I've another question about Coniugatio periphrastica passiva. If I'm a girl and I wanted to say I need to read, would it be:
Mihi legendum est.
Mihi legenda est.
So, does the gerundivum stay in neuter or not?
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The gerundive should be neuter if you just want to say "I need to read". Any other form than singular neuter should only be used when the gerundive modifies a noun. The modified noun can in principle be left implicit; consider:
Ubi est ista scriptio? Mihi legenda est!
Where is that writing? I have to read it!
The fact that the gerundive is not neuter in Latin corresponds here to adding the explicit object "it" in English (referring to the feminine scriptio). Hardly anyone would repeat scriptio in the second sentence, but it is easily understood and therefore supplying the feminine legenda makes sense.
The feminine gender is purely due to agreement with scriptio. It doesn't matter who is obliged (cf. suus), and it doesn't even have to be specified. Legendum est is impersonal like "reading must happen", although the latter is not very idiomatic English.
If there is no specific object, go with the singular neuter.
It's necessary to distinguish between gerund and gerundive. The former is an active verbal noun, declinable, but with no plural. The gerundive is a passive verbal adjective, declinable in both numbers.
Your first example translates to reading is for me, or even it's time for me to read. Think of Horace's 'Cleopatra Ode' (Odes 1, 37), beginning Nunc est bibendum, usually translated as something like 'Now's the time for drinking'. To my mind, this is unquestionably a gerund, though others see it differently.
Mihi is a dative pronoun of either gender and, if you want to make it clear that it's a girl that is doing the reading, you must indicate gender by some other device. It can't be done as you are trying to do it in your second example which, as it stands, is impossible. Legenda can only be gerundive and, being adjectival, ought to have an associated noun. Nodding to Joonas's suggestion, this might be scriptio, producing scriptio est mihi legenda.
Note that legenda cannot be defended as a plural gerund — see my opening paragraph — but, even were that possible, the verb would then have to be sunt, and not est.
If a verb is transitive, it is usual to prefer the gerundive (this is known as 'gerundive attraction'). It carries then a sense of obligation. The gerund is, even so, preferred in certain circumstances which, like all the other tricky exceptions and modifications of syntax possible with this pair of verbal parts, would be better understood by consulting a grammar.
The gerundive, again, makes indirect speech look like paradise! Here: "mihi legenda est" giving "by me it-ought-to-be-read". A gerundive with a part of sum is the gerundive-of-obligation. The person upon whom the obligation falls goes into the dative; here, "mihi"; but, the gender of the gerundive refers to the "it" in "it-ought-to-be...", not to the gender of the person upon whom the obligation is falling!
The neuter form, without a noun, provides an impersonal expression e.g. faciendum est = it-ought-to-be-done. North & Hillard Ex. 210: Blosius refuses to condemn his late friend, Gracchus, before the Senate; thereby, inviting his own execution. "si moriendum erit, moriar amicis fidelis." "If I am to die (if it-will-have-to-be-death), let me die loyal to my friends."