You always solve parentheses first before solving for exponents, multiplication/division and addition/subtraction, but for the following problem 6/2(2+1), if solved division first then parentheses it still comes out to the same answer of 9... Is there a problem more definitive I can use to show that parentheses has to come first?

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You always solve parentheses first before solving for exponents, multiplication/division and addition/subtraction, but for the following problem 6/2(2+1), if solved division first then parentheses it still comes out to the same answer of 9... Is there a problem more definitive I can use to show that parentheses has to come first?

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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Actually solving parens doesn't really matter so long as you do solve them before you remove them. You can do them first or last it will still work properly.
It absolutely does matter, especially in more advanced problems... Which is why the rule is there to begin with, but I was looking for a simpler problem that takes the use of parentheses and has you apply the rule of order of operations instead of just being bypassed like you can in the equation given in my last text.
I disagree. You don't need to solve the inside of an expression first. You only need to solve it before you take off the parens. I can only really come up with 3 cases: Addition/subtraction: 5 + (6-3) Obviously fine (-2+3) - 4 No issue here Multiplication/division: 4/5(3+2) Still doesn't matter 5/(3+2)7 Nope Exponents: 4(4+2)^5 etc. Can you come up with any example where evaluating the inside of the parens is required for correctness?

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