BODMAS riddle - which is correct?

Question

I fully understand the order of BODMAS - It's the order of operations in maths equations.

So lately this little puzzle/riddle has been going around on social media - [url=http://9gag.com/gag/ab0y1br?ref=fbp]Solve carefully - 9GAG[/url] . I understand that it's a play on grammar because they actually mean $5!$ as in the factorial.

The thing i notice is that some people argue that the answer is $-180$ and others argue that it's $120$ - for the simple adding and subtracting, not the factorial itself.

$$25-55+(85+65) =25-55+(150) =25-205 =-180.$$

Others state $$ 25-55+(85+65) =25-55+(150) =-55+150+25 =-55+175 =120.$$

Which is correct and why?

Thanks

Ps. I feel quite silly for asking this.

Answer 1

If you are just asking about $25-55+(85+65)$, then the correct answer should be $120$. Note that to get your other answer of $-180$, you would also need a negative sign in front of $(85+65)$; since there is only a single minus sign, the only term being subtracted off is $55$, so you can compute it as $$ 25-55+(85+65)$=25+150-55=175-55=120. $$

Answer 2

$$ 120 = 5! $$

is correct.

$$ 25-55+(150) \ne 25-205. $$

For that to be true you'd need another set of parentheses: $$ 25-(55+(150)) = 25-205. $$

Answer 3

For this particular example, you do not need the brackets since $a+b+(c+d)=a+b+c+d$. In our case, we can directly add and subtract the numbers. $$25-55+(85+65)=25-55+85+65=120=5!$$

The order of operations states to evaluate brackets first. In our case, the brackets are evaluated by performing addition, which is a associative. Thus, we can drop the brackets and add directly.