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"Cuantía" is a noun which is often translated as "quantity", and "cantidad" is a noun which is often translated as "amount". Learn more about the difference between "cuantía" and "cantidad" below.
la cuantía(
kwahn
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tee
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ah
)A feminine noun is almost always used with feminine articles and adjectives (e.g., la mujer bonita, la luna llena).
1. (sum)
2. (figurative) (degree)
A phrase used as a figure of speech or a word that is symbolic in meaning; metaphorical (e.g., carrot, bean).
a. extent 
A las personas mayores les preocupa que la cuantía de la crisis económica les impida cobrar una pensión.Seniors are worried that the extent of the financial crisis will stop them from drawing their pension.
b. importance 
Los asuntos de mayor cuantía serán los primeros que se tratarán al principio de la reunión.Those matters of greater importance will be dealt with at the beginning of the meeting.
c. significance 
La cuantía de este evento no se puede subestimar.The significance of this event cannot be underestimated.
la cantidad(
kahn
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tee
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dahd
)A feminine noun is almost always used with feminine articles and adjectives (e.g., la mujer bonita, la luna llena).
1. (portion)
a. number  (only with countable nouns)
Vimos una cantidad sorprendente de patos ayer que fuimos al lago.We saw a surprising number of ducks yesterday when we went to the lake.
a. ton 
Hubo cantidad de gente en el centro el domingo.There were a ton of people downtown on Sunday.
5. (commerce)
An adverb is a word that describes a verb, an adjective, or other adverbs (e.g., to run quickly, very tired).
6. (colloquial) (lots)
A word or phrase that is commonly used in conversational speech (e.g., skinny, grandma).