8 / 4 (4-2) = ? What is answer? [duplicate]

Solution 1:

Don't get insulted by my next sentence, as I promise I elaborate after writing it:

This is a stupid question.

You are not stupid for asking it, and I guess it must be asked sometime, but I hope the continuation of my answer explains how irrelevant and pointless questions like these are.

The "perfect answer" to this question depends completely on the order of operation you have in mind, and obviously, the first thing to do is to perform the subtraction (because it is in brackets), meaning $$8/4(4-2)=8/4*2.$$

The next step is where it gets weird. Using the incredibly annoying PEMDAS rule, you need to first perform multiplication, then division, so $$8/4*2=8/(4*2)=1.$$

However, that's if you went to an American school. If you went to school in Slovenia (central Europe), you were taught that division is equivalent to multiplication, so you would get $$8/4*2=(8/4)*2=4.$$

In the end, the answer is completely ambiguous and depends on the conventions you were taught.

Now, my main point:

You may well ask why this question is "stupid" in my opinion. I mean, why would it be stupid just because the answer is "depending on convention"?

Well, the point is that knowing the answer to this question is completely meaningless. Even when you know the answer, you also know that, since conventions differ, you will in future use parentheses to make sure your meaning gets across.

The only true purpose of questions like this is to stir up "controversy", and many schools waste hours and hours of lessons to imprint either PEMDAS or some other rule into the skull of young kids. The result is that 10 year olds, instead of being excited about mathematics, end up thinking that mathematics is an algorithmic process in which you perform tasks a robot can perform much faster, and the result of these tasks is some number that the teacher then grades.

Then, you encounter someone that was taught a different set of conventions, and you find a problem (like the one here) in which the two conventions yield different results, and often times, people then conclude Huh, those silly mathematicians, they can't even decide on the rules they preach.

The end result of questions like this, therefore, is that mathematics gets a bad rep.

Solution 2:

This all comes down to your conventions. If your conventions dictate that $8/4(4-2)$ is shorthand for $(8/4)(4-2)$, then it equals $4$. If you they dictate that $8/4(4-2)$ is shorthand for $8/(4(4-2))$ then it equals $1$. As a general rule, if something looks ambiguous, don't write it without adding in some brackets to help the reader.

By the way, there are systems of rules that disambiguate every such expression; some programming languages implement such things. However, in my opinion, its best not to leverage these kinds of "forced disambiguation conventions." You want to be writing for the reader, not against them.

Solution 3:

It is not clear what you mean with the expression $8\ /\ 4\ (4-2)$. Do you mean: $\frac{8}{4(4-2)}$ or $\frac{8}{4}\cdot (4-2)$? The first expression is equal to $1$ and the second equal to $4$.