Brazil | which method is correct | BODMAS rule | PEMDAS rule 

1 Implicitly connected GROUPS of factors and coefficients are treated as single values throughout mathematics. Distance divided by circumference is equal to revolutions. D÷2πr=D÷πd must be calculated as D÷(2πr)=D÷(πd) to avoid failing dimensional analysis. It can be shown that the viral equations 8"÷2(2"+2")=? And 6"÷2(2"+1")=? Are both, in fact, forms of D÷2πr= revolutions. And must be calculated as 8"÷[2(2"+2")]=1. And 6"÷[2(2"+1")]=1 Or arrive at experimentally, verifiably false results of 16in²and 9in² respectively. Even, or especially, when the radius dimensions are a sum of hub and tread thickness. 120"÷[2π(11"+1")]=120"÷[π(22"+2")]=1.59 revolutions. Volume divided by area to determine depth of contents, V÷πr²=depth must be evaluated as V÷(πr²)=depth, to avoid failing dimensional analysis. 1000ft³÷[π(13'-1')]=2.21' deep Volume divided by spherical volumes V÷4/3πr³=number of flasks filled And must be calculated as V÷[4/3πr³] in order to pass dimensional analysis and not arive at 6 dimensional space in the spurious results. 300in³÷4/3π(3in-0.12in)³= 300in³÷[4/3π(3in-0.12in)³]=3 This is also a good example of how the different division notations are used differently. V÷4/3πr³=V÷[4(1/3)(π)(r³)]=quantity D÷2πr is interpreted as D÷[2πr] a quotient with an implicit grouping of factors and coefficients in the denominator. While D/2πr represents a product of the factors D(1/2)(π)(r) that would not be equal to rotations made by a wheel. In fact, each and every instance of Implicitly joined groups of factors and coefficients must be resolved prior to even acknowledging any other explicit operations in the rest of an equation. To omit this grouping relationship means to arrive at spurious results each and every time. The implicit grouping relationship is inherent in the implicit notation and cannot simply be ignored, without expecting incorrect results. So PEMDAS must be interpreted as Parenthetical expressions(including coefficients) First, also using PEMDAS. Then, Exponents Multiplication Division Addition Subtraction The example problem is in no way excluded from these mathmatical behaviors.