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Scientists will generally use their brains to solve math or other problems. Once they have established the mathematical formula to be solved, they would use a computer or (scientific) calculator to evaluate the math problem and get a solution.
by experimenting..
Calculus was invented to solve physics problems, so the importance of studying calculus is to solve physics problems.
There is no single method to solve all types of fraction problems. Some problems and their solutions are relatively simple, others are extremely difficult.