When a Kanji is by itself and it doesn't make a word, how is it read?

I have a text book and it says give the reading on the following kanji: 女, 川, 千, 上, 万, 火, 円, 土, 小さい, and 大きい and there is only space enough for one or two readings.

I memorized all the readings (on-yomi and kun-yomi)for it and something like ookii is easy, but i got 3 of them wrong for using the wrong reading. The answers uses both on and kun yomi readings so which is the correct option for the kanjis and how do I know which to use?

Kun'yomi is more common but on'yomi is also possible. For instance, か and ど can be used solely for 火 and 土, meaning Tuesday and Saturday, respectively.

It's sort of pointless to learn the two types of reading without understanding the difference between the two types, which is why you got tangled up here.

A single kanji is quite capable of representing a word. In a nutshell, that's precisely what the kun'yomi are. Native Japanese words (think: part of the language before kanji were introduced). They can be combined into compound words sometimes, but can also stand alone. Like "book" and "shelf" can make "bookshelf" in English.

The on'yomi are Chinese readings that were borrowed along with the characters. They're used most typically for words formed by combining kanji (and which don't fit the kun'yomi compound word style). If separated into single kanji readings, they don't stand alone as words. English has typically done this with words formed from Latin or Greek parts: "photograph"; "microscope"; "telemetry". We know what meaning "tele" and "metry" convey because of their roots, but the word can't be split into two free-standing parts that are words in their own right. On'yomi are like that.

See the difference now?

I think I understand, thank you. You are saying a kanji that can make a word is usually read in kun-yomi and it is able to make a compound word. When a kanji is read in on-yomi it's usually followed by another kanji to make a word, but it can't make a word on its own. Like a prefix.

I still don't get in the text book has a specific answer to the problems, and uses both on and kun readings. Are you saying I should use the reading that turns the kanji into a word? Like hachi (eight) is an on-yomi, but i think hachi it self can make its own word.

The textbook is checking to see if you can use context clues to choose the correct reading. You have to develop an awareness of whether words are "native" Japanese or are words cobbled together from Chinese origins. Kanji have Chinese origins, but not all Japanese vocabulary does. This is where you have to learn what many beginners seem not to understand: that the Japanese language and the system for writing the Japanese language aren't the same thing.

Oh, okay. Thank you very much for the replies.