Quick answer
"On their own" is a phrase which is often translated as "por su cuenta", and "alone" is an adverb which is often translated as "solo". Learn more about the difference between "on their own" and "alone" below.
on their own
A phrase is a group of words commonly used together (e.g once upon a time).
1. (by themselves)
a. por su cuenta
Children must do their homework on their own, without their parent's help.Los niños deben hacer la tarea por su cuenta, sin la ayuda de sus padres.
b. por sí mismos (masculine)
The patients can't change their clothes on their own.Los enfermos no pueden cambiarse por sí solos.
c. por sí mismas (feminine)
The girls can tie their shoes on their own.Las niñas pueden atarse los cordones por sí mismas.
d. por sí solos (masculine)
These robots can repair themselves on their own.Estos robots se pueden reparar por sí solos.
e. por sí solas (feminine)
The old ladies can't get up on their own.Las ancianas no se pueden levantar por sí solas.
2. (on their)
a. en su propio
It was a heated debate, but I beat them on their own ground.Fue un debate candente, pero los vencí en su propio terreno.
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An adverb is a word that describes a verb, an adjective, or other adverbs (e.g. to run quickly, very tired).
1. (by oneself)
a. solo
I don't feel comfortable when I'm home alone.No me siento cómodo cuando estoy en casa solo.
b. a solas
We were alone after dinner.Estuvimos a solas después de la cena.
2. (only)
a. solo
Your parents alone can give you permission.Solo tus papás te pueden dar permiso.
b. solamente
You alone know what decision will make you happy.Solamente tú sabes qué decisión te hará feliz.
3. (by oneself)
a. solo
He likes to work alone.Le gusta trabajar solo.
An adjective is a word that describes a noun (e.g. the big dog).
4. (by oneself)
a. a solas
We were alone after dinner.Estuvimos a solas después de la cena.
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