Bedlam with BODMAS and BEDMAS

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Suppose you have this calculation:

One third of 3^2 + 1

Depending on the order in which you do the operations, you could get either 2 or 4 as answer. My intuition tells me you should get 4, i.e. if we combine the BODMAS and BEDMAS rules, we should get BEODMAS, not BOEDMAS.

Any comments from our fine mathematical minds here?

As it stands, the result is 10/3. That’s because the wordy part of the question enjoys the lowest priority, and the question is not (32)/3+1 = 4, but instead (32+1)/3 = (9+1)/3 = 10/3, or 3.333…

I don’t see how you can get 2. Even 9 is more likely: (32+1)/3 = 27/3 = 9.

'Luthon64

And if I rephrase:

1/3 of 3^2 +1 ?

What do we get now?

In short, BODMAS and BEDMAS seem to be in potential conflict. How do we resolve the conflict? What gets precedence, "of" or the exponent? Is it BEODMAS or BOEDMAS? Or neither, and if so, what then?

What gets precedence, "of" or the exponent?

The exponent. "Of" is the same as "multiply with what follows".

1/3 of 3^2 +1 = ⅓ x (32 +1) = 10/3

r.

The mathematical/arithmetical formulations always take precedence over the worded parts. That’s the way I’ve both seen it treated and treated it myself. Thus, “1/3 of 3^2 +1” is still “1/3×(3^2 +1)”, as before.

Any mathematician worth their salt would in any case carefully avoid such potential ambiguities.

'Luthon64

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