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- What is 48÷2(9+3)? [duplicate] 4 answers
Unlike with addition, subtraction and multiplication where the order of operations will lead to an unambiguous result when the rules of BIDMAS (or PEMDAS) are applied, this does not hold true for division.
For example: 5 + 3 x 5 x 7 - 2 = 5 x 7 x 3 + 5 - 2 = -2 + 5 + 7 x 5 x 3
Of course, BIDMAS states we must group our multiplications together but within that grouping the order of multiplications makes no difference to the result. Furthermore, following the rules of BIDMAS and performing the multiplications first, the subsequent order of the arithmetic also makes no difference. Right?
In the above example, for instance, 3 x 5 x 7 = 105. So: 5 + 105 - 2 = -2 + 105 + 5, etc...
However, operation order DOES affect the result when dividing! For example:
(1/4)/27 does NOT equal 1/(4/27).
We know this, right!
I always took it for granted that the order of operations when presented with multiple divisions must be performed in the order it is presented; ie from left to right. That is what we were taught at kindergarten, right?
a/b/c/d = ((a/b)/c)/d
Well that's what I believed all my life and took this for granted. But now my sanity is being challenged by Casio's most recent scientific calculators which do not obey this rule!!!!
If you were to type in a/b/c/d into a modern Casio scientific calculator using its fraction key for '/' rather than the division button, the calculator yields a/(b/(c/d))!!!!!
Using the division button instead of the fraction key gives a conflicting (but what I believe to be the correct) answer; that is:
a divided by b divided by c divided by d = ((a divided by b) divided by c) divided by d
I feel sure that the older Casio scientifics (pre 1991) gave the correct result following the rules as I have explained above. But I cannot get hold of one to check my theory.
So my question is: What is the correct order of operation with multiple consecutive divisions? That is, what is the order of division for:
as written without any parenthesis? Are the new Casio calculators giving the wrong answer or have I been living a lie?
PS: I am aware that the calculators give what I believe is the correct answer if the right cursor key is pressed after the keying in of each denominator. Bu that is a fudge. By using the right cursor, you are applying implicit parenthesis.
As inputted, either the calculators are giving the wrong answers or I have been living a lie. Can someone please confirm the order of division should indeed be from left to right!
PS: I have searched everywhere I could on the internet and in many maths text books but have not been able to find anything that addresses the ambiguity in the order of multiple consecutive division operations.