*Presumably, teachers explain that it means "Parentheses — then Exponents — then Multiplication and Division — then Addition and Subtraction", with the proviso that in the "Addition and Subtraction" step, and likewise in the "Multiplication and Division" step, one calculates from left to right.*This fits the standard convention for addition and subtraction, and would provide an unambiguous interpretation for a/bc, namely, (a/b)c.Likewise, because addition and subtraction constitute one "family" of operations, and multiplication and division another, and perhaps also because the slant "/" doesn't seem to separate two expressions as much as a or − does, we are ready to read a/b c etc. But when it comes to a/bc, where the operations belong to the same family, the left-to-right order suggests doing the division first, while the "unseparated letters" notation suggests doing the multiplication first; so neither choice is obvious.

*Presumably, teachers explain that it means "Parentheses — then Exponents — then Multiplication and Division — then Addition and Subtraction", with the proviso that in the "Addition and Subtraction" step, and likewise in the "Multiplication and Division" step, one calculates from left to right.*This fits the standard convention for addition and subtraction, and would provide an unambiguous interpretation for a/bc, namely, (a/b)c.Likewise, because addition and subtraction constitute one "family" of operations, and multiplication and division another, and perhaps also because the slant "/" doesn't seem to separate two expressions as much as a or − does, we are ready to read a/b c etc. But when it comes to a/bc, where the operations belong to the same family, the left-to-right order suggests doing the division first, while the "unseparated letters" notation suggests doing the multiplication first; so neither choice is obvious.

Dan Roe, test editor: Right but it's multiplication/division, not multiplication then division Morgan: BUT multiplication with parentheses trumps division. Kit Fox, special projects editor: Isn’t the question and ambiguity here on when the parentheses disappear? Or do they go away once you solve the mini equation inside the parens first. I am on team 1I also have not taken a math class in over 10 years Trevor Raab, photographer: My question is to what real world scenario would this apply to Brad Ford, test editor: Math class?

Trevor: ahh the classic learn to do math to learn to do more math Bobby: school ain't real world Morgan: Generating heated and polarizing office discussion Brad: Bobby, tell that to a 6th grader.

To render it unambiguous, one should write it either as (48/2)(9 3) or 48/(2(9 3)).

This applies, in general, to any expression of the form a/bc : one needs to insert parentheses to show whether one means (a/b)c or a/(bc).

Either way, the meaning is clear from the way the expression is written.

The use of the slant in writing fractions is convenient in not creating extra-high lines of text; but for that convenience, we pay the price of losing the distinction that came from how the terms were arranged horizontally and vertically.

Here’s a heated chat between the editors who stopped doing any semblance of actual work for the day to solve an equation designed to flummox fourth graders—and make many enemies in the process—followed by insight from real mathematicians and physicists who begrudgingly responded to our request for comment to solve the enraging math debate, once and for all. What if you want to do it the long way and use the distributive property and distribute the 2 first? Or does the distributive property suddenly no longer apply? Derek: I trust Morgan because she's had a math class this decade. Dan: smart Berkley people say it's too ambiguous to say; PEMDAS isn't a mathematical convention as much as a teaching method Pat: multiplication/division::right/wrong Taylor Rojek, associate features editor: Biggest takeaway isn't that anyone sucks at doing math, but that this person sucks at writing out clear equations Bill Strickland, editorial director: MAKE IT CONTENT! Pat: The equation is not written according to ISO standards, leaving ambiguity of interpretation and the real answer is we need to teach better math writing.

Pat: Wikipedia says you hate America if you get 16. Ambiguous PEMDASAmbiguous problems, order of operations, PEMDAS, BEMDAS, BEDMASaka..Taylor said, but from Harvard Morgan: aka...teach the distributive property instead of random acronyms Pat: When written according to ISO standard, the answer is 1.

From correspondence with people on the the 48/2(9 3) problem, I have learned that in many schools today, students are taught a mnemonic "PEMDAS" for order of operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

If this is taken to mean, say, that addition should be done before subtraction, it will lead to the wrong answer for a−b c.

## Comments Order Of Solving Math Problems

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