• Queue
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    9 months ago

    For anyone like me who has math as their worst subject: PEMDAS.

    PEMDAS is an acronym used to mention the order of operations to be followed while solving expressions having multiple operations. PEMDAS stands for P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction.

    So we gotta do it in the proper order. And remember, if the number is written like 2(3) then its multiplication, as if it was written 2 x 3 or 2 * 3.

    So we read 8/2(2+2) and need to do the following;

    • Read the Parentheses of (2 + 2) and follow the order of operations within them, which gets us 4.
    • Then we do 2(4) which is the same as 2 x 4 which is 8
    • 8 / 8 is 1.

    The answer is 1. The old calculator is correct, the phone app which has ads backed into it for a thing that all computers were invented to do is inaccurate.

    • a_fine_hound@lemmy.world
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      1 year ago

      Well that’s just wrong… Multiplication and division have equal priorities so they are done from left to right. So: 8 / 2 * (2 + 2)=8 / 2 * 4=4 * 4=16

        • Correct! 2(2+2) is a single term - subject to The Distributive Law - and 2x(2+2) is 2 terms. Those who added a multiply sign there have effectively flipped the (2+2) from being in the denominator to being in the numerator, hence the wrong answer.

          But it’s not called “implicit multiplication” - it’s Terms and/or The Distributive Law which applies (and they’re 2 separate rules, so you cannot lump them together as a single rule).

      • nutcase2690@lemmy.dbzer0.com
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        1 year ago

        Not quite, pemdas can go either from the left or right (as long as you are consistent) and division is the same priority as multiplication because dividing by something is equal to multiplying by the inverse of that thing… same as subtraction being just addition but you flip the sign.

        8×1/2=8/2 1-1=1+(-1)

        The result is 16 if you rewrite the problem with this in mind: 8÷2(2+2)=8×(1/2)×(2+2)

        • Omega_Jimes@lemmy.ca
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          1 year ago

          I’ve never had anyone tell me operations with the same priority can be done either way, it’s always been left to right.

          • nutcase2690@lemmy.dbzer0.com
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            1 year ago

            I’ve always heard it that way too but I think it is for consistency with students, imo Logically, if you are looking at division = multiplying by inverse and subtraction = adding the negative, you should be able to do it both ways. Addition and multiplication are both associative, so we can do 1+2+3 = (1+2)+3 = 1+(2+3) and get the same answer.

            • ReveredOxygen@sh.itjust.works
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              1 year ago

              But subtraction and division are not associative. Any time you work on paper, 2 - 2 - 2 would equal -2. That is, (2-2)-2=0-2=-2. If you evaluate right to left, you get 2-2-2=2-(2-2)=2-0=2

              • nutcase2690@lemmy.dbzer0.com
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                1 year ago

                Correct, subtraction and division are not associative. However, what is subtraction if not adding the opposite of a number? Or division if not multiplying the inverse? And addition and multiplication are associative.

                2-2-2 can be written as 2 + (-2) + (-2) which would equal -2 no matter if you solve left to right, or right to left.

                In your example with the formula from right to left, distributing the negative sign reveals that the base equation was changed, so it makes sense that you saw a different answer.

                2 - (2 - 2) = 2 + ((-2) + 2) = 2

          • I’ve never had anyone tell me operations with the same priority can be done either way, it’s always been left to right

            It’s left to right within each operator. You can do multiplication first and division next, or the other way around, as long as you do each operator left to right. Having said that, you also can do the whole group of equal precedence operators left to right - because you’re still preserving left to right for each of the two operators - so you can do multiplication and division left to right at the same time, because they have equal precedence.

            Having said that, it’s an actual rule for division, but optional for the rest. The actual rule is you have to preserve left-associativity - i.e. a number is associated with the sign to the left of it - and going left to right is an easy way to do that.

    • CaptDust@sh.itjust.works
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      1 year ago

      Uh… no the 1 is wrong? Division and multiplication have the same precedence, so the correct order is to evaluate from left to right, resulting in 16.

    • nutcase2690@lemmy.dbzer0.com
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      1 year ago

      The problem with this is that the division symbol is not an accurate representation of the intended meaning. Division is usually written in fractions which has an implied set of parenthesis, and is the same priority as multiplication. This is because dividing by a number is the same as multiplying by the inverse, same as subtracting is adding the negative of a number.

      8/2(2+2) could be rewritten as 8×1/2×(2+2) or (8×(2+2))/2 which both resolve into 16.

      • Zagorath@aussie.zone
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        1 year ago

        You left out the way it can be rewritten which most mathematicians would actually use, which is 8/(2(2+2)), which resolves to 1.

      • Division is usually written in fractions

        Division and fractions aren’t the same thing.

        fractions which has an implied set of parenthesis

        Fractions are explicitly Terms. Terms are separated by operators (such as division) and joined by grouping symbols (such as a fraction bar), so 1÷2 is 2 terms, but ½ is 1 term.

        8/2(2+2) could be rewritten as 8×1/2×(2+2)

        No, it can’t. 2(2+2) is 1 term, in the denominator. When you added the multiply you broke it into 2 terms, and sent the (2+2) into the numerator, thus leading to a different answer. 8/2(2+2)=1.

    • amtwon@lemmy.world
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      1 year ago

      not to be That Guy, but the phone is actually correct… multiplication and division have the same precedence, so 8 / 2 * 4 should give the same result as 8 * 4 / 2, ie 16

    • agamemnonymous@sh.itjust.works
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      1 year ago

      P E M D A S

      vs

      P E M/D A/S

      The latter is correct, Multiplication/Division, and Addition/Subtraction each evaluate left to right (when not made unambiguous by Parentheses). I.e., 6÷2×3 = 9, not 1. That said, writing the expression in a way that leaves ambiguity is bad practice. Always use parentheses to group operations when ambiguity might arise.

    • hallettj@beehaw.org
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      1 year ago

      The problem is that the way PEMDAS is usually taught multiplication and division are supposed to have equal precedence. The acronym makes it look like multiplication comes before division, but you’re supposed to read MD and as one step. (The same goes for addition and subtraction so AS is also supposed to be one step.) It this example the division is left of the multiplication so because they have equal precedence (according to PEMDAS) the division applies first.

      IMO it’s bad acronym design. It would be easier if multiplication did come before division because that is how everyone intuitively reads the acronym.

      Maybe it should be PE(M/D)(A/S). But that version is tricky to pronounce. Or maybe there shouldn’t be an acronym at all.

    • Cornelius_Wangenheim@lemmy.world
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      1 year ago

      Ignore the idiots telling you you’re wrong. Everyone with a degree in math, science or engineering makes a distinction between implicit and explicit multiplication and gives implicit multiplication priority.

    • Coreidan@lemmy.world
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      1 year ago

      PEMDAS evaluated from left to right. If you followed that you’d get 16. 1 is ignoring left to right.

    • Turns out I’m wrong, but I haven’t been told how or why. I’m willing to learn if people actually tell me

      Well, I don’t know what you said originally, so I don’t know what it is you were told was wrong - 1 or 16? 😂 The correct answer is 1.

      Anyhow, I have an order of operations thread which covers literally everything there is to know about it (including covering all the common mistakes and false claims made by some). It includes textbook references, historical Maths documents, worked examples, proofs, memes, the works! I’m a high school Maths teacher/tutor - I’ve taught this topic many times.