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@subignition

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Joined 1 year ago
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Cake day: June 11th, 2023

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  • […] the question is ambiguous. There is no right or wrong if there are different conflicting rules. The only ones who claim that there is one rule are the ones which are wrong!

    https://people.math.harvard.edu/~knill/pedagogy/ambiguity/index.html

    As youngsters, math students are drilled in a particular
    convention for the “order of operations,” which dictates the order thus:
    parentheses, exponents, multiplication and division (to be treated
    on equal footing, with ties broken by working from left to right), and
    addition and subtraction (likewise of equal priority, with ties similarly
    broken). Strict adherence to this elementary PEMDAS convention, I argued,
    leads to only one answer: 16.

    Nonetheless, many readers (including my editor), equally adherent to what
    they regarded as the standard order of operations, strenuously insisted
    the right answer was 1. What was going on? After reading through the
    many comments on the article, I realized most of these respondents were
    using a different (and more sophisticated) convention than the elementary
    PEMDAS convention I had described in the article.

    In this more sophisticated convention, which is often used in
    algebra, implicit multiplication is given higher priority than explicit
    multiplication or explicit division, in which those operations are written
    explicitly with symbols like x * / or ÷. Under this more sophisticated
    convention, the implicit multiplication in 2(2 + 2) is given higher
    priority than the explicit division in 8÷2(2 + 2). In other words,
    2(2+2) should be evaluated first. Doing so yields 8÷2(2 + 2) = 8÷8 = 1.
    By the same rule, many commenters argued that the expression 8 ÷ 2(4)
    was not synonymous with 8÷2x4, because the parentheses demanded immediate
    resolution, thus giving 8÷8 = 1 again.

    This convention is very reasonable, and I agree that the answer is 1
    if we adhere to it. But it is not universally adopted.