The reason this problem seems 'ambiguous' to people is because they lack understanding of the Order of Operations. Division and multiplication are the same and should be performed in the same step, from left to right. Subtraction and addition are the same and should be performed at the same step.
Note that when I say 'division and multiplication are the same,' I am saying that you can rewrite all division as multiplying by the reciprocal. The division happens to anything directly after the division sign. If there are no parentheses grouping the denominator (like a fraction bar naturally does), then only the first thing after the division sign is divided. Implied multiplication shouldn't take any more precedence than 'regular' multiplication that is shown. Also, when I say 'subtraction and addition are the same,' I am saying that subtraction can be rewritten as adding the opposite.
The order of operations in this problem is as follows:
Work inside parentheses (1+2=3).
Divide 6 by 2 (3).
Multiply 3 by 3 to get 9.
Any perceived 'ambiguity' is from a substandard understanding of the Order of Operations and/or understanding of division/multiplication features. This article suggests that someone jotting down 1/3x means 1/(3x) which is flat out untrue. Jotting that down while intending it to be 1/(3x) shows you don't understand how the Order of Operations ACTUALLY works.
The reason this problem seems 'ambiguous' to people is because they lack understanding of the Order of Operations. Division and multiplication are the same and should be performed in the same step, from left to right. Subtraction and addition are the same and should be performed at the same step.
Note that when I say 'division and multiplication are the same,' I am saying that you can rewrite all division as multiplying by the reciprocal. The division happens to anything directly after the division sign. If there are no parentheses grouping the denominator (like a fraction bar naturally does), then only the first thing after the division sign is divided. Implied multiplication shouldn't take any more precedence than 'regular' multiplication that is shown. Also, when I say 'subtraction and addition are the same,' I am saying that subtraction can be rewritten as adding the opposite.
The order of operations in this problem is as follows:
Work inside parentheses (1+2=3).
Divide 6 by 2 (3).
Multiply 3 by 3 to get 9.
Any perceived 'ambiguity' is from a substandard understanding of the Order of Operations and/or understanding of division/multiplication features. This article suggests that someone jotting down 1/3x means 1/(3x) which is flat out untrue. Jotting that down while intending it to be 1/(3x) shows you don't understand how the Order of Operations ACTUALLY works.