Order of operation (division) in algebra

I'm just learning algebra.

The order of operation rule i learned pre-algebra is: PEMDAS. And you do multiplication and division from left to right as they occur. I also learned that with fractions you solve the numerator first, then you solve the denominator, then you divide. Thats all correct, right?

In my algebra text book it said that in algebra you always write a division sign as a fraction. "Okay, fair enough, i'll obey that rule too" i said.

But then i get a question like this:

9xy / 3x * 2y^2 * 4x^3

So the order of operation states that i do 9xy / 3x first and THEN multiply the rest of the terms to get the answer. Which gives the CORRECT answer.

But the book, as i mentioned earlier, told me the rule with algebra is to write division as a fraction. So if you do that you end up in effect doing this: 9xy / (3x * 2y^2 * 4x^3) because you simplify the numerator and then you simplify the denominator and then you divide numerator by denominator.

So what the ****? Why would the book tell you this rule when it is sometimes wrong and will lead you to get the wrong answer. Am i missing something here? Or was the book right and i have just misunderstood something? Or am i right? Should you look at the question and obey the PEMDAS rule above all else before changing division signs into fractions in algebra questions?

This is the "ambiguous" case: Do you divide only the first factor, or do you regard all the factors as being one big chunk, with the whole chunk divided into the 9xy?

It would appear that the book intends the latter to be the rule for this special case. Unfortunately, common practice is not consistent, nor are graphing calculators (if you'd been using numbers instead of variables) or other software (such as spreadsheets).

It would likely be wise to draw this specific exercise to your instructor's attention, and specifically ask what will be the rule on the test. Your instructor will have a preference, and you'll want to know, sooner than later, what that it. :wink:

einstein said:

9xy / 3x * 2y^2 * 4x^3

Click to expand...

IF appears like this in "the book":
then you MUST show like this:
9xy / (3x * 2y^2 * 4x^3) ; kapish?