Question

Which is a correct way of evaluating the expression 25x + 40x for x = 4?

Answer 1

The Order of Operations would tell you
1. substitute the value of the variable
2. evaluate multiplications
3. evaluate the sum

25*4 +40*4
100 +160
260


Personally, I would combine terms and rewrite it to be
.. (25 +40)x
.. 65x
.. 65*4
.. 65*2*2
.. 130*2
.. 260

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The Order of Operations is the rule book for evaluating expressions. However, we know that multiplication and addition are associative and commutative, and that the distributive property applies.

If you are evaluating expressions in a computer program, there are methods for assuring minimum round-off and truncation errors that have little to do with any of the above, but everything to do with how numbers are represented in a computer and the way compilers work.