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

by Gereltod   Last Updated August 14, 2019 06:20 AM

What is answer for 8 / 4 (4-2) = ?

My answer is 4. But some says it's 1. And arguing each others. They even using some calculators for prove them. Even those calculators showing both 1 and 4 as result. What should I tell to those who saying 1? Or my answer is wrong?

Answers 6

There is no right/wrong answer to the question because the question itself isn't well defined.

March 30, 2015 08:34 AM

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.

March 30, 2015 08:34 AM

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 $4$.

March 30, 2015 08:35 AM

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.

March 30, 2015 08:38 AM

Depending how your read $$8/4~(4-2)$$ can be $$\frac 84 \times (4-2)=4$$ or $$\frac 8{4\times(4-2)}=1$$ As said in answers and comments, the notation you use is more than ambiguous. Use brackets to enclose the expressions.

Claude Leibovici
Claude Leibovici
March 30, 2015 08:41 AM

I guess the most likely answer is $4$. Almost all programming languages (and some mathematiciens) would agree that

  • multiplication and division are at the same level of operator precedence

  • things on the same level are evaluated from left to right

so $8/4 (4-2)$ is a short hand for $8/4 \cdot (4-2)$, which is evaluated from left to right $(8/4)\cdot (4-2)=2*2=4$

to claim that it should be $1$ is to claim that $$ 8/4 (4-2) = 8/(4\cdot (4-2)) $$ which would be a strange convention.

Of course this problem is boring: in case of a tiny hint of a small possiblity of ambiguity use brackets.

March 30, 2015 08:46 AM

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