"Five out of Four People Have Trouble with Fractions" - S. Wright
April 24, 2021 4:32 PM Subscribe
How to calculate fractions. Tanya Zakowich runs TikTok channel pinkpencilmath offering quick math tips!
Kind of like when A&W tried to outdo McDonalds by have a third pounder burger instead of quarter pounder and people thought it was smaller because 4 is bigger than 3.
posted by blue shadows at 5:08 PM on April 24, 2021 [10 favorites]
posted by blue shadows at 5:08 PM on April 24, 2021 [10 favorites]
I designed a public park a while back and a pedestrian ramp was needed, so I arranged to meet engineer (new and Very attached to his code book) on-site.
I said "that's a nice slope, I should be able to get a 1:20 ramp there", he looked puzzled, "but the code says 1:12..., I had to go to some length to explain, some folks seem fine with fancy functions, less so with everyday.
posted by unearthed at 5:34 PM on April 24, 2021 [4 favorites]
I said "that's a nice slope, I should be able to get a 1:20 ramp there", he looked puzzled, "but the code says 1:12..., I had to go to some length to explain, some folks seem fine with fancy functions, less so with everyday.
posted by unearthed at 5:34 PM on April 24, 2021 [4 favorites]
Kind of like when A&W tried to outdo McDonalds by
At last count, 200% of all A&W mugs are still unaccounted for.
posted by clavdivs at 5:40 PM on April 24, 2021 [2 favorites]
At last count, 200% of all A&W mugs are still unaccounted for.
posted by clavdivs at 5:40 PM on April 24, 2021 [2 favorites]
At last count, 200% of all A&W mugs are still unaccounted for.
That's almost half of them!
posted by BozoBurgerBonanza at 5:58 PM on April 24, 2021 [10 favorites]
That's almost half of them!
posted by BozoBurgerBonanza at 5:58 PM on April 24, 2021 [10 favorites]
I once had an exceptionally long discussion with a superior about the pizzas i was ordering for a party. They were expensive. I pointed out that they were 18” rather than 16”. That’s not much was the reply. I had to do the geometry in front of them. To their credit, they backed down.
posted by GenjiandProust at 6:34 PM on April 24, 2021 [7 favorites]
posted by GenjiandProust at 6:34 PM on April 24, 2021 [7 favorites]
It was a hey, wait a minute … moment when someone told me that
x% of y = y% of x(they're both x · y ÷ 100). So sometimes it's easier to swap them around:
16% of 14 = 2.24 = 14% of 16 17% of 9 = 1.53 = 9% of 17 20% of 12 = 2.40 = 12% of 20 20% of 21 = 4.20 = 21% of 20 28% of 17 = 4.76 = 17% of 28 4% of 6 = 0.24 = 6% of 4 7% of 19 = 1.33 = 19% of 7 8% of 11 = 0.88 = 11% of 8 9% of 19 = 1.71 = 19% of 9 9% of 29 = 2.61 = 29% of 9posted by scruss at 7:17 PM on April 24, 2021 [19 favorites]
Marker math with Vi Hart: Fractal Fractions
posted by bartleby at 7:43 PM on April 24, 2021 [1 favorite]
posted by bartleby at 7:43 PM on April 24, 2021 [1 favorite]
I loved fractions at school. Some teachers saw me as a trouble-maker, and they would send me over to the math teacher, who was having class with some other grade, and she would give me a stack of fractions to calculate. It was great. What was supposed to be a punishment was in fact a treat, and she and I knew it.
But now? I stumble. Always having a calculator at hand makes me lazy. Maybe I should do an online course during the holidays.
I do sums every day at the supermarket, adding on the prices in my head and rewarding myself with a smile if I hit the right sum at the end.
posted by mumimor at 12:41 AM on April 25, 2021 [3 favorites]
But now? I stumble. Always having a calculator at hand makes me lazy. Maybe I should do an online course during the holidays.
I do sums every day at the supermarket, adding on the prices in my head and rewarding myself with a smile if I hit the right sum at the end.
posted by mumimor at 12:41 AM on April 25, 2021 [3 favorites]
It was a hey, wait a minute … moment when someone told me that x% of y = y% of x
I remember having a similar moment as a kid, when I first twigged that "of" in the sense above means exactly the same thing as "multiplied by", and that "%" is nothing more than a shorthand notation for "÷ 100". Somehow, nobody had ever explicitly pointed these things out to me. They should have. Would have saved quite a bit of confusion.
posted by flabdablet at 2:05 AM on April 25, 2021 [3 favorites]
I remember having a similar moment as a kid, when I first twigged that "of" in the sense above means exactly the same thing as "multiplied by", and that "%" is nothing more than a shorthand notation for "÷ 100". Somehow, nobody had ever explicitly pointed these things out to me. They should have. Would have saved quite a bit of confusion.
posted by flabdablet at 2:05 AM on April 25, 2021 [3 favorites]
> I hope those 5 people do not work in construction.
80 out of 64 Americans working in construction are scary good at binary fractions though. Car mechanics too.
posted by kleinsteradikaleminderheit at 3:45 AM on April 25, 2021 [1 favorite]
80 out of 64 Americans working in construction are scary good at binary fractions though. Car mechanics too.
posted by kleinsteradikaleminderheit at 3:45 AM on April 25, 2021 [1 favorite]
I once had an exceptionally long discussion with a superior about the pizzas i was ordering for a party. They were expensive. I pointed out that they were 18” rather than 16”. That’s not much was the reply. I had to do the geometry in front of them. To their credit, they backed down.
For the longest time, on our kitchen whiteboard we had the price per square inch of pizza for each of the sizes at our local place (FTR, other than small the unit prices were surprisingly close).
posted by fairmettle at 6:24 AM on April 25, 2021 [6 favorites]
For the longest time, on our kitchen whiteboard we had the price per square inch of pizza for each of the sizes at our local place (FTR, other than small the unit prices were surprisingly close).
posted by fairmettle at 6:24 AM on April 25, 2021 [6 favorites]
A man walks into a pizza shop and orders a large pizza. “Do you want that cut into six or eight slices?” the counter person asks. The man thinks it over and replies, “Better make it six. I don’t think I could eat eight slices.”
posted by Thorzdad at 8:49 AM on April 25, 2021 [8 favorites]
posted by Thorzdad at 8:49 AM on April 25, 2021 [8 favorites]
A man walks into a pizza shop and orders a large pizza. “Do you want that cut into six or eight slices?” the counter person asks. The man thinks it over and replies, “Better make it six. I don’t think I could eat eight slices.”
hexapod-ist!
posted by lalochezia at 10:53 AM on April 25, 2021 [1 favorite]
As someone who makes the mistake too often of assuming algebra is obvious, I often find things like this really counterintuitive. My arithmetic isn't any better than anybody else's. Worse than most. But. . . the number of ordered rules here is a lot and it never would have occurred to me to teach it like that. I'd definitely start with "dividing is just multiplying by the inverse" and skip division entirely from then on.
Which isn't to say these ways of presenting things aren't more useful. It probably says I need to better learn how to teach math to other people who haven't spent much time doing such things recently. This is a nice resource. Thanks!
posted by eotvos at 11:16 AM on April 25, 2021 [1 favorite]
Which isn't to say these ways of presenting things aren't more useful. It probably says I need to better learn how to teach math to other people who haven't spent much time doing such things recently. This is a nice resource. Thanks!
posted by eotvos at 11:16 AM on April 25, 2021 [1 favorite]
I'd definitely start with "dividing is just multiplying by the inverse" and skip division entirely from then on.
In a previous life, you were the teacher who made me forever terrified of math.
posted by Thorzdad at 11:46 AM on April 25, 2021 [3 favorites]
In a previous life, you were the teacher who made me forever terrified of math.
posted by Thorzdad at 11:46 AM on April 25, 2021 [3 favorites]
That sucks, Thorzdad. Everybody has a place where there's a missing stair to their maths knowledge and it's on educators to help each person build the full set of stairs. I'm sorry yours also came with being scared of failing the teacher. (It's possible you got advanced degrees while being terrified the whole time, please excuse the presumption you did not study much maths.)
I think maybe eutvos could frame this better -- that adding and subtracting both have a direction and are each other's opposites, and likewise multiplication and division are each other's opposite where multiplication takes you away from 0 and division brings you back toward 0.
posted by k3ninho at 2:05 PM on April 25, 2021
I think maybe eutvos could frame this better -- that adding and subtracting both have a direction and are each other's opposites, and likewise multiplication and division are each other's opposite where multiplication takes you away from 0 and division brings you back toward 0.
posted by k3ninho at 2:05 PM on April 25, 2021
The math teacher who protected me all through middle school was a genius teacher, and probably so good at math and computing she wouldn't have been a teacher in this age where women have more equal access. Those of us who enjoyed her teaching were well into highschool and college stuff.
When I eventually arrived at high school, expecting to continue being the best in class, we had a teacher who hated her life as a teacher, and who simply repeated whatever was in the textbook and refused to even look at alternative methods (our middle school teacher loved geometry for everything). I lost all my joy of math, as did all the other students who had also previously done very well. Some of the others caught up at university, but I changed directions and went to art school. It's ironic that I am teaching at a tech university now. Geometry for everything is useful, though.
posted by mumimor at 2:18 PM on April 25, 2021 [4 favorites]
When I eventually arrived at high school, expecting to continue being the best in class, we had a teacher who hated her life as a teacher, and who simply repeated whatever was in the textbook and refused to even look at alternative methods (our middle school teacher loved geometry for everything). I lost all my joy of math, as did all the other students who had also previously done very well. Some of the others caught up at university, but I changed directions and went to art school. It's ironic that I am teaching at a tech university now. Geometry for everything is useful, though.
posted by mumimor at 2:18 PM on April 25, 2021 [4 favorites]
The tricks in these Tiktoks are just that, tricks. Specifically with the fractions, circling random things for each operation just obscures the real relationships that are going on and turns fractions into (yet another) list of procedures to memorize.
My feeling is that if such a trick works for a person, that's fine, and I'm glad they found something that they can use. But they shouldn't replace actual understanding.
Interested readers might enjoy Nix the Tricks, a document put together by some Twitter math teachers talking about why common tricks like this are harmful and how to explain the ideas in a better way instead.
(The TikTok adding fractions method also fails to produce the least multiple. Think about adding 1/2 + 3/4. This method would produce 10/8 which needs to be reduced whereas the more direct method of scaling 1/2 to 2/4 and adding would give 5/4. This is even worse when variables sneak in there like in (2/x)+(5/x^2). )
posted by Wulfhere at 5:20 PM on April 25, 2021 [5 favorites]
My feeling is that if such a trick works for a person, that's fine, and I'm glad they found something that they can use. But they shouldn't replace actual understanding.
Interested readers might enjoy Nix the Tricks, a document put together by some Twitter math teachers talking about why common tricks like this are harmful and how to explain the ideas in a better way instead.
(The TikTok adding fractions method also fails to produce the least multiple. Think about adding 1/2 + 3/4. This method would produce 10/8 which needs to be reduced whereas the more direct method of scaling 1/2 to 2/4 and adding would give 5/4. This is even worse when variables sneak in there like in (2/x)+(5/x^2). )
posted by Wulfhere at 5:20 PM on April 25, 2021 [5 favorites]
likewise multiplication and division are each other's opposite where multiplication takes you away from 0 and division brings you back toward 0.
But that doesn't work, because multiplication by things between -1 and 1 takes you toward 0, and division likewise takes you away.
posted by flabdablet at 9:10 PM on April 25, 2021
But that doesn't work, because multiplication by things between -1 and 1 takes you toward 0, and division likewise takes you away.
posted by flabdablet at 9:10 PM on April 25, 2021
the more direct method of scaling 1/2 to 2/4 and adding would give 5/4
The way I taught these things to little ms. flabdablet involved starting with the idea that if you're going to add things to each other, or subtract things from each other, they have to be the same kind of thing before you start.
You can't add dollars to doughnuts and get a result that makes sense, for example. The first step has to be to work out how to make the things you're adding into the same kind of thing. So you start by converting your doughnuts amount into dollars, or your dollar amount into doughnuts, whichever you'd prefer your result to be in; then add them up.
Then I taught her that the names of the two parts of a fraction - numerator and denominator - actually mean something. "Denominator" is clearly derived from the same root as "to nominate", which means the same thing as "to name"; it identifies the kind of thing the fraction is. "Numerator" and "to number" are likewise related; the numerator says how many of the thing you have. Which is also why the numerator always sounds like an ordinary number, because it is, and the denominator doesn't.
So if we need to add ½ to ¾, the denominators are different; these are different kinds of thing. So the first step toward adding them has to involve converting halves to quarters, or quarters to halves, or both to something else, whichever is easiest. And from there it's all different kinds of pizza slices.
posted by flabdablet at 9:29 PM on April 25, 2021 [10 favorites]
The way I taught these things to little ms. flabdablet involved starting with the idea that if you're going to add things to each other, or subtract things from each other, they have to be the same kind of thing before you start.
You can't add dollars to doughnuts and get a result that makes sense, for example. The first step has to be to work out how to make the things you're adding into the same kind of thing. So you start by converting your doughnuts amount into dollars, or your dollar amount into doughnuts, whichever you'd prefer your result to be in; then add them up.
Then I taught her that the names of the two parts of a fraction - numerator and denominator - actually mean something. "Denominator" is clearly derived from the same root as "to nominate", which means the same thing as "to name"; it identifies the kind of thing the fraction is. "Numerator" and "to number" are likewise related; the numerator says how many of the thing you have. Which is also why the numerator always sounds like an ordinary number, because it is, and the denominator doesn't.
So if we need to add ½ to ¾, the denominators are different; these are different kinds of thing. So the first step toward adding them has to involve converting halves to quarters, or quarters to halves, or both to something else, whichever is easiest. And from there it's all different kinds of pizza slices.
posted by flabdablet at 9:29 PM on April 25, 2021 [10 favorites]
Good point, Wulfhere. Thanks for the Nix Trix book!
posted by storybored at 10:03 PM on April 25, 2021
posted by storybored at 10:03 PM on April 25, 2021
Funny aside that I read in a math book somewhere: students are often perplexed by the concept of a complex number being represented by a tuple of real numbers - the real part, and the imaginary part (like "5 + 2i"), but they should not be, since they were already exposed to the idea that you need two channels, as it were, of digits to represent some numbers, when they were taught fractions.
posted by thelonius at 10:19 PM on April 25, 2021
posted by thelonius at 10:19 PM on April 25, 2021
>>likewise multiplication and division are each other's opposite where multiplication takes you away from 0 and division brings you back toward 0
>But that doesn't work, because multiplication by things between -1 and 1 takes you toward 0, and division likewise takes you away.
It's workable in that it didn't scare people away from engaging, and, while imperfect, we've worked together to make it better. You now get to introduce a multiplier between (0,1) that's the opposite of a multiplier greater than one.
posted by k3ninho at 12:53 AM on April 26, 2021
>But that doesn't work, because multiplication by things between -1 and 1 takes you toward 0, and division likewise takes you away.
It's workable in that it didn't scare people away from engaging, and, while imperfect, we've worked together to make it better. You now get to introduce a multiplier between (0,1) that's the opposite of a multiplier greater than one.
posted by k3ninho at 12:53 AM on April 26, 2021
I once had an exceptionally long discussion with a superior about the pizzas i was ordering for a party. They were expensive. I pointed out that they were 18” rather than 16”. That’s not much was the reply. I had to do the geometry in front of them. To their credit, they backed down.
I had a similar argument with a restaurant about how, no, the two eight inch pizzas they had brought to me were not the equivalent of one sixteen inch pizza. I think I might have drawn a diagram.
posted by Omission at 2:17 AM on April 26, 2021 [3 favorites]
I had a similar argument with a restaurant about how, no, the two eight inch pizzas they had brought to me were not the equivalent of one sixteen inch pizza. I think I might have drawn a diagram.
posted by Omission at 2:17 AM on April 26, 2021 [3 favorites]
It's possible you got advanced degrees while being terrified the whole time, please excuse the presumption you did not study much maths.
No worries. There were no advanced degrees for me. In fact, I had to take a summer class in high school just to get the minimum passing grade in algebra-1. I never stepped foot in a math class again.
When I hit university, I discovered that the math department was grouped into the same school as history, psychology, sociology, etc. and I had to acquire x-hours in the school, not any given department. So, I took a ton of history classes.
To be fair, my math problem began in second grade. I couldn't grasp "new math" and melted down. Feared math ever since.
posted by Thorzdad at 4:41 AM on April 26, 2021 [2 favorites]
No worries. There were no advanced degrees for me. In fact, I had to take a summer class in high school just to get the minimum passing grade in algebra-1. I never stepped foot in a math class again.
When I hit university, I discovered that the math department was grouped into the same school as history, psychology, sociology, etc. and I had to acquire x-hours in the school, not any given department. So, I took a ton of history classes.
To be fair, my math problem began in second grade. I couldn't grasp "new math" and melted down. Feared math ever since.
posted by Thorzdad at 4:41 AM on April 26, 2021 [2 favorites]
→
Ah, I was taught "of" first. ISTR pages of arithmetic books with '3 of 2' and '5 of 4'. Being very ADHD but undiagnosed until much later, I was utterly terrible at arithmetic but kick-ass at maths (unless you expected me to add up the terms correctly).
posted by scruss at 6:19 AM on April 26, 2021 [1 favorite]
"of" in the sense above means exactly the same thing as "multiplied by"
Ah, I was taught "of" first. ISTR pages of arithmetic books with '3 of 2' and '5 of 4'. Being very ADHD but undiagnosed until much later, I was utterly terrible at arithmetic but kick-ass at maths (unless you expected me to add up the terms correctly).
posted by scruss at 6:19 AM on April 26, 2021 [1 favorite]
But I think the "away / towards 0" thing helps show how people end up hating fractions. You have a fine rule for multiplying and dividing positive whole numbers, but once you start using fractions, sometimes it's the exact opposite.
posted by RobotHero at 6:21 AM on April 26, 2021
posted by RobotHero at 6:21 AM on April 26, 2021
To be fair, my math problem began in second grade. I couldn't grasp "new math" and melted down.
I started elementary school in 1973, so I'm assuming that I was exposed to "New Math"? This was the units about sets and base 8? That the teachers seemed to have no idea why they were teaching? The non-decimal base just confused the hell out of everyone, that is a bit abstract for children still trying to learn the elements of representing and operating on numbers in the decimal base system, I'm with Principal Skinner here.
Maybe it went farther than that, and the teachers in my school mostly blew it off. I remember the 4th grade teacher just taught us old-school long division, and in 9th grade the teacher used old textbooks and disdained the one that tried to teach geometry as all rotations and translations, iirc, not with Euclidean proofs.
posted by thelonius at 9:42 AM on April 26, 2021
I started elementary school in 1973, so I'm assuming that I was exposed to "New Math"? This was the units about sets and base 8? That the teachers seemed to have no idea why they were teaching? The non-decimal base just confused the hell out of everyone, that is a bit abstract for children still trying to learn the elements of representing and operating on numbers in the decimal base system, I'm with Principal Skinner here.
Maybe it went farther than that, and the teachers in my school mostly blew it off. I remember the 4th grade teacher just taught us old-school long division, and in 9th grade the teacher used old textbooks and disdained the one that tried to teach geometry as all rotations and translations, iirc, not with Euclidean proofs.
posted by thelonius at 9:42 AM on April 26, 2021
I had a similar argument with a restaurant about how, no, the two eight inch pizzas they had brought to me were not the equivalent of one sixteen inch pizza.
lol it's exactly half as much pizza
posted by thelonius at 9:55 AM on April 26, 2021 [2 favorites]
lol it's exactly half as much pizza
posted by thelonius at 9:55 AM on April 26, 2021 [2 favorites]
I started elementary school in 1973, so I'm assuming that I was exposed to "New Math"?
Second grade, for me, was around '65 or so, so I'm not certain my "New Math" was the same as yours. It wouldn't be too "new" by '73, though. I do somewhat recall something to do with sets, though, but I've blocked those memories pretty well.
posted by Thorzdad at 12:44 PM on April 26, 2021 [1 favorite]
Second grade, for me, was around '65 or so, so I'm not certain my "New Math" was the same as yours. It wouldn't be too "new" by '73, though. I do somewhat recall something to do with sets, though, but I've blocked those memories pretty well.
posted by Thorzdad at 12:44 PM on April 26, 2021 [1 favorite]
This might not even be enough to help someone like me. When I was a kid, I wasn't half bad (hah) at math, but in 5th grade, my dad, sister, and I drove out to Minnesota in fall to pick up my mom and drive her back with us to Washington, after she'd flown out for a family funeral. And there was such a flurry of activity around all of us visiting that my assignments kept getting shunted into the background, precisely when we were learning fractions. I was struggling really hard with understanding them, and I mostly cry when I'm frustrated rather than when I'm sad or something, and I remember hunching over my much-older cousin's dining room table, crying into my math textbook, while all around me everyone was making food, playing with kids, going through photo albums, etc. By the time we returned to Seattle, I was so far behind I never caught up. And I've struggled with, and hated, math ever since.
Though I do remember my last year of junior high, being called in to the counselor's office and told that I was failing algebra (no surprise there, I didn't understand it at all and it wasn't helped by my dad hitting me every time I got things wrong when he "helped" me with my homework) and I had to go in before school every morning to go over the previous day's assignments with my algebra teacher. He was a nice guy, but it was heinous for a born night owl to go in at 7 a.m. to be tortured by math. Which made it all the more surprising when I sailed through geometry in high school a year later, aced every quiz, and was so good at it that the teacher let me be his TA when I was a junior. No one was more shocked than I was to be good at something math-related.
posted by kitten kaboodle at 2:23 PM on April 26, 2021 [1 favorite]
Though I do remember my last year of junior high, being called in to the counselor's office and told that I was failing algebra (no surprise there, I didn't understand it at all and it wasn't helped by my dad hitting me every time I got things wrong when he "helped" me with my homework) and I had to go in before school every morning to go over the previous day's assignments with my algebra teacher. He was a nice guy, but it was heinous for a born night owl to go in at 7 a.m. to be tortured by math. Which made it all the more surprising when I sailed through geometry in high school a year later, aced every quiz, and was so good at it that the teacher let me be his TA when I was a junior. No one was more shocked than I was to be good at something math-related.
posted by kitten kaboodle at 2:23 PM on April 26, 2021 [1 favorite]
I quite enjoyed tricks like this when I was a kid. The only one I still remember is multiplying two-digit numbers. (Unfortunately, I don't get to use it all that often....)
Ultimately, though, I'm with Wulfhere; tricks can cover up a lack of understanding. (My most frequently-uttered complaint while grading is "why can't they math?" I had a student write something like 7.6*100 = 0.0076 some time ago, and I never figured out how that happened.) I really appreciate the recommendation to Nix the Tricks!
posted by invokeuse at 7:14 PM on April 26, 2021
Ultimately, though, I'm with Wulfhere; tricks can cover up a lack of understanding. (My most frequently-uttered complaint while grading is "why can't they math?" I had a student write something like 7.6*100 = 0.0076 some time ago, and I never figured out how that happened.) I really appreciate the recommendation to Nix the Tricks!
posted by invokeuse at 7:14 PM on April 26, 2021
My most frequently-uttered complaint while grading is "why can't they math?" I had a student write something like 7.6*100 = 0.0076 some time ago, and I never figured out how that happened.
Matt Parker has been looking into this kind of thing for some while now.
posted by flabdablet at 11:53 AM on April 27, 2021
Matt Parker has been looking into this kind of thing for some while now.
posted by flabdablet at 11:53 AM on April 27, 2021
Perhaps they simply misapplied a shortcut that a teacher had told them about moving the decimal place when multiplying by powers of ten. They just moved it the wrong way. It's disappointing if they did this and did not stop to consider what the numbers they started and ended with were, and what happens when you get a hundred copies of a thing, but I'd not be surprised if a lot of kids do just that.
posted by thelonius at 12:16 PM on April 27, 2021
posted by thelonius at 12:16 PM on April 27, 2021
They just moved it the wrong way
and by the wrong amount as well. This kind of mistake is absolutely typical of people whose entire experience of mathematics has involved beating their heads against an inscrutable wall of inapplicable meaningless scribbled gibberish that they are punished in various ways for failing to memorize correctly and/or being unable to write down sufficiently tidily.
I know several people who had always thought of themselves as just terrible at maths until they found themselves doing unexpectedly well on first exposure to geometry. This makes perfect sense to me.
posted by flabdablet at 8:02 PM on April 27, 2021
and by the wrong amount as well. This kind of mistake is absolutely typical of people whose entire experience of mathematics has involved beating their heads against an inscrutable wall of inapplicable meaningless scribbled gibberish that they are punished in various ways for failing to memorize correctly and/or being unable to write down sufficiently tidily.
I know several people who had always thought of themselves as just terrible at maths until they found themselves doing unexpectedly well on first exposure to geometry. This makes perfect sense to me.
posted by flabdablet at 8:02 PM on April 27, 2021
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