I am trying to understand what is seemingly basic arithmetic that is causing a divide amongst my colleagues
$$ 8÷2(2+2) $$
To me respecting the order of operations it would appear the answer is 16 while others say it is 1. The latter value is coming from a colleague is quoting the distributive property having implicit brackets and thus should be 8÷2×(2+2).
Apologies if this is too simple of a question for this exchange.
On
$ 8 ÷ 2 (2 + 2) $
Considering the use of BODMAS, lets begin by evaluating the arithmetic operation in the Bracket (B), i.e.
$ 8 ÷ 2 (2 + 2) $ $ = 8 ÷ 2 × 4 $
After that, consider Division (D), i.e.
$ 8 ÷ 2 × 4 $ $ = 4 × 4 $
Finally, we end it via Multiplication (M), i.e.
$ 4 × 4 $ = $ 16 $ ...Ans.
The answer is 16.
$8\div2(2+2)=8\div2\times(2+2)=8\div2\times4$. When there are concatenated $\div$ and $\times$ the calculation should just be run from left to right. So, $8\div2\times4=4\times4=16$
Even though it's a handy mnemonic, I'm not a fan of BODMAS because, if you follow it to the letter, then $8-2+4=2$, which is incorrect.
Your colleague is incorrect to say that there are implicit brackets. It might be that they are thinking of something like $8+2(2+2)$, where the expansion has to happen first, but only because $\times$ has to happen before $+$. This could be seen as implying brackets, something like $8+(2(2+2))$, but the extra brackets are unnecessary.