Learn Spanish (Latin America): Tú necesitas medir el aceite cuidadosa y correctamente. - You need to measure the oil carefully and correctly.

When you have two or more adverbs ending in -mente joined by y (and), only the last adverb keeps the -mente ending. The first one drops it and stays in its feminine singular adjective form (cuidadosa). This makes the sentence flow better by avoiding the repetition of the long -mente sound!

The word aceite is masculine (el aceite). Shouldn't the first adverb be masculine (cuidadoso) to match it?

No, because cuidadosa and correctamente are adverbs modifying the verb medir (how you measure), not adjectives describing the oil. To make an adverb in Spanish, you always use the feminine singular form of the adjective (cuidadosa, correcta) and add -mente. When dropping -mente from the first word in a list, it simply stays in that base feminine form.

Could I swap the adverbs around and say correcta y cuidadosamente?

Absolutely! The rule applies no matter the order. The first word in the pair is always just the feminine adjective (correcta) and the final word gets the full adverb ending (cuidadosamente).

Just as a refresher, why is medir left in its infinitive (the dictionary form) here?