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Hello Teachres!

IS an article "the" is essential part before the superlative degree of an adverb like an adjective.

1.HE jumped the highest of all the boys.

2.He jumbed highest of all the boys.

If the usage of "the" is mandatory here ,then why these two given below are correct?

1.Which subject do you like best?

2.Whuch subject do you the best?

Thanks.
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In formal grammar, 'the' is required when the adjective/adverb immediately precedes its referent. If the referent is not in that position, then 'the' is optional.

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Your sentences are all correct.

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Hanuman

As for adverbial superlatives, you can use the superlatives either with 'the' or without 'the'. Forms of 'the+superlative' are more often used in AmE than in BrE. In the case of 'best', even Americans prefer 'zero+best' to 'the+best'. But when an adverbial superlative is followed by phrases like "of a people's group" they tend to add 'the' to the superlative.

google results
[com: mostly by Americans and uk: by Brits]
(1) He/she jumped the highest. [com 355/ uk 33]
He/she jumped highest. [com 145/ uk 113]
(2) I like him the best. [com 897/ uk 38]
I like him best. [com 2420/ uk 48]
(3) Who do you like the best of us? [com 100/ uk 7]
Who do you like best of us? [com 0/ uk 0]

paco