How do you identify the necessary information that is missing from a problem?

  It depends

Step-by-step explanation:

Identifying what is not there is always difficult. In the general case, the range of possibilities is infinite.

For relatively simple math problems, the problem statement usually gives a context and asks a question. The context will generally tell you the nature of the relationships that apply. The question will generally be answered by making use of the relationships to relate given information to requested information.

If a relationship involves 4 items, one is "unknown" (that you're asked to find), and only 2 are given, then you know the missing information is the remaining item in the relationship.

Often, you can work a problem a number of ways, so the information that is missing depends on the method you choose for working the problem.

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In complicated multi-step problems, relationships may need to be developed, theorems proved, massive amounts of data examined, and more. In some cases, whole new areas of mathematics may need to be invented.