i'm completely against genocides but those people that think its 1 better hope i don't come to power
(1 vote)
6÷2(1+2)=???
i'm completely against genocides but those people that think its 1 better hope i don't come to power
Comments
(Old Spike)
Well, they are not. Just rewrite the equation substituting "÷2" with *(1/2) and you have the correct answer (brackets for clarification):
6*(1/2)*(1+2)
The "ambiguity" only comes into play if the "*" was left out in this part of the equation "2(1+2)" with the purpouse of prioritising "2*(1+2)", however then brackets should have been used i.e.:
6÷(2*(1+2))
(Site Administrator)
The * is implied when you put the 2 next to brackets.
It's ambiguous because it's all on a single line & you can't tell if the bracketed part is part of the denominator or belongs next to the 6/2
IE:
(6/2)*(1+2) OR 6/(2*(1+2)) - you can't tell which is is with the notation given
(Old Spike)
The first part of your reply is what I said, however that does not give it priority, only brackets would or if you would write it as fractions. The "direction of reading" the equation has NO influence on the result. "Loosing" the "*" does not give this part of the equation priority. It is easier to understand when we first resolve the brackets:
6÷2(1+2) = 6÷2*3 = 3*6÷2 = 3÷2*6
however:
6÷2(1+2) =/= 6÷(2*3)
only
6÷(2(1+2)) = 6÷(2*3)
So if written out correctly you indeed can tell exactly which is the notion.
(Site Administrator)
the direction is supposed to have an influence..
multiplication & division are evaluated with the same priority in terms of the order things are calculated & when both appear you go from left to right - that's the rule
just in this case there's an argument for both & my reasoning isn't even the correct mathy one, it's just the one that makes the most sense to me.. I hate these QWERTY keyboard versions of formulae. I doubt you'd see this type of annotation in any serious exam.
(Old Spike)
"the direction is supposed to have an influence"
nope, neither is there an argument for both.
Just take any calculator and type in:
"6÷(2*(1+2))=" the result will be 1
as opposed to:
"6÷2*(1+2)=" the result will be 9
Also "6÷2*3 = 3*6÷2 = 3÷2*6 =" will all come to the same result, and this would be handwritten exactly like that on paper, just substitute "÷" with ":", that is how I was taught in school and later in University.
Lastly "÷2" equals "*(1/2)" which equals "*0,5".
(Site Administrator)
"6÷2*3 = 3*6÷2 = 3÷2*6"
the answer in each case is 9 but they're not the same expressions.
lookup the order of operations if you need a refresher.
(Old Spike)
Order of operations does not negate what I said.
(Short Spike)
nein nein nein!
(Site Administrator)
Juan Juan Juan
(Old Spike)
IIRC, numbers in brackets get done first, right? So, it's 1.
(Site Administrator)
In classical mathematics the rule is exactly that, yes!. But I'm thinking some folks have gotten used to how computers would read it and in that case the bracket would be handled as a mere multiplier, with the functions handled in the order they are encountered left to right. But for us humans, the answer is 1.
(Short Spike)