I had to look this up as I didn’t grow up in the States. It was A&W.

https://www.snopes.com/news/2022/06/17/third-pound-burger-fr...

Crazy.

This story has to be apocryphal, as fractions aren't _that_ rare, especially in the U.S. with its imperial system and third of a cup measurements or quarter inches or half miles and so on.

It's not that they're rare, it's that it legitimately is an easy error to make even if you understand it to be an error. Even people who work with equations every day will occasionally make careless mistakes like this. That's why mathematicians joke about how it's important to make an even number of sign errors.

To not make this mistake, you have to be able to call to mind that the map x -> 1/x reverses the inequality sign. That's a fairly abstract thing to remember especially if you haven't taken math for years. Yes you could draw it or write down the equation, or convert to decimal... But it's enough of a cognitive barrier that it doesn't surprise me that it would impact the behavior even of people who would answer correctly on a test.

Where it does get easy is if you work with the same set of fractions every day. For example, if you work in construction in the US you can probably quickly order the fractions commonly used for measurement, e.g. 1/4, 1/8, 1/16, 3/4 etc. But 1/3 isn't one of these. Now that I think about it, they probably should have just chosen a fraction that you can find on a tape measure, like 3/8.

For fractions like 1/3rd and 1/4th all it takes is common sense.

I do not really like the term "common sense" as it is more like common experience. It is not hard to learn what fractions are but I do not think it is something that any one is born with and there is other notation to deal with fractions that work differently.

I speak, and thus think, in both English and Japanese.

English says "1/4", or "1 over 4", or "1 quarter".

Japanese says "4 bun no 1", or the practical equivalent of saying "4 under 1" in English.

I consequently routinely say the numbers in reverse, confounding both myself and anyone around me before I realize my brain engaged in furious tentacle sex with the numbers.

It seems like the obvious solution is to offer Americans what they want in terms of a burger named after a bigger denominator.

1/5th pound burger is going to sell better than the quarter pounder while using less beef.

> I speak, and thus think, in both English and Japanese.

The vast majority of processing is happening outside language-related areas of the brain. There's certainly leaky interfaces between areas of the brain, but if you literally thought in a language, and that distinction persisted throughout the brain, that would seem to imply that speaking 3 languages would require 3x the number of connections in the brain.

The strong Sapir-Whorf hypothesis would presumably be true if we literally thought in a language, but the strong form of the Sapir-Whorf hypothesis has been thoroughly discredited.

In other words, "thinking in a language" is an illusion.

I think this is partially correct. Inner monologue is not an illusion, and choosing a wrong linguistic construct for your audience (sometimes from another language) through temporarily forgetting to context switch does happen. However, thinking something without ever having done so in words does seem to strongly correlate with your assertion.

Tangentially, I realised in high school that I was doing almost all math operations as word transformations. I reasoned this was why even familiar procedures for which I confidently & consistently got correct results were taking substantially longer than everybody else. I was translating everything twice.

> To not make this mistake, you have to be able to call to mind that the map x -> 1/x reverses the inequality sign. That's a fairly abstract thing to remember especially if you haven't taken math for years. Yes you could draw it or write down the equation, or convert to decimal...

You absolutely don't have to remember that x |-> 1/x is order reversing, and, for most people, shouldn't—you immediately give two or three other methods (I don't understand what "write down the equation" means) that are a much better way for the average person to check this.

Yes, but I was also speaking generally about fractions since that was the context of the comment I was responding to.

For example, consider: 1/1123 < 1/1092. Is that inequality true? The fastest way to check is to compare the denominators and adjust for the way division interacts with the inequality.

You can't really draw that pie chart quickly. You could write the equation down and multiply both sides though.

For 1/3 vs 1/4 yes you could draw it quickly. Or you could fill a glass 1/3 full of water and one 1/4 and compare them. But that's a pretty special case for small enough denominators.

3/8ths is 0.375 while 1/3rd is 0.333~ so it's even bigger while still larger than 1/4th (0.250), without being that much bigger.

3/8ths is a pretty good marketing point since all the numbers are bigger and it should be intuitive, plus you can more easily see that it's also 50% bigger than 1/4th => 2/8ths. The harder sell is the 'double whatever' being equal to 3 patties of the competitor.

I did teacher's college in Canada and the teacher who taught math said his biggest surprise when he moved from Europe to Canada is how terrible people were with fraction. I think he asked a barista to fill his cup to 2/3 and they couldn't do it because they didn't know what 2/3 was.

I had the same shock but with reading. They're very much ahead in Europe in terms of reading levels.

Anecdotally, it seems like working with fractions is where a lot of people fall off the math-train and never get back on.

… yes, that early.

Fractions and negative numbers.

And, to be fair, they're the first math concepts that aren't intuitive.

Which IMHO leads to some people not studying, then feeling lost, then rationalizing their lack of effort as "I'm bad at math" or "Math is hard."

Fractions are pretty intuitive. Is the pizza or cake analogy really that advanced?

One third times one fifth loses a lot of folks. As does addition and subtraction of fractions that don’t start with the same denominator, for that matter. They might figure out what to do to pass the test, but they may not get it.

Fractions are just division. When kids learn division, it's about splitting into equal groups.

Fractions are a bit different though - you're splitting a single thing into equal chunks. Hence, slices of pie.

Multiplying by 1/5 is really dividing by 5. Introduce that first. We already know how to do this. You split your 1/3 slice into 5 equal slices.

Do the same to the other 2/3 slices, count all the slices, and you have 15. Hence, 1/15.

As an aside, common core math is amazing. They gave my daughter a model for the distributive property that can be used to show how to do long multiplication.

There's a difference in type of thinking in moving from operations on numbers (basic whole number math) to operations-on-operations-on-numbers (anything with fractions).

Suddenly, you need to begin to understand the rules around operators, sequencing, and what operations are legal and illegal.

Absent that understanding, even...

   1/4 x 2/5

... gets very complicated trying to reason with physical analogs.

So it's the point at which math becomes "pure" rather than strictly physically-mapped.

And if multiplying fractions is simple. Before that addition is done. Which is more complicated.

Actually I think we do very little addition of fractions later in math. But it is a concept that confuses the multiplication or division.

IDK, I did fine with them and find thinking in them natural (I think of fractional division as division, in fact, though I certainly understand the multiplication analogy); I’ve just known enough people who lost track of math at fractions that I doubt it’s coincidence.

I’m not saying I don’t get it, I’m saying others have told me that they found the explanations and instructions they were given nonsensical.

Have you tried dumping all the sockets out of a socket set and putting them back in order? Do you find it's easier to order the metric ones than the imperial ones which have a lot of different denominators on adjacent sizes? I certainly do but I'm not American so maybe it's my background limiting me.

Just to save you some time: the numbers written on the sockets indicate the size of the socket. So you don't even need to read them, just put them in order of size and you'll have them in order of number automatically.

I was thinking of mine which has the same OD for many adjacent sockets. Guess it doesn't work if they're all different.

Can confirm - While I was decent at math up to a point, fractions and long division in 4th Grade sent me down a hole that took me years to get out of...until Algebra II as a junior in HS crushed me.

I blame this on my Chemistry teacher - a class which I was also taking at the time - who spoke little English and had never taught in the United States until the year I landed in her class. I actually did reasonably well in Algebra for the first quarter or so until it all fell apart.

I re-invented what turned out to be short division (no joke! I wouldn’t learn it had a name until I was in my late 20s) because I hated long division so much, same year we started doing long division in school (4th grade? 3rd? IDK).

Fits in about the same space as the original problem unless it’s printed so small that you have to rewrite it, and way less room for transcription errors. I also find it clearer but that may just be me (fwiw I’m “bad at math”—I find it incredibly boring and basically can’t follow proof- and equation/identity-based stuff, I have to turn it all into algorithmic thinking to have a prayer of understanding it; i.e. my opinion on the superiority of short division is that of a mathematical imbecile, so, grain of salt)

> I blame this on my Chemistry teacher - a class which I was also taking at the time - who spoke little English and had never taught in the United States until the year I landed in her class.

It doesn’t help that in chemistry, 1 + 1 may be 1. Or 3. :-)

[edit] short division:

https://en.m.wikipedia.org/wiki/Short_division

Under the “example” section, the little superscripts are what you write in by hand on the problem as you work it, at least as I did it. 9/4 in the hundreds place is 2 with 1 remainder, so write 2 up above as part of the solution and a 1 superscript next to the 5 in the problem itself (tens place), now that’s 15, divide that, 3 goes in the tens place of the solution, write the remainder (3) next to the digit in the ones place as a superscript and do it again, if you need to keep going just add a decimal point and zeroes as required.

Way faster than working long division, takes up less space, and less error prone (imo). What’s actually going on is clearer (again, imo)

I’ve seen a later fall-off point at factoring. Feels pointless (the motivations are… distant at best), tedious as hell, lots of guessing involved. “So much for math making sense, fuck this, guess I’m out.”

I'm ok with fractions, but fractional and/or negative exponents always give me problems. I suspect it might be something to do with being taught that "multiplication is repeated addition, exponentiation is repeated multiplication". The model doesn't extend properly.

It actually doesn't shock me that many people would be confused, especially if they didn't work with fractional quantities--e.g. for cooking--on a regular basis. Maybe it's a myth but it wouldn't surprise me if it weren't. And even if they've sort of internalized 1/4, 1/2, 3/4 without necessarily fully getting fractions--1/3 is something people encounter a lot less day to day.

Forty years ago we learned fractions with chocolate bars. A trustworthy child would be chosen to walk from the primary school to the local store (about 5 minutes walk for an adult, probably about two minutes for a child who was just given money by a responsible adult to buy chocolate) and bring back some chocolate, and then kids who raise their hand and give the correct answer to fraction questions get the fraction in its physical form as chocolate. What's half of this third of the bar? A sixth, and now because I knew that I get to eat 1/6 of a bar of chocolate, whereas the kid who enthusiastically answered that it's a quarter does not because that's wrong.

I thought so as well but A&W backs that version:

https://awrestaurants.com/blog/aw-third-pound-burger-fractio...

Reportedly that’s the answer they got in focus groups when they tried to figure out why it failed.

4 > 3.

So why didn't they start selling 1/5 pounders?

Quarter and pounder rhymes so rolls off people's tongues.

Fifta-Pounder?

Fifth-Pounder?

Five-Pounder?

For all we know, marketing vetoed it cause they were lazy.

How 'bout a five-ouncer ?

Or would that suffer by seeming microscopic when listed close to "32 ounce" drinks ?

> This story has to be apocryphal, as fractions aren't _that_ rare, especially in the U.S. with its imperial system and third of a cup measurements or quarter inches or half miles and so on.

I literally had an argument with a room full of US university professors about whether or not 30% and 1/3 were the same thing.

... and what was your answer?

> ... and what was your answer?

The correct one, that 30% is less than 1/3.

Average Americans that frequent QSR’s don’t math so good.

Or perhaps all those people on here who defend US Standard measurements over metric and quote the fractions they know over decimals as an advantage are a minority?

Perhaps the average Joe would be better off with mm rather than 1/16" increments.

Wait, did Snopes say this was real because of a news article that contain hearsay?

Do people think the NY Times reports hearsay as fact?

Here, straight from the horse's mouth:

https://awrestaurants.com/blog/aw-third-pound-burger-fractio...

Based on a "focus group" discussion which are well known for selecting the brightest bunch of people who have nothing better to do than answer questions for 2 hours and get a coupon for free fries.

It's also important to take any corporation's explanation for increasing their own margins with an extremely large grain of salt. I'm not doubting in the slightest that consumers had some confusion around the fractions, but all it would take for the company to revert their campaign is for the increase in sales to insufficiently offset the increase in their own costs. Blaming it on consumer stupidity afterwards washes their hands of any responsibility for backpedaling, and makes for a memorable and repeatable story that increases brand recognition while simultaneously painting them as heroically trying to offer more value for the same cost.

  VINCENT: And in Paris, you can buy a beer at McDonald's. And you know what they call a Quarter Pounder with Cheese in Paris?

  JULES: They don't call it a Quarter Pounder with Cheese?

  VINCENT: No, they got the metric system there, they wouldn't know what the f*** a Quarter Pounder is.

  JULES: Then what do they call it?

  VINCENT: They call it Royale with Cheese.

  JULES: Royale with Cheese. What do they call a Big Mac?

  VINCENT: Big Mac's a Big Mac, but they call it Le Big Mac.

Aside: a lot of tax preparation services, or their services that let you upload your data - the privacy policy says they can all "use" your financial info.

Personally I prefer Big Kahuna Burger

You say “this is America”, but my mother (who grew up in USSR/Russia and was in her mid 30s at the time) was seriously asking middle-schooled me on multiple occasions whether 0.7 liters of milk was less than 0.55 liters. I don’t remember the exact numbers, i just remember that the smaller volume one had 2 digits past the decimal, and the larger one just had 1 digit.

And no, she wasn’t testing my knowledge, she was seriously confused, as she would ask me that even later in life. Mind you, she has a masters degree. She is in her early 50s right now, and she is fully of sound mind to this day, not senile or anything like that.

Imo, this type of silliness is rather common across many different places, but Americans just tend to own it and not be afraid of coming off silly (if that’s how they genuinely end up behaving in a given situation).