MoonlitSunshine

It only works out as 9 doing the multiplication first if you assume that there are parentheses around the (6/2).

In order to get any one, unique answer, you have to add one set of parentheses:

(6/2)*(1+2) = 9
6/(2*(1+2)) = 1

There are your two choices. I will add that Google gives the 9 answer because calculators, indeed all computer programs, are designed to evaluate from left to right in the absence of proper syntax, similar to how you can figure out what someone is saying even if they have atrocious spelling. Doesn't make their spelling any more correct, though. I will also point out that if you put the equation into Google, it adds a pair of parentheses in the position it is assuming you mean due to your incorrect syntax:



if you break the equation down into a, b and c, to represent the parts which there is argument about, it's a lot easier to see what's going on. In the following, a=6, b=2, and c=(1+2):

a/b*c = ... ?

Now, one interesting thing worth noting is that Canwllcorfe, among others, has chosen to see this as (a*c)/b, which is interesting as it totally changes the order. It is however equivalent to (a/b)*c, which is one solution to the problem, so it's fine as an answer, but it just goes to show that "left to right" isn't always even correct, as you can manipulate such an ambiguous statement to have the inverse order of operations.

Your choice, however, boils down to (a/b)*c or a/(b*c). If you substitute back in the values, you will (hopefully) note that this equals 9 and 1 respectively.

Do you still feel that the "parentheses or lack thereof makes no difference"?

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midnight rain

Yes, because the parenthesis you showed that Google had on them are unneccessary. They only make it easier for people to see how the process is. Lack of parentheses implies that it's a 6/2 fraction.

CanwllCorfe

That's what I was thinking. I mean, I know the inclusion of another pair of parentheses would certainly alleviate any real confusion, but I don't think they're necessary. I certainly didn't look at the problem and read it as 6/(2*(1+2)), because those parentheses aren't there. So I figure, by default, it should be (6/2)*(1+3). It also seems, to me anyway, more logical.

EDIT: But do note that I'm just explaining my mindset. You could be completely right Moonlit (in that, ironically, there is no definite answer).

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