The Order of Operations is Wrong

What people said

Recommends Arthur · 2017-09 · Mathematics Stack Exchange · on “Soft question: What if BODMAS/PEDMAS wasn't used. Would maths still "work"?”

As long as B / P is first, anything can be made unambiguous by adding brackets. The whole reason to have a standardised order of operations is to make it so that we don't need as many brackets. See, for instance, this MinutePhysics video [this video] . The standardised order of operations is something we humans as a whole have adapted to make reading mathematics easy to read and write. There is no real, objective, deep mathematical reason it should be the way that it is, it's just what corresponds best to how we think about quantities.

Recommends Arthur · 2018-07 · Mathematics Stack Exchange · on “What is a/b/c/d? That is: What is the correct order for multiple consecutive division operations?”

While addition and subtraction is conventionally evaluated left-to-right, multiplication and division isn't. If we have a sequence of multiplications and divisions without parentheses, and there is a division which is not the rightmost operation, then the expression is inherently ambiguous. Thus: $5\cdot 4\div 3$ is unambiguous. $5\div 4\cdot 3$ is ambiguous. There may be convention on this, but it is not universal, which means that any time you see such an expression you cannot be certain that the author followed the convention, which makes it ambiguous. Turn it around, and I recommend that any time you write such an expression you use fractions and brackets to clarify. PS: see this youtube

Cites Cisplatin · 2013-05 · Mathematics Stack Exchange · on “What is $2 - 1 + 1$?”

$2-1+1$ ; a fairly straightforward question, but I (well, not me, but Henry Reich [this video] ) found something strange. Most people would evaluate it as $2+(-1)+1 = 2$ ; however, this goes against the famed, and fairly standard B.E.D.M.A.S./P.E.D.M.A.S., which states that addition goes first, and then subtraction. If this is the case, then the answer is $2 - (1 + 1) = 2-2 =0$ . Which is the correct answer, and why is the conventional way (B.E.D.M.A.S./P.E.D.M.A.S.) so ambiguous?

Cites Isaac · 2014-10 · Mathematics Stack Exchange · on “Dividing by 2 numbers at once, what is the answer?”

[this video] Take 8-2+1 for example. In reality, it actually equals (8/1)+(-2/1)+(1/1) . Applying the same logic to 4/1/5 you get: (4/1)/(1/1)/(5/1) =(4/1)x(1/1)x(1/5) =(4x1x1)/(1x1x5) =4/5 With (P|B)EDMAS, 6/3/3 could be: 6/(3/3) =6/1 =6 or (6/3)/3 =2/3 whereas 6/3/3 actually equals (6/1)/(3/1)/(3/1) =(6/1)x(1/3)x(1/3) =(6x1x1)/(1x3x3) =6/9 =2/3