posted on Mar, 2 2014 @ 07:38 AM
reply to post by Arbitrageur
You are not interpreting the article properly.
The point of the article was that addition and multiplication have associative and commutative properties, so the order of doing multiplication and
addition doesn't actually matter. Hence the distinction about either doing multiplication or addition left-to-right are not necessary to be taught
because they do not matter
. 1*2=2. 2*1=2.
Now obviously division is not the same in that way as multiplication. Order does matter, i.e. 1/2 is not the same as 2/1. But here is the key point in
that document with regard to division.
Moreover, they also know that subtraction is the adding of a negative number and division by c is multiplication by 1/c.
Hence another way to interpret the equation according to the paper is:
(48)*(1/2)*(9+3) = 288.
Check the end of page 5, because it gives a very similar example:
The example in (3) is perhaps a bit extreme, and was concocted to make a
point. However, the next one is taken from p. 207 of a school mathematics review
Evaluate 4 + 5 * 6 / 10.
Now one never gets a computation of this type in real life, for several reasons. In mathematics, the division symbol basically disappears after grade
7. Once fractions are taught, it is almost automatic that 6/10 would be replaced by 6*(1/10). Moreover, if anyone wants you to compute 4 + 5*6/10, he
would certainly make sure that you do what he wants done, and would put parentheses around 5*6/10 for emphasis.
So according to your own source, the answer is 288.
If you don't replace division by c with a multiplication 1/c, as suggested in the article, then you end up having to go left-to-right to get the same
answer. And that's the way pretty much all calculators do it, and they do it that way for a reason.
You also stated:
Multiplication and division can be similarly expressed so the order of execution makes no difference.
The only way you can possibly get 2 is if you use a specific order of execution by multiplying before dividing!
edit on 2/3/14 by C0bzz
because: (no reason given)
edit on 2/3/14 by C0bzz because: (no reason given)