If the sentence does not indicate the nature of the operation (whether addition, subtraction, multiplication, or division), then we are forced to use very specific words for the outcome of each operation:

For addition, we use المجموع ("sum")
For subtraction, we use الباقي أو الفرق ("remainder" or "difference")
For multiplication, we use الحاصل ("product")
For multiplication, we use الخارج ("quotient").

But if the operation is mentioned, then I see no harm in using حاصل for the outcome of any operation. In common parlance, حاصل simply means ناتج or نتيجة. There should not be any problem in using

حاصل الجمع
حاصل الطرح
حاصل الضرب
حاصل القسمة

The meaning will be clear if the name of the operation is mentioned. Even mathematicians realize this. Notice that even when they use the term حاصل for the outcome of multiplication, they almost always specify it as حاصل الضرب because they know that for most people, حاصل simply means outcome and is not strictly associated in the minds of the general public with the mathematical notion of "product." Therefore, حاصل by itself will not be clear enough.

The same thing is observed regarding the word خارج. For most people, it simply means "output," so mathematicians are careful to state it as خارج القسمة

On the other hand, the terms المجموع and الباقي are specific enough. The nature of the operation is unambiguously understood.

The choice among الباقي or الفرق or even حاصل الطرح will depend on what is being discussed and how it is discussed. The style will have a great impact on which of these options to choose.