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Evaluation and simplification of an expression

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--What is the difference between evaluation and simplification of an expression?
--3,4,5 are consecutive whole numbers. -13, -12, -11 are consecutive integers. Is it possible to write consecutive rational numbers? If yes, give an example. If not, explain why not.
--How does a term differ from a factor?

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The solution contains detailed explanation of the difference between evaluation and simplification of an expression.

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--What is the difference between evaluation and simplification of an expression?

I will include an example to address this question. Consider the following expression where x is a variable.
(x^2-1)/(x^2-3x+2)
To simplify it, we want to cancel out all common factors of both top and bottom. So,
(x^2-1)/(x^2-3x+2)
=[(x-1)(x+1)]/[(x-2)(x-1)]
=(x+1)/(x-2)

But the evaluation of an expression is to find value for a certain value of x. For instance, evaluate ...

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  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
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  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
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