Translation:Is this free?
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I think the easiest way for an English speaker to understand 是…的 is to realize that the noun at the end of sentence has been left out because it is understood in the context.
When you want to equate two nouns, you say:
Noun1 是 noun2.
When you want to add an adjective description to a noun, you use:
adjective 的 noun.
So if you want to declare that a certain thing (noun) has a certain property (description), that becomes:
Noun1 是 adjective 的 noun2.
Example: This is a free book. 这是免费的书。
However, in reality, noun2 is often understood from the context and can therefore be omitted. This is the case in English as well.
Example: This is free. 这是免费的。
Note that when noun2 is understood, the English adjective looses the article that it needs before a noun ("a free book" became "free.") IN CONTRAST, the Chinese adjective must keep its 的 so that it can remain a descriptor of the understood noun (免费的书 becomes 免费的). Without the 的, 免费 would have to be interpretted as a noun, not a adjective, and the (ungrammatical) sentence would mean something nonsensical like "This book literally is the abstract state of having no cost."
And that's why you need the 的.
So when you see "Noun 是adjective 的“ remember that there's an understood noun2 at the end.
There are two ways to use adjectives in Chinese:
- 很 + adjective
- 是 adjective 的
- 我哥哥很聪明 (Literal translation: My brother is [very] smart)
- 我哥哥是聪明的 (Literal translation: My brother [belongs to] smartness.)
Normally these two are interchangeable, with 是。。。的 often used for greater emphasis. However, 是。。。的 construction becomes mandatory when the adjective is a simple ”to be or not to be“ description.
Take 很好 for example. Although the 很 is only used as a place filler and doesn't necessarily mean "very good", it implies that there is a range of "good" that's possible. you can swap out the 很 for 非常, 太，真 to imply various degrees of "good".
However, when we say something is free, you do not differentiate between whether something is "slightly free" or "very free". If it's free, it's free. That's why the 是。。。的 construction is mandatory for this particular adjective.
"这个地址是错的“ is another one. Which you may remember from previous lessons. In the context of addresses, we do not differentiate whether the address is very wrong or slightly wrong. If it doesn't get you where you need to be, it's just simply the wrong address.
There are a few others like this. As long as you remember this rule, you should have all of them down.