Sorry, but what problem are you exactly talking about. If you are talking about a random math problem than it really depends. Math word problems, if they are hard, then yes, definitely take steps. Good Luck :)
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An algorithm is the series of steps to solve problem, so you would be looking for the series of steps to solve a math problem.
Scientific Method.
When you analyze a problem you look it over which is what analyzing means. You look over the problem and then you solve it. When you solve a problem you solve it and you use certain steps and solve it but of course everyone has there ways to solve a problem but some people have ways to solve it by just analysing it. That is the difference.
The answer to 744 times 31 equals 23064. To solve this math problem you will have to take the number 744 and add it 31 times.
It is a Scientific Method.