There is very subtle difference between decide sth and decide on sth.
Decide on is used to choose something from a number of almost similar possibilities(ppssibilities that would yield almost similar results, but it depends on your personal choice )
We are still trying to decide on a venue.
This sentence implies that we have different venues that we can choose from.
I have decided on yellow for this table.
It implies we have different colours available like red, green etc.
When you say
We have yet to decide on the share of the profit we will give them.
This means you have different shares that you can give for example you can give them 5% share,2% share and 9% share.
If you say
We have yet to decide the share of the profit we will give them.
It does not necessarily mean you have different equal possibilities (possiblities having similar results)