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When I was taught long division for decimal quantities, the first step I was given was to multiply both numbers by the same power of ten (i.e. 10, 100, 1000, etc). Pick the power of ten such that you eliminate all decimal places. If the divisor didn't fit into the numerator, what I needed to do was to multiply the numerator by 10, and then move the decimal place in the answer over one. I agree that if you can manage it the easiest way is to just drop the decimals entirely, and then add them back in afterwards to make sure you have the same magnitude.
Order of operations. Perentheses, exponents, multiply/divide, add/subtract.
Pederson and ArcticChicken have come the closest as to why the division has to come first in your particular problem.
---------------------------------------------------------------------------------------------- Order of Operations Agreement:
1. Please Inside Parentheses {and any other grouping symbols} first
2. Excuse Exponents (and roots)
3. My Dear Multiply and Divide AS THEY OCCUR FROM LEFT TO RIGHT
4. Aunt Sally Add and Subtract AS THEY OCCUR FROM LEFT TO RIGHT
------------------------------------------------------------------------------------------------
So without any parentheses, the division MUST be done before the addition.
Everything will be ok in the end. If it's not ok, it's not the end.
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