I assume you’re talking about the top page rather than the neuter gender
The neuter/neutral gender is harder to spot in Spanish since it typically ends in -o; it’s easier to think of it as “agender” meaning that when you see lo, alguno, ninguno, esto, eso, aquello you’re talking about a thing as a concept or an abstract idea, not as a thing
That’s why you’ll see por este motivo “for this reason” or por esta razón “for this reason” and then por esto “because of this” where no noun was actually used
If I had to guess it’s talking about times when the noun isn’t specifically stated and what you should do. In general, you treat it as agender which largely looks masculine aside from what I mentioned above, unless you have a specific noun in mind in which case you follow normal direct object pronouns lo, la, los, las
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As for how often you use random feminine articles: fairly often, it depends on the phrase… The listed examples aren’t totally the most common but I think I see what they’re going for
In other words: the specific words/phrases sometimes, but the general concept they’re describing - yes you see it a lot
As for the overall concept… I don’t know if the source mentions this but what I think you’re having a hard time with is why it’s feminine plural. That’s part of an overall linguistic trend in Spanish called femenino de indeterminación which is “feminine of/due to being undetermined”
It’s a trend in Spanish that in some cases you will see a feminine object or adjective used in cases where there isn’t something specific used as a noun
It’s important to note that this is in the absence of a clear noun, which is why I can’t 100% say that they’re all necessarily accurate/necessary - jugárselas as “to risk everything” can also be phrased as jugárselo todo it’s just with todo as a clear noun it keeps it as lo instead of las
But this can exist as adjectives or in singular or plural
Really common examples:
- (tomar algo) a la ligera = (to take something) lightly, to not take seriously
- a la buena de Dios = “left up to fate”, “whatever happens happens” [lit. “to the good of God”, but kind of like “however God wills it”]
- por las buenas = the easy way
por las malas = the hard way - a sabiendas = “knowing full well”
- a solas = “one-on-one”
- a escondidas = “in secret”, “behind someone’s back”
- a secas = “no frills”, “only”, “with nothing else”
[as an example if you said una milanesa de pollo a secas what you’re describing is “a breaded chicken cutlet with nothing else” as in no sauce, no bread, no vegetables just a cutlet - that’s what a secas means; with non-food things it comes out as “plain and simple”]
There’s no specific reason why it’s feminine. And two men could talk a solas and it’s not a matter of any grammatical gender or agreement… it’s more of a quirk that happens every so often with specific phrases like the ones you listed and the ones above
Another really common one that’s a bit of a regionalism is saying pasarla bien [or more intense pasarla en grande] which is like “to have a great time”, like vamos a pasarla muy bien “we’re going to have a great time”. Sometimes people use lo but la seems to be more common….. And I say it might be a regionalism because a different common expression is pasarlo bomba meaning “to have a blast” almost always with lo instead of la from what I can recall
Another, and I don’t know if this is specifically Spain, is liarla parda which means “to make a mess (of something)” and some people use it as like partying “to tie one on” or “to go wild” or “to go on a bender” sort of thing, or it could possibly just mean to actually “make a mess”. Literally though it’s hard to explain; it means “to tie (a brown one)” but some people believe it meant “to catch a brown hare” [la here would be la liebre “hare”, synonymous with el conejo “rabbit” in modern contexts; but pardo/a is specifically a brownish coloring in animals]… whether or not it’s a hare, people use that expression as if it were feminine
Side Note: I would also say traérselas is more like “to be difficult to deal with” not necessarily treacherous in the way of will betray you but like “that will trip you up” or if it’s a person it’s like “they’re a tough nut to crack” but it tends to be said of something rather than someone and it’s like perplexing or confusing - they’re working with limited space so I get it)
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Out of those that I saw listed, the ones I see the most are vérselas, apañárselas or arreglárselas although this is the infinitive form and it’s considered idiomatic and fairly advanced as far as language learning
For example - tendrás que vértelas conmigo is “you’ll have to deal with me” which is like saying there will be a confrontation; the con is almost always with someone so in this case conmigo “with me”, but could possibly rephrase the thing to say contigo “with you” or con (alguien) “with someone”… like ellos tendrán que vérselas con el rector “they’ll have to deal with the principal”
To note further, the reflexive pronoun here is now te to adhere to tendrás which is also tú …that’s important because vérselas if you saw it by itself is infinitive showing that you use a reflexive pronoun here with it, but that it will apply to the subject… which is why I said tendrán que vérselas as plural, but it could be tengo/tendré que vérmelas “I have to deal with/face off against (something/someone)”
Another example as a command: apáñatelas which is something like “deal with it” but could be plural - apáñenselas [as in a sentence like apáñenselas ustedes solitos which reads like “you all figure it out by yourselves” or “you deal with it yourselves”]
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So keep that in mind, if you’re saying something like me las doy de chef “I’m something of a chef” or “I fancy myself a chef” etc it has to be in agreement with your subject; that’s how reflexive pronouns work, but they use se in that infinitive form so you know that it takes reflexives
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As far as why it is that way… I couldn’t really tell you. People tend to believe that it’s a substitute for la cosa or las cosas a lot of the time
With vérselas for example some people use the expression verse las caras which is “to face off against someone”, literally “to see each others’ faces” which is possibly why it’s las
In most cases you can phrase it other ways or put a noun in and then it isn’t feminine anymore, but some expressions like a sabiendas or a escondidas are so commonplace that you find them eventually… With verbal expressions it’s something to be aware of as you go forward even if you’re not totally comfortable reproducing it… and just know if you see it randomly feminine, that’s a known thing
You can probably find more examples of it if you look up femenino de indeterminación though - what I could find was mostly all in Spanish or German so I didn’t know quite how to recommend sources for further reading