Adding an opened yeast packet may mean adding dead yeast, unfortunately. Once the package is opened, it's only viable for a couple of days since it absorbs moisture and ruins the yeast. Normally, one full package is the amount used for 1-6 gallons so there isn't any reason to use a partial package or save a partial package.
I'd stir well to add oxygen, and add more yeast. Buy several packages, to have some in the fridge, as it keeps well (for years) unopened in the fridge just in case you ever need it. Wine yeast is about .79 cents a pack at most homebrew stores.