PEMDAS evaluating problem

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316matrix

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I had this problem for homework on evaluating. -5b [div symbol] 2a. Where b=8 and a=-5. I put 100 and got it wrong. They said the answer was 4. I thought the order of operations must be followed, but they are saying that the -5b is supposed to be divided by the 2a. But PEMDAS says to go left to right and that means you divide by 2 first before you multiply. I attached a screen shot. Thx!!
 

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316matrix said:
I had this problem for homework on evaluating. -5b [div symbol] 2a. Where b=8 and a=-5. I put 100 and got it wrong. They said the answer was 4. I thought the order of operations must be followed, but they are saying that the -5b is supposed to be divided by the 2a. But PEMDAS says to go left to right and that means you divide by 2 first before you multiply. I attached a screen shot. Thx!!
Click to expand...
The trouble here is that some textbooks teach PEMDAS strictly, as you are applying it, left to right:

[MATH]-5b\div 2a = (-5)\cdot 8\div 2\cdot(-5) = (-40)\div 2\cdot(-5) = (-20)\cdot(-5) = 100[/MATH]​

A few teach an additional "rule" that multiplication indicated by putting numbers next to one another is done before the division, because that product is thought of as a single unit:

[MATH]-5b\div 2a =(-5)\cdot 8\div (2\cdot(-5)) = (-40)\div (-10) =4[/MATH]​

And I've heard that some books that teach the former, do the latter in the answers to exercises!

Now you know how your book does it; if it doesn't somewhere teach the second way, then you can point it out to your teacher. They should not be inconsistent.

My own opinion is that the special rule makes a sort of sense, but since it isn't accepted by everyone, we should never write expressions like this in the first place.

Here is an explanation of all this that I wrote as a result of long experience with the issue.
 
Thank yous o much for your time. I do understand what you are saying!

So a better way of writing this would be -5b div (2a). Put the 2a in parenthesis and the argument is gone!
 
316matrix said:
Thank yous o much for your time. I do understand what you are saying!

So a better way of writing this would be -5b div (2a). Put the 2a in parenthesis and the argument is gone!
Click to expand...

Exactly. Or, if you want it the other way, (-5b÷2)a.
 
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