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