Quote:
Originally Posted by svandamme
Order of operations - Wikipedia, the free encyclopedia
The standard order of operations, or precedence, is expressed in the following chart.
#1 terms inside brackets
#2 exponents and roots
#3 multiplication and division
#4 addition and subtraction
a
16 ÷ 2[8 – 3(4 – 2)] + 1
Apply #1
16 ÷ 2[8 – 3(2)] + 1
16 ÷ 2[8 – 3 x 2] + 1
#3 within the square brackets
16 ÷ 2[8 – 6] + 1
#1
16 ÷ 2[2] + 1
16 ÷ 2 x 2 + 1
Rule 2
8 x2+1
#3
16 +1
#4
17
So it is 17 after all.
48 ÷ 2(9+3)
Rule 1
48 ÷ 2(12)
48 ÷ 2x 12
Rule 3
24 x12
288
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See the part I bolded in your quote. Technically, you changed the meaning of the equation there. The implied multiplication of the adjacent parentheses is considered a higher precedence than an otherwise notated mult/div operation and thus gets done first. Just like we tend to simply the entire numerator and denominator first when we see an equation notated in that style.
All of these are still just examples of poorly written equations. Parentheses are free, don't be miserly with them.