"She adds those numbers."
Translation:Ella suma esos números.
I don't think "echar" can apply to numbers, I couldn't even find "add" as a definition of "echar" in my dictionary. I guess in some contexts where "echar" is used to mean "apply" you could also translate it as "add", but that has nothing to do with numbers.
Echar usually means "throw", "cast", or "pour".
I am from Spain.... My mother language is Galizian, though, but i have been 26 years speaking fluent spanish in Spain so I can tell you yes, you can translate add to many different verbs without context (including echar). Yet it is true what you say...echar and numbers do not fit properly, but still añadir sumar agregar and many other verbs yes....indeed, that was my complain, not concretely about "echar". "Ella suma/añade/agrega/... esos numeros" is possible
Anyway, You cannot often "echar those numbers", thats for sure and if you read what i wrote you can see i have already said so..........Well, we do say in spanish "echar esos números" but only when you talk about the lotery numbers....yet it is true you cannot apply that example here, i guess....
but as general translation of add you can "echar many things" with the translation of add....for example adding ingredients to a pot (as you said).....so definitely there is some overlapping between the meanings of echar and add.