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Quick answer
"Understand" is a transitive verb which is often translated as "entender", and "work out" is an intransitive verb phrase which is often translated as "hacer ejercicio". Learn more about the difference between "understand" and "work out" below.
A transitive verb is a verb that requires a direct object (e.g. I bought a book.).
transitive verb
1. (to comprehend)
a. entender
He lived in Paris for three years and still doesn't understand a word of French.Vivió en París tres años y aún no entiende ni una palabra de francés.
b. comprender
My fifteen-year-old daughter can understand even the most complex math problems.Mi hija de quince años puede comprender aun los problemas matemáticos más complejos.
2. (to interpret)
a. entender
The troop movement can only be understood as a provocation.El movimiento de tropas solo se puede entender como una provocación.
3. (to have heard)
a. tener entendido
From what I understand, she got divorced.Según lo que tengo entendido, se divorció.
4. (to feel empathy for)
a. entender
I understand you, but I think you have to overcome the victim mentality.Te entiendo, pero creo que debes abandonar la mentalidad de víctima.
An intransitive verb is one that does not require a direct object (e.g. The man sneezed.).
intransitive verb
5. (to comprehend)
a. entender
I hear what you are saying and I understand.Oigo lo que me dices y entiendo.
b. comprender
I was paying attention in class but I just didn't understand.Estaba prestando atención en clase pero simplemente no comprendí.
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work out(
An intransitive verb phrase is a phrase that combines a verb with a preposition or other particle and does not require a direct object (e.g. Everybody please stand up.).
intransitive verb phrase
1. (to train)
a. hacer ejercicio
I work out three days a week at the gym.Hago ejercicio tres días a la semana en el gimnasio.
b. entrenar
I have to work out at home because the gym is closed.Tengo que entrenar en casa porque el gimnasio está cerrado.
2. (to succeed)
a. salir bien
Fortunately, things worked out for me and Laura.Por suerte, todo salió bien entre Laura y yo.
A transitive verb phrase is a phrase that combines a verb with a preposition or other particle and requires a direct object (e.g. Take out the trash.).
transitive verb phrase
3. (to find a solution to)
a. resolver
My roommate and I need to work things out.Mi compañero de cuarto y yo necesitamos resolver nuestra situación.
4. (to calculate)
a. calcular
Did you work out how much money we need to go to Las Vegas for a week?¿Ya calculaste cuánto dinero necesitamos para ir a Las Vegas por una semana?
5. (to devise)
a. idear
A group of prisoners worked out a plan to escape from jail.Un grupo de prisioneros ideó un plan para escapar de la cárcel.
6. (to understand)
a. entender
I can't work out what the boss wants from me.No entiendo lo que quiere el jefe de mí.
7. (to exhaust)
a. agotar
When the miners worked out the mine, they became unemployed.Cuando los mineros agotaron la mina, se quedaron sin trabajo.
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