modellingman wrote:a/bc is not equal to
a/(bc)eepee wrote:I fail to understand the a/(bc) given above.
The inequality is true for all non-zero real numbers
a,
b and
c, so it is true for any specific set of values. Therefore
let
a represent the initial 6 of "6/2(2+1)"
let
b represent the 2 immediately to the right of the "/" (division) symbol
let
c represent the expression "(2+1)" (which obviously evaluates to 3)
With these values for
a,
b and
c, what I am saying through my inequality is that 6/2(2+1) is not the same as 6/(2(2+1)).
6/2(2+1) is 9, whereas 6/(2(2+1)) is 1.
Thanks for the Wikipedia link. Interesting to know that there is
PEMDAS,
BEDMAS and
BIDMAS as well as our old friend
BODMAS and that the editors of a few obscure scientific journals have decided to re-write the conventions of mathematical notation to give an implied multiplication operator a higher precedence than division or explicit multiplication operators.
Dod101 wrote:If modellingman is correct then I have been wrong for the last 70 or so years. It has done me no harm.
Seriously though, he is now changing the rules. I am sure we all assumed that the / was intended to be the division line so that 6/2(2+1) was simply another way of writing 6 as the numerator and 2(2+1) as the denominator. He is now saying that 6/2 is one term which equals 3 and (2+1) is another which equals 3. Obviously the two terms together equal 9. So I do not think there is a 'correct' answer. it depends what the / is intended to mean.
Dod
The whole point about teaching and using the conventions of mathematical notation is to avoid the need to make any assumptions about the intended meaning of an expression.
It is also part of the conventions that where an operand is omitted between two numerical values, there is an implied multiplication operator. If the expression had instead been written equivalently in fuller form as 6/2x(2+1) would you still argue that the denominator to the division operation is 2x(2+1)?
If the answer is yes, then this flies in the face of convention by applying a right-to-left (rather than left-to-right) prioritisation of the multiplication and division operations. If it is no then that says that two mathematical expressions, equivalent except that one is using an implied multiplication sign and the other an explicit sign, can evalute to completely different values - which seems nonsensical to me.
Someone else as well as the editors of a few obscure scientific journals also seems to be changing the rules (ie the conventions of mathematical notation), but its not me.