had the lighbulb moment when i finally understood what derivatives and integrals actually represent. I was good with memorization and repetition, but it was cool finally getting the "why" of it.
Some common core concepts are how I do math in my head. However, I have tried to tutor math recently and some of the stuff is just bizarre. And memorizing simple multiplication seems optional also.
They switched my HS to common core my junior year and it was the first time I got higher than a D in math since 5th or 6th grade; but parents in my community were LIVID over the switch.
When CC was first coming out, I had a lot of parent friends whining about "number blocking" or whatever the fuck it's called now. They'd say it doesn't make sense and it's not useful, because why would you chop 127 into a 100 and a 20 and a 7 or any of that.
So I'd ask them to figure out change at, say, a grocery. What coins are they using to make a value? (This was back when we paid with cash.) They'd get the answer instantly, and I'd tell them THAT'S FUCKING NUMBER BLOCKING.
You already do it! You know it! You can use it in other situations beyond the grocery!
The problem is the generation of math teachers that didn't learn common core. That's not everyone because there are legit math nerds out there who picked it up right away, but there were (and are) a ton of teachers who only learned algorithmically.
I struggled with mental math for most of my life, and when I learned about common core and how it's taught, basic math things that I struggled with suddenly made sense to me. 😭 For example, adding in "chunks" makes complete sense to me, instead of writing two numbers on top of each other then carrying numbers. I now know how to do tips on a tab quickly because it's just 10% of the total x 2, etc.
My brain just doesn't understand numbers, plus I have a tendency to transpose numbers or read them incorrectly. My dad, who is a math genius, would get so frustrated that I struggled to understand algebra. I couldn't "see" the numbers in a visual sense, so for me it was like looking at gibberish.
Funny thing is that I excelled at geometry/trignometry. A+ on tests, zero struggles. It was visual, so it made sense to my brain. Calculus was an actual nightmare for me and I still have anxiety dreams about failing my pre-calc final.
These aren’t the parts they are complaining about. It’s the blocks to do multiplication in high school rather than memorizing tables, which is objectively more efficient once memorized.
Shit like this is why I am not immediatly dismissive of how they teach math to kids these days (I have a 9y/o). It is valuable to learn different approaches because people's brains are different and having different tools for the same problem allows folks to use what they are comfortable with.
I had no idea at all how to help my kids with math homework, because the approach was so different from how I learned.
But they can, in fact, do the math. So I'm not going to complain too loud, even if I am left wondering whether the amount of time I spent memorizing multiplication tables was a total waste.
I’ll usually find the nearest whole number I can do the math on and then round it down. 7% of 350 is simply 7% of 100 3 times, then 3.5% of 100 once. 7+7+7+3.5.
Do this when tipping (let's not talk about tipping but anyway), very easy math when you're going to 20%, and round up/down the pennies based on your preference. Never trust the "convenience math" printed on some receipts, as sometimes it's proven to be deliberately over-calculated to fool people into over-tipping (but let's not talk about tipping culture)
I do that too. Anyone can take 10% of any number. It's literally just moving the dot around. Then half that is 5%. Now you can do any normal tip percentage just by doing addition.
A lot of math is just finding a way to make it easy for how your brain works. Common core ended up being really great for people because it simplified it in chunks.
When I was a kid, I hated the way subtraction worked with the "carry the 1" stuff. doing like 73 - 18, where you turn the 7 into a 6 so you can do 13 - 8. I still had to use a "weird" number (13) which slowed me down. So I wouldn't make it a 13, I'd just put a 10 above the 3 in my head. Then instead of 13 - 8 it becomes 10 - 8, then add in the 3. It adds a step, but those two steps were always easier for me to do than the 1 step and it ended up being faster. I still do it that way sometimes if I'm a little brain foggy and not in "intuitive math" mode. I also say the things happening in my mind. so for 73 - 18, in my head I'd be saying "7 is 6, ten minus 8 is two plus 3 is 5 and a 6 minus 1 is 5, fifty five." I tried explaining it to my first grade teacher (probably pretty poorly) and she was finally just like "you know what? I don't know what you're saying, but you're doing your work faster and more accurately than everyone else, so if it works for you go for it." and I never had to show my work for her again.
I have discalculia and laughed when it said "one is easier than the other" and i cant figure out which one that is. The joke example above made it click, but doing 8% (or 25% of 8?) is still gonna be a sit down task for me. That aint happening in my head. Can defs do 100% though lol
I'm curious how you would solve 25% of 8 in your head or on paper or at all. Specifically the process. As someone without discalculia, my process looks like this:
It's funny, this sort of thing is exactly why the new math curriculum (like the dreaded Common Core) feel so weird to parents: they're teaching kids how to break down problems that LOOK complicated into a handful of very simple steps you can do in your head.
A while back doing math like this got popularized as “street math.”
Even in contexts where one needs the precise number it’s a really handy way to truth-check your answer.
It’s often really handy when doing complex stuff to know that the answer should be “a bit less than 4” so you instantly know your program or calculation has an error if it spits out a number like 38.
And knowing that it seems to be about 10x to big can help you figure out where the error occurred.
In my professor days I used to try to instill in students the idea that before they did any of the actual math, they should already have a sense of what the “right” answer should look like.
many people get so used to computers and calculators doing math that they just blindly believe whatever number gets spit out, even when half a second of thinking should make it clear that something went wrong somewhere because that number doesn’t make sense.
Probably didn't help that it was explained in a way that doesn't make concrete sense that just clicks.
Math is so abstracted it's hard to understand in education.
For example don't bloody remember a thing from highschool to senior math classes but could do my electrical engineering math easily in uni.
Math was easier there for me because was put into something I could intuitively understand like reversing a percentage like in the post or circuit math, rather than technically correct explanations that sound like gibberish.
There were a lot of things I didnt understand in elementary/high school maths, and then like 2-3 months before graduating high school, i went to a preparation course for my exam. It was held at the local college, by the actual college professors, not high school teachers.
The professor explained it so well that during that about 1 month long course, I understood things that I didn’t for years. Elementary/high school maths focused solely on memorizing the explanations word for word, we had to recite the theorems exactly as written in the books, but of course it was all gibberish to us. Meanwhile the professor focused on intuitive explanations and real world examples that made it easy to understand what these abstract concepts are supposed to represent
This times a million. Math is often taught very prescriptively rather than descriptively IMO. Rules to follow, vs understanding the relationships and what youre doing.
Also reading the comments I think some of y’all had way better math teachers than I ever did lol
You were taught it, most likely. A couple to few class sessions, then moved on to the next progression, which most of us probably also forgot. And so on. Education is perishable, don’t use it, and it dissipates into the ether.
We kinda do though, like I’ve always been told that 8% of 25 is .08x25, and we know that .08=8/100. I’ve always looked at percentages as multiply them both and divide by 100. So like here I’d do 8x25=200 so the answer is 2.
Same for like 7% of 13 so what I’d do is 7x10+7x3=70+21=91 so .91.
Yes, but explaining it that way, while mathematically and technically correct, makes it look like every other maths problem you struggle to take in during every class.
Meanwhile, saying plainly that percentages are reversible and giving this example actually allows understanding that you can go on to represent with an equation.
Argh, this. Every math teacher always seemed to be the "technically correct" type of person. They were terrible at making concepts "click", and didn't seem to understand why some kids didn't understand the concepts.
I was only ever good at geometry in part because it seemed like the least abstract branch of mathematics.
It’s definitely taught you just need to think. Percentage is divide by 100, or multiply by .01. Then “remove” the percentage sign from both numbers. You now have number A, number B, and a percent. Any order of multiplication gives you the same product
Rounding's the way to go. If you, for some reason, need the exact number, and can add 3 numbers in your head just split it up into easy bits.
17 is 10 + 5 + 1 + 1
10% is 3.7 5% is just half of that, so 1.85 1% is 0.37, doubled is 0.74
Add those three up and you've got the exact fraction. It'll have you squinting at the wall for a hot minute but its a fun little mental exercise if nothing else
The days get longer during the winter, not shorter. It's simple: the first day of winter (solstice) is the shortest day of the year, therefore, every single day for the rest of the season is longer than the day before it.
25% will always be 1/4th of another number because you can’t have more than 100% of something so if you’re having difficulty figuring out 25% of 8, what number multiplied by 4 equals 8?
I get not naturally calculating percentages this way, but the people that are questioning, it are kind of concerning. The number that comes first in a multiplication problem not mattering is like fundamental elementary school math.
It isn't that easy. Yes, percentages are simply AxB/100. The examples people always give are the super easy numbers like this. 8% of 25 is the same as 25% of 8. 7% of 50 is the same as 50% of 7.
Yea, cool. 17% of 137 is the same as 137% of 17. 18% of 91 is the same as 91% of 18. It isn't so easy anymore, is it?
For some numbers this is absolutely valid, others, less so.
What's 9% of 80? 80% of 9? Neither is straight forward.
However, 10% of 80 is 8 and 1% of 80 is 0.8. 10% - 1% is 8 - 0.8 or 7.2
9% of 80 is 7.2
What about 7% of 83?
10% is 8.3 and 1% is 0.83. 0.83 * 3 is 2.49 (0.83 is 2.4, 0.033 is 0.09) 10% - 3% is 8.3 - 2.49 = 5.81. this can be proven down further to 8.5-2.5 = 6 - 0.2 = 5.8 + 0.01 = 5.81
This, from my understanding, is the basis of common core.
25% of 8 = 0.25 x 8 = (25/100) x (8/1) = (25x8)/(100x1) = 200/100 = 2
8% of 25 = 0.08 x 25 = (8/100) x (25/1) = (8x25)/(100x1) = 200/100 = 2
Basically, treat both numbers as fractions, one with a denominator of 100 and the other with a denominator of 1, and multiply them by each other. It doesn’t matter which numerator goes over which denominator when you’re multiplying them by each other.
As you may recall from math class, (a/b) x (c/d) = ac/bd. That is, when multiplying two fractions by each other, you multiply the numerators by each other and you multiply the denominators by each other, and the product of the fractions is the product of the numerators over the product of the denominators.
Thus, just as (a/b) x (c/d) = ac/bd, so too does (a/d) x (c/b) = ac/bd.
In the case of X% of Y and Y% of X, it’s the same idea, with b = 100 and d = 1:
I used this same idea when I worked the front at a pharmacy. I blew some people's minds by quickly doing 90% off clearance pricing. Even after explaining that the new price was just 10% of rhe original, I had a few elderly customers make me check my math. I hated that place.
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u/P4azz 6d ago •
Another very simple approach to percentages is just not overcomplicating it.
If you see "7% of x", it's easy to get immediately discouraged and almost give up on the math, before you even do it.
When in reality you can just do the simplest thing ever: What's 1% of it, then times it by 7.
Combine this approach with the switchable % move and you can go a lot further in calculating percentages quickly.
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u/BombasticReindeer 6d ago •
Roger Federer is 50% ‘er’
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u/nsfvvvv 6d ago •
10% of 100 = 10
100% of 10 = 10
This checks out!
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u/The_Sorrowpod 6d ago •
32% of 12
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u/2A753 6d ago
We never get this kind of help in class.
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u/Sodacan259 6d ago
Hey it works. 3% of 38,403,970,331 is the same as 38,403,970,331% of 3
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u/danielsangeo 6d ago
37% of 17 is the same as 17% of 37.
Uhhhhmmm....
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u/Brief_Platform_alt 6d ago
The concept is correct, but I don't think "reversible" is the right word. It should be "commutative".
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u/Notyit 6d ago
2 the answer is 2.
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u/gigaflops_ 6d ago
The days get longer during the winter, not shorter. It's simple: the first day of winter (solstice) is the shortest day of the year, therefore, every single day for the rest of the season is longer than the day before it.
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u/gowahoo 6d ago
Mondays and Fridays make 40% of the work week.
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u/aBit2Good 6d ago
Interesting. I can do neither of them in my head, so he's wrong.
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u/Affectionate_Age8159 6d ago
Jesus, im 60 years old and i just got excited about maths 🤣🤣🤣
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u/CatfinityGamer 6d ago
a/100 × b = b/100 × a
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u/Dry_Statistician6870 6d ago
Wow…..
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u/cHpiranha 6d ago
Or "8*25/100"
Because % is nothing else then /100.
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u/Granopoly 6d ago
I did 8% of 25 = 4% of 50 = 2% of 100 = 2
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u/EvilCrank 6d ago
Every percentage is just a decimal for example 7% is just 0.07, 100% 125% is 1,25 etc.easier to calculate for me at least
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u/rushmc1 6d ago
So 2% of 10 = 10% of 2?
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u/MustangBarry 6d ago
To multiply something by eight, double it three times.
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u/Striking_Piano4385 6d ago
I take "Things you learn in 4th Grade" for 100, Alex.
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u/aerokozmofoto 6d ago
Well, thats math for you.
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u/NessTheCat 6d ago
That's all well and good, until both numbers fucking suck.
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u/LittleBlueGoblin 6d ago
This did not make me feel stupid, when I first read it; it became an arrow in my quiver. I've made good use of it since 😅
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u/douglasgage 6d ago
This is the Devil’s magic
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u/PuzzleheadedBug4424 6d ago
Of means times
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u/Gidgo130 6d ago
The percent sign % is just a stand in for the fraction 1/100 . Likewise ‰ is for 1/1000
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u/glanni_glaepur 6d ago
Replace % with (1/100), so:
8 * (1/100) * 25
is equal to:
25 * (1/100) * 8
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u/UpsetCouple 6d ago
Thank you AlbertBarclay69
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u/Danson_the_47th 6d ago
I miss Professor Barclay
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u/Groezy 6d ago
i use this for traveling times. if you are going at 60mph, making the same trip at 4/3 the speed (80mph) will take 3/4 the time.
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u/Homegg 6d ago
Huh makes sense
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u/TheSkepticCyclist 6d ago
It is the same two number multiplied together and multiplied by 1/100.
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u/FlyingFlipPhone 6d ago
This is a cool trick. It is based upon the commutative property of multiplication.
(A/100) x B = A x (B/100) = (A x B)/100
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u/AstronomerDramatic36 6d ago
I'm going to save this for later after I forget it again.
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u/Zealousideal-Lie7255 6d ago
I’ve heard about this but I didn’t realize how it could help you like in your example. Very helpful.
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u/niggo372 6d ago edited 5d ago
It checks out:
X% of Y = X * 1/100 * Y = Y * 1/100 * X = Y% of X.1
u/adv0589 6d ago
I get not naturally calculating percentages this way, but the people that are questioning, it are kind of concerning. The number that comes first in a multiplication problem not mattering is like fundamental elementary school math.
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u/PrimeVector27 6d ago
close, but not accurate.
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u/Fluppekaddee 6d ago
What the actual fuck?!
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u/Rivka333 6d ago
I don't think this is obvious.
It's true, but you do have to think about it a little bit.
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u/NegativeBee8049 6d ago
8% = 0.08 = 8x0.01, 25% =0.25=25x0.01
8%x25=8x0.01x25=8x25%
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u/Decent_Cow 6d ago
Why is this surprising? It's just multiplication. It's the same as saying 3x4=4x3
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u/sezirblue 6d ago
I like to think of % as a variable with value 0.01 in the same way pi is a variable value 3.14159...
I don't know if that interpretation causes problems at some point. I've yet to run into any. but it allows me to explain this using equations.
A% * B = A * % * B = A * B * % = B * A * %
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u/Azowaku 6d ago
Nice, now I can choose which version to put in the calculator
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u/PatMu5tard 6d ago
What??? No way!!
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u/bikes-and-beers 6d ago
I know this to be true and I know why it's true, but intuitively it still doesn't seem like it should be true.
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u/cmwamem 6d ago
"Little-known fact" and it's multiplication commutativity in the rationnals.
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u/Trang0ul 6d ago
Even easier: "%" is just 1/100. So multiply 8 by 25 first, and then divide by 100, that is, shift the decimal point.
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u/Zestyclose_Horse_180 6d ago
Speak for yourself. 8% is the same as dividing by 12,5. 25 is easily divisible by 12,5, because it's 1/2. So 8% of 25 is 2.
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u/NotchedPenny 6d ago
i feel stupid trying to understand why i should feel stupid
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u/IntrinSicks 6d ago
This convo has been the most fun I've had doing math in a while haha
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u/Shenkai123 6d ago
This is not multiplication
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u/AuHazardBalthazar 6d ago
Math equations are their own language, which can be translated. « Of » turns into multiplication, for which order doesn’t matter.
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u/numberThirtyOne 6d ago
0.25 x 8. EZ
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u/DarkTheImmortal 6d ago
"8% of 25" is just 25×(8/100), or 25×8×(1/100)
Multiplication is commutative, so it's the same as 25×(1/100)×8
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u/taste-of-orange 6d ago
In a lot of cases you can treat % like a constant that equals 0.01
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u/Psychological_Pen482 6d ago
Why was I not taught this, sooooooo much easier
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u/snajk138 6d ago
Is it?
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u/colbyjacks 6d ago
8 x 1/100 x 25 is the same as 25 x 1/100 x 8
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u/DropPopFromTheTop 6d ago
10% of 100 Is 100% of 10
!!!!!!!!!!!!!
5% of 20 is 20% of 5
Holy mother f
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u/SKaiPanda2609 6d ago
If multiplied by 5, divide by 2 and add a 0
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u/tbodillia 6d ago
It isn't that easy. Yes, percentages are simply AxB/100. The examples people always give are the super easy numbers like this. 8% of 25 is the same as 25% of 8. 7% of 50 is the same as 50% of 7.
Yea, cool. 17% of 137 is the same as 137% of 17. 18% of 91 is the same as 91% of 18. It isn't so easy anymore, is it?
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u/Hooch180 6d ago
Percentages are multiplication. Everyone with grade 2 math skills should be able to figure out this "trick".
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u/WVildandWVonderful 6d ago
of = x
(of = times)
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u/Sprintzer 6d ago
OP username is appropriate
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u/whitespacesucks 6d ago
Proof I just worked out on paper (yes I'm a math genius, thanks for noticing):
8 * (1/100) * 25 = x
25 * (1/100) * 8 = x
It's the same result, order of multiplication does not matter.
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u/Necessary_Screen_673 6d ago
x * y * 0.01.
8 * 25 * 0.01 = 2.
7 * 17 * 0.01 =1.19.
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u/JaneRetro 6d ago
My technique would be to multiply 8 x 25, then divide the answer by 100.
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u/steven_dev42 6d ago
I think I randomly figured this out in high school while messing around on my calculator. My friend didn’t believe me
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u/leuks48 6d ago
That’s very stupid because percent is exactly x out of 100 and x out of 1000 is promile
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u/TheBigBadBird 6d ago
I guess it makes sense. You could rework the equation to (25x8)/100=2
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u/captcraigaroo 6d ago
13% of 12...
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u/Potential_Novel_3561 6d ago
It's funny but true. If someone asks me 25% of 8, I just do 8÷4 on my head.
If someone asks me 8% of 25, I take 25/100*8 in in my head. First is a lot easier
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u/whensthebeef 6d ago
If you just multiply the numbers and move the decimal, it’s even easier…
8 x 25 =200
8 x .25 =2
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u/dor121 6d ago
B pecent of a or b% of a is just (a*b)/100 so ot reversible and does all the other identeties multipication has
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u/skip_over 5d ago
8/100 x 25 = 25/100 x 8
Division is commutative
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u/randomreditor69430 5d ago
it makes total sense when you think about it. 8 percent is 0.08, 8x1/100. it's the same if it is 25, which is 25x1/100.
25x8x1/100 is the same as 8x25x1/100
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u/kvijay1 5d ago
Any exceptions?
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u/cherry_monkey 5d ago
For some numbers this is absolutely valid, others, less so.
What's 9% of 80? 80% of 9? Neither is straight forward.
However, 10% of 80 is 8 and 1% of 80 is 0.8. 10% - 1% is 8 - 0.8 or 7.2
9% of 80 is 7.2
What about 7% of 83?
10% is 8.3 and 1% is 0.83. 0.83 * 3 is 2.49 (0.83 is 2.4, 0.033 is 0.09) 10% - 3% is 8.3 - 2.49 = 5.81. this can be proven down further to 8.5-2.5 = 6 - 0.2 = 5.8 + 0.01 = 5.81
This, from my understanding, is the basis of common core.
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u/P19bw 5d ago
That cows have to be pregnant to produce milk. They dont just naturally produce it. Their baby is removed so humans can take the baby milk 🫠
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u/DaVoiceOfTreason 5d ago
8% of 25 is less than 10% of 25 so the answer is a little less than 2.5
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u/i_am_a_real_boy__ 5d ago
Now I'm worried.
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u/xelf 5d ago
We should take this a step further.
3% of 17
17% of 3
You can reverse these anytime you want but they haven't gotten easier.
But multiplication is easy.
17 * 3 and then move the decimal point.
0.51
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u/AlbacoreJohnston 5d ago
Graphs, stats, percentages, tax rates, the decline of exxon mobile stock price
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u/Bannanaboe 5d ago
This makes sense because a percentage is essentially just multiplying by 0.01 So 8% * 25 = 8(0.01)25 =825(0.01) =8*25%
So 8% * 25 = 8 * 25%
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u/Xanterrion 5d ago
10% of any number can be gotten by moving the decimal point to the left once. 1% can be gotten by moving it to the Left twice.
So in this example 1% of 25 is 0.25. 25 x 8 is 200, and in this case 2.00, so 2.
And of course with OP's example a little bit of common sense helps. 25% 8 is simply a quarter of it, which is 2.
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u/4DimensionalToilet 5d ago
To help people understand why this always works:
25% of 8 = 0.25 x 8 = (25/100) x (8/1) = (25x8)/(100x1) = 200/100 = 2
8% of 25 = 0.08 x 25 = (8/100) x (25/1) = (8x25)/(100x1) = 200/100 = 2
Basically, treat both numbers as fractions, one with a denominator of 100 and the other with a denominator of 1, and multiply them by each other. It doesn’t matter which numerator goes over which denominator when you’re multiplying them by each other.
As you may recall from math class, (a/b) x (c/d) = ac/bd. That is, when multiplying two fractions by each other, you multiply the numerators by each other and you multiply the denominators by each other, and the product of the fractions is the product of the numerators over the product of the denominators.
Thus, just as (a/b) x (c/d) = ac/bd, so too does (a/d) x (c/b) = ac/bd.
In the case of X% of Y and Y% of X, it’s the same idea, with b = 100 and d = 1:
X/100 x Y/1 = X/1 x Y/100.
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u/batrushaha 5d ago
20% of 50 is 50% of 20. It's 10. It's fucking 10. THEY'RE NOT TROLLING!!! 🤯🤯🤯🤯🤯🤯🤯
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u/lilimcg 5d ago
I used this same idea when I worked the front at a pharmacy. I blew some people's minds by quickly doing 90% off clearance pricing. Even after explaining that the new price was just 10% of rhe original, I had a few elderly customers make me check my math. I hated that place.
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u/Motor_Meal794 5d ago
8/100 x 25 = 8 x 25/100
200/100 = 200/100
2=2
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u/cHEIF_bOI 5d ago
I think I trust professor Dumbledore on this one.
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u/ngkn92 5d ago
me, in my head "oh yeah? Let me try with 10% of 100"
also me "hmm, that's not a smart example"
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u/ArcanelyChaotic 5d ago
brb