<PRE><B>Question 661216</B>
Divide 5/4 first. So say the rules for order of operations.
{{{(13)-(5)}}}/{{{4=13-5}}}/{{{4}}}, because those parentheses are meaningless and unnecessary.
(Write them only if your teacher wants them at this point). 
Then, {{{13-5}}}/{{{4=13-5/4}}} or {{{13-1.25}}},
and {{{13-5/4=52/4-5/4=47/4=11&amp;3/4}}} or {{{13-1.2=11.75}}},


When people progressed from indicating one operation at a time to giving a multi-step formula,
like {{{(24-11)}}}-{{{(3+2)}}}/{{{4}}},
they needed to agree on what the long expressions meant.
Parentheses were an easy fix.
They mean that the expression inside those brackets is meant to be calculated first.  
It may have always seemed obvious to everyone,
but RULE NUMBER 1 is parentheses first.
So, {{{(24-11)-(3+2)}}}/{{{4=13-5}}}/{{{4}}}.
The parentheses in {{{(13)-(5)}}}/{{{4}}} do not mean anything,
because {{{(13)=13}}} and {{{(5)=5}}},
and there is nothing to calculate inside those brackets.
 
NOTE:
When people decided to save even more parentheses,
they agreed that a long  horizontal fraction line means that
what&#39;s on top of that line (the whole expression)
is divided by the whole expression that is below the line, so
{{{(3+2)}}}/{{{4}}} and {{{(3+2)}}}/{{{(5-1)}}} (they are the same thing) can be written as
{{{(3+2)/4}}} and as {{{(3+2)/(5-1)}}}
 
RULE NUMBER 2 is that (unless otherwise indicated by parentheses)
multiplications and divisions are done before addition and subtraction.
When people got tired of writing things like
(25X12)+(13x9)+(32x5)+(45X2)
to indicate the amount obtained by selling
15 cows for 12 coins each, plus 13 hogs for 9 coins each,
plus 32 lambs for 5 coins each, plus 45 chickens for 2 coins each,
they decided to skip some parentheses by agreeing that
multiplications would be done first,
and that 25x12 + 13x9 + 32x5 + 45X2 would mean the same thing,
without writing all those parentheses.
(That saved a lot of ink).
 
If there is a bunch of multiplications and divisions in a row, you do them from left to right, so
4X5/2/5X8=20/2/5X8=10/5X8=2X8=16
Multiplication does not have priority over division.
 
Teachers try to help you remember those rules by telling you the mnemonic
PEMDAS = Please Excuse My Dear Aunt Sally, or
PEMDAS = Parentheses Multiplication Division Addition Subtraction.
I do not like it so much because multiplication does not have priority over division,
and addition does not have priority over subtraction, either.
In fact, once I got to college, I learned that subtraction and division do not really exist;
they are just the reflections of addition and subtraction.
Subtracting {{{3}}} is really adding the negative number {{{(-3)}}},
and dividing by {{{2}}} is really multiplying by the fraction {{{1/2}}}.</PRE>