In arithmetics, “to carry out an operation” generally implies using a written or mental calculation algorithm. However, for many years now, effective electronic tools have appeared in classrooms: pocket calculators, scientific calculators, programmable calculators, tablets, computers, etc. Increasingly, the instruction “to calculate” will consist of using these tools to conduct more complex tasks – keeping in mind the students’ learning levels – and obtain results more quickly and more precisely.
In algebra, “carrying out an operation” most often consists of applying an algorithm to transform an expression in order to expand it or simplify it.
In the fields of relations, functions, geometry, statistics, etc., the expression “to carry out an operation” can have even more meanings, depending on the context.