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6/2(1+2)=6/2(1+2)=6/23=(6/2)3=(3)3=9 This is pretty well defined, I feel: - Expand implicit multiplication to explicit multiplication (e.g. 2(1+2) becomes

6/2(1+2)=6/2*(1+2)=6/2*3=(6/2)*3=(3)*3=9 This is pretty well defined, I feel: - Expand implicit multiplication to explicit multiplication (e.g. 2(1+2) becomes 2*(1+2)) - Left-to-right precedence for operators of equal-precedence (divide and multiply) The 2 is no more bound to the parenthesis than it is to the division operator. Am I missing something?

gizmo686 14y ago
When you have 6/2(3), it is not well define if the correct expansion is 6/(23) or (6/2)3. In my experience with math, the intuitive answer is that implicit multiplication takes precedence. For example, say instead of 6/2(3), you had 6/2x. Following your convention, that would expand to (6/2)x, not 6/(2x). You might say that the () around the last number make a difference. However that would imply that 6/2x!=6/2(x). Which I find deeply unsettling if true. Ultimitly, this is why we tend to use notation which uses placement to resolve these issues unambiguasly, without alot of parentheses.
- armadillowarran 14y ago
  I find it interesting you feel this way. In my experience, it is pretty well defined: 0. Evaluate (the inside of!) parenthesis, then 1. Evaluate exponentials, then 2. Evaluate division and multiplication operators, left to right e.g. 1 / 2 * 3 / 4 = (1/2) * 3/4 = ((1/2)*3)/4 3. Evaluate addition and subtraction operators, left to right Your issue seems to stem from the left-to-right concept (in order in which operators are encountered as you read, left-to-right). Your example of 6/2x to me is clearly (6/2)x. What is 1/2x ? In my experience, textbook authors/professors/math teachers tend to be disambiguous and either use the horizontal line for clarity or use parenthesis. I attended public schools in Ontario, Canada if it makes any difference. Edit: Oh yeah, also I have never felt that implicit operators would take precedence. Interesting!

6/2(1+2)=6/2*(1+2)=6/2*3=(6/2)*3=(3)*3=9 This is pretty well defined, I feel: - Expand implicit multiplication to explicit multiplication (e.g. 2(1+2) becomes

gizmo686 14y ago

When you have 6/2(3), it is not well define if the correct expansion is 6/(23) or (6/2)3. In my experience with math, the intuitive answer is that implicit multiplication takes precedence. For example, say instead of 6/2(3), you had 6/2x. Following your convention, that would expand to (6/2)x, not 6/(2x). You might say that the () around the last number make a difference. However that would imply that 6/2x!=6/2(x). Which I find deeply unsettling if true. Ultimitly, this is why we tend to use notation which uses placement to resolve these issues unambiguasly, without alot of parentheses.

armadillowarran 14y ago
I find it interesting you feel this way. In my experience, it is pretty well defined: 0. Evaluate (the inside of!) parenthesis, then 1. Evaluate exponentials, then 2. Evaluate division and multiplication operators, left to right e.g. 1 / 2 * 3 / 4 = (1/2) * 3/4 = ((1/2)*3)/4 3. Evaluate addition and subtraction operators, left to right Your issue seems to stem from the left-to-right concept (in order in which operators are encountered as you read, left-to-right). Your example of 6/2x to me is clearly (6/2)x. What is 1/2x ? In my experience, textbook authors/professors/math teachers tend to be disambiguous and either use the horizontal line for clarity or use parenthesis. I attended public schools in Ontario, Canada if it makes any difference. Edit: Oh yeah, also I have never felt that implicit operators would take precedence. Interesting!