Quote:
Originally Posted by sammyg2
|
yes, and
anyone that follows your thinking will be wrong
yes, there is a rule that says to perform all possible operation inside the parenthesis
It is actually not necessary to perform all the operations inside the parenthesis as there are rules for handling situations where it is not possible or desireable for one reason or another.
It is just usually a best practice to do so,
the next rule to follow is to perform any unary operations on the parentheses, the most common unary operation is exponent, in this case the exponent on the parenthesis is 1 and so does not change the value inside the parenthesis and so it says to do nothing
and yes, you correctly mention that the parenthesis stays, the only thing that every removes a parenthesis is when something out side the parenthesis multiplies it.
Here is where your understanding of mathematics is faulty.
There is no rule that says you are to perform the multiplication on the parenthesis. You have confused and bastardized the rule you used above to try to use it in a situation where it does not apply.
once again the rule is
perform all possible operation inside the parenthesis followed by
perform any unary operations on the parentheses
multiplication is a binary operation it requires 2 arguments in this case 2 & (12)
in the absence of the division operation to it's left, yes, you would perform the multiplication,
but we have that other pesky rule perform all operations which are at the same precedence level from Left to right. Since multiplication and division are at the same precedence level the division is performed first followed by the multiplication
Perhaps evaluating the expression(it is not an equation and so cannot be solved) in a different ways(I'm an optimist
) will show you the error of your ways
for the sake of demonstration lets suppose that we don't wish to perform the addition first, it is entirely reasonable though not usually done this way. In fact lets just substitute some other value which is equivalent to the parenthesis. You remember substitution rule? =s may be substituted for ='s
lets say for the moment that 9+3 =
a
can we agree that this does not violate anyones understanding?
48/2(9+3)
48/2(
a)
Now it should be obvious that there are 2 operations of equal precedence, division and multiplication which need to be performed left to right
24(
a)
resubstitute
24(9+3)
add
24(12)
288
or to prove a statement I made above, you do not have to add first, use the distributive property of multiplication over addition
24*9 + 24*3
now since there are no parenthesis to confuse anyone, multiply
216 + 72
add
288