Fall or fall down?

We can use fall as a noun or a verb. It means ‘suddenly go down onto the ground or towards the ground unintentionally or accidentally’. It can also mean ‘come down from a higher position’. As a verb, it is irregular. Its past form is fell and its -ed form is fallen. Fall does not need an object:

Mrs McGrath had a terrible fall yesterday. She’s in hospital now. (noun)
Four trees fell in the storm. (verb)
Oil prices have fallen recently.

Fall down is a phrasal verb. We use it when something falls to the ground from its normal position:

The picture keeps falling down. (from the wall to the ground)
He slipped and fell down.

warning

We use fall, not fall down, when trees drop their leaves during the autumn:

As autumn came and the leaves fell from the trees, she began to feel sad.
Not: … ~~the leaves fell down~~ …

We can’t use fall down to mean ‘come down from a higher position’:

House prices have fallen a lot this year.
Not: ~~House prices have fallen down a lot~~ …