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January 29th, 2016, 07:24 AM   #1
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Math, use my head to calculate, or write down the formula?

Hello, my name is Joseph, and I am new in the forum. I have an essential related question. When I calculate math problems I often feel that to use my head is quite slow. Because when i write it down the problem, it is much more easier to solve in written format, than just use my head.

It is a philosophic question, but in Math it is goal to calculate problems as mush as possible in my head, or it is completely acceptable when I use paper, and calculate step by step?

Thank you for your answer.
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January 29th, 2016, 07:44 AM   #2
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The goal in mathematics is to determine the results. Normally people try to do too much in their head which leads to errors in the worst case, or working that is difficult for others to follow.

As a general rule, write down every step. Experience will later tell you which steps you can leave out without making it difficult to follow.

Of course, you can have too much of a good thing. It is possible (but generally unlikely) that you write down too much of your working. When that happens, reading through becomes like reading a book where the descriptive passages are so long and the plot moves so slowly that you forget what (if anything) has happened.
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February 9th, 2016, 08:41 AM   #3
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When I worked as a tutor in college, the single most helpful thing I could tell the student was to use his pencil and to stop staring at the blank sheet of paper and/or at the ceiling. Once he wrote down what he knew and started thinking about the obvious ways to modify his equation, like multiplying both sides by the same number, it all fell into place.

Recently, I went to the pet store to buy a couple of 35# bags of dog food that were on sale for 19.95. They were out but had lots of 24# bags, so I suggested that they sell me three of the smaller bags at the same price per pound as the two big bags I had wanted. They were okay with this but didn't know how, so we soon had the other clerk, the stock boy and the manager in a huddle. The scene reminded me of nothing so much as that famous picture of the troupe of monkeys puzzling over a piece of rope with some knots in it. Nobody thought to write anything down - they were all trying to do it in their heads. And of course they wouldn't listen to me because they assumed that their customer would try to cheat them.

Finally I got the clerk to give me a piece of cash register tape. I wrote $\displaystyle \frac{x}{24}=\frac{19.95}{35}$ on it and wordlessly handed it to the manager. I could almost see the light bulb come on over her head and in a matter of minutes she had rung up my three 24# bags at $13.68 apiece!
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