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Perhaps this one is a silly question but how do I know I am to simplify an expression? For instance: Suppose $a=5+3$, why on earth I am to perform the addition and make $a=8$. Are there rules to know when not to simplify an expression: sums, fractions, etc...?

Matt Samuel
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ceip7bavSi ceip7bavSi
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    There aren't any rules, really. It depends on the context. Sometimes one form is easier to work with, sometimes another is. Like most things, it's a matter of practice. As a final answer though, I think everyone would agree that $8$ is preferable to $5+3$. – saulspatz Dec 16 '20 at 21:06
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    I think this question demonstrates that you are thinking about expressions in the right way. People often think that simplifying mathematical expressions is about 'getting to the answer', but really it is about making information more clear. When we write $5+3=8$, we mean that $5+3$ represents the same number as $8$. It doesn't mean that $5+3$ 'makes' $8$. In fact, the only reason we would bother to simplify $a$ is because it aids communication and makes what we are working with clearer and easier to manipulate. – Joe Dec 16 '20 at 21:19

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There is not really any standard practice for when or how much to simplify and expression, and it is not always clear what 'simplify' means. For example, the expression $(x+2)(x+1)$ can be written as $x^2+3x+2$ which is in a sense simpler, since the multiplication has been done out, but it also obscures the factorization, making it less simple. It just depends on context.

Noah Solomon
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As the other users have noted, it depends on context. Integers are almost always preferable to expressions which would evaluate to make an integer, but carrying out that evaluation could obscure some key property of your expression.

Duncan Ramage
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