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Yes, The use of appropriate diagrams, drawings, and illustrations often helps a person to understand a problem and to explain a problem to others.
Ah, problem solving is like painting a beautiful landscape. First, you identify the problem, then gather information about it. Next, you brainstorm possible solutions and choose the best one. After that, you create a plan and take action to solve the problem. Finally, you evaluate the results and make any necessary adjustments. Just like adding happy little trees to a painting, each step builds upon the last to create a masterpiece of problem solving.
it often simplifies arithmetic
That depends on the type of problem. For example, if you have equations involving radicals, it often helps to square both sides of the equation. Note that when you do this, you may introduce additional solutions, which are not solutions to the original equation.
Here's how I do it: 1. Read through the entire question and identify exactly what you are being asked to do. 2. Decide what formula is needed to solve the problem, then write it down. 3. Go back through the problem and pull out the data needed for the formula (quite often there is a lot of data that you will not need). 4. Solve the problem. 5. (and this part is really important) Look at your answer and compare it to what is being asked. Ask yourself if the answer is reasonable; does it make sense?