Simple BODMAS question including bracket expansion

Question

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.

16 is correct. We can place /, *, +,- , () in any order, multiple interpretations can be possible. In order to avoid confusion we agree upon the BODMAS rule. the proper way to write this is $$\frac{8}{2}\times(2+2)$$As division is a binay operator then it can only take 8,2 are as its operands — Sonal_sqrt, Jul 31 '19 at 07:03
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to. — José Carlos Santos, Jul 31 '19 at 07:03
Update: looks like it's a been answered here as an "ambiguous notation" - https://math.stackexchange.com/questions/33215/what-is-48÷293 — Jay Wick, Jul 31 '19 at 09:07
Thanks @HansLundmark, looks like it is answered there: it is ambiguous and this notation should not be used. Flagged it as dupe — Jay Wick, Aug 01 '19 at 00:02

score 1 · Answer 1 · answered Jul 31 '19 at 08:21

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.

score 0 · Answer 2 · answered Jul 31 '19 at 08:28

$ 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.

Simple BODMAS question including bracket expansion

2 Answers2