Another
Another is used to refer to one more or additional. For example: I’d like another piece of cake. (In this sentence the word ‘piece’ is both countable and singular. The speaker doesn’t care which piece of cake he gets, he just wants more cake.)
Another can also be used to refer to something that is different, or an alternative. For example: I’m going to live in another city next month.
Note that another can sometimes be used with plural nouns. For example: This contract is valid for another five years. (Although ‘five years’ is plural it is considered one/singular period.) Note also that you cannot say ‘the another…’
Other
Other is used to refer to a person or thing that is different to the one already mentioned. For example: Which jacket should I wear? This one or the other one?
Other is also used with a plural noun. For example: This book contains other information about Malta. (In this sentence ‘information’ is both uncountable and plural.)
Complete the following sentences using ‘other’ or ‘another’.