How to Say "reciprocally" in Spanish
The Spanish word for “reciprocally” is “mutuamente” — B1 level. This is a very common word in everyday Spanish.

Examples
Ellos se respetan mutuamente a pesar de sus diferencias.
They mutually respect each other despite their differences.
Nuestras ideas son mutuamente beneficiosas para el proyecto.
Our ideas are mutually beneficial for the project.
Al final del debate, se felicitaron mutuamente por el esfuerzo.
At the end of the debate, they congratulated each other (mutually) for the effort.
Always Unchanging
As an adverb, 'mutuamente' always stays the same regardless of who is performing the action or how many people are involved. It is an 'invariable' word.
Reinforcing 'Se'
When used with verbs that involve two or more people doing something to each other (like 'amar' or 'ayudar'), 'mutuamente' often follows the pronoun 'se' to emphasize that the action is definitely shared, not self-directed.
Using it with Singular Verbs
Mistake: “La pareja se ama mutuamente.”
Correction: La pareja se aman mutuamente. (The verb must be plural since the action involves both people.)
Confusing Adverb and Adjective
Mistake: “Tienen un mutuo acuerdo.”
Correction: Tienen un acuerdo mutuo. (Use the adjective 'mutuo/a' to describe a noun like 'acuerdo,' not the adverb 'mutuamente.')
Related Translations
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