Learn Spanish (Latin America): Yo pago la mitad y tú pagas el resto.

In Spanish, noun fractions like mitad (half) or multiples like doble (double) usually need a definite article (el or la) when they stand alone as a noun. You cannot just say Yo pago mitad, you must say Yo pago la mitad.

Could I use medio instead of la mitad in this sentence?

No, because medio is mostly used as an adjective (like medio litro for "half a liter"). When you are talking about "the half" as a specific portion or piece of something, you must use the feminine noun la mitad.

Since Spanish usually drops subject pronouns, why are yo and tú used here?

Including yo and tú creates a strong contrast. It emphasizes exactly who is responsible for which part: "I am paying this part, and you are paying that part."

The lesson mentions la mitad de. How would I say "I pay half of the rent"?