Please solve 😩 9 ÷ 3(1 + 2)

[meaningfulmind]

 

[Dr.Peterson]

I assume you saw this somewhere and saw people give different answers.

The solution to this sort of problem is never to write ambiguous expressions, and not to take the bait when people ask about them.

Different people have different opinions about this sort of thing; some will say 9, and some (who I think are more reasonable) will say 1. Arguing about it gains nothing.

 

[meaningfulmind]

I only get the answer one from the two different ways to solve. Isn’t there literally one right answer? I’ve always thought math was black and white

 

[stapel]

I only get the answer one from the two different ways to solve. Isn’t there literally one right answer? I’ve always thought math was black and white

Yes, after an application of relevant rules, there can be only one answer. But, because the posted expression is ambiguous, we can't be sure which rules are being used. Therefore, people can arrive at two different answers, depending upon which rule(s) they have assumed were to be applied.

This is why one should avoid ambiguous expressions such as the one you've posted, and arguing about it won't solve the problem. Only a clarification of the intended meaning will help.

 

[lookagain]

I only get the answer one from the two different ways to solve. Isn’t there literally one right answer? I’ve always thought math was black and white

meaningfulmind, according to the Desmos online calculator, and the TI calculators, they calculate it as such

\(\displaystyle 9 \div 3(1 + 2) \ = \)

\(\displaystyle 9\div3(3) \ = \)

\(\displaystyle 3(3) \ = \)

\(\displaystyle 9 \)

 

[Dr.Peterson]

I only get the answer one from the two different ways to solve. Isn’t there literally one right answer? I’ve always thought math was black and white

The reason some people get 9 is that they have been taught to do multiplications and divisions from left to right, and follow that rule rigidly, unaware that in practice, many (if not most) users of algebra think of factors joined by juxtaposition as a single unit, effectively doing that multiplication first. So these people are following a different rule than you. Some authors explicitly teach "juxtaposition first"; but more, in my experience, just don't give examples like this, so students either follow what they were taught, or just do what feels right, when they see such an expression. (I don't know whether any textbooks explicitly teach that you should not make the distinction!)

Calculators, too, differ.

Even if a rule is taught, it is easy to interpret something like 1/2x as either (1/2)x, or 1/(2x), depending on what you are expecting. That's why it's best just to avoid writing anything like that. The link I included (whose author you'll recognize) explains this at greater length.

 

[mario99]

There are usually four types of people who encounter this type of expression. All of them agrees that:

[imath]9 \div 3(1 + 2) \ = 9\div3(3)[/imath]

The argument comes after that.

1
These people have multiplication and division have the same strength and they evaluate what comes first from the left. They will tell you the answer is [imath]9[/imath]. (Most of programmers.)

2
These people have a multiplication involving brackets [imath]n(n)[/imath] is stronger than normal multiplications [imath]n\times n \ \text{and} \ n*n[/imath] AND divisions [imath]n \div n \ \text{and} \ n / n[/imath]. They will tell you the answer is [imath]1[/imath]. (I worked in a laboratory and I was surprised they used this method.)

3
These people will ask you: Do you mean [imath]\displaystyle \frac{9}{3}(3)[/imath] or [imath]\displaystyle \frac{9}{3(3)}[/imath]? If you say that you don't know, don't be surprised to get 1 or 2.

4
These people will ask you: Do you mean [imath]\displaystyle \frac{9}{3}(3)[/imath] or [imath]\displaystyle \frac{9}{3(3)}[/imath]? If you say that you don't know, they will not answer you. They will tell you that the question is ambiguous and you have to provide the exact intended expression.

 

[lev888]

I only get the answer one from the two different ways to solve. Isn’t there literally one right answer? I’ve always thought math was black and white

Math is very much black and white. But a problem needs to satisfy certain requirements to be considered a _math_ problem.
If I write a math problem on a piece of paper and then erase 30% of it, is it still a math problem? How about a problem written in a language you don't know well?

 

[Otis]

9 ÷ 3(1 + 2)

When I see the ÷ operator used like that, then I interpret it as a fraction bar.

In other words, when an author provides no context to the contrary, I treat the expression the same as [9]/[3(1+2)].

 

[khansaheb]

9÷3(1+2) =9÷3(3)

If the "stated problem is:
9/3 * (1+2) then the answer is 3*3 = 9 ..........................No argument there.

If the "stated problem is:
9/{3 * (1+2)} then the answer is 9/9 = 1 ..........................No argument there.

If the problem is stated in "Neither" of those form (Like your problem is ) - then the problem is "non-sense" - like giving a problem to a Greek written Sanskrit.

 

[Steven G]

The answer is 9. Why would anyone here think otherwise.

 

[lookagain]

The answer is 9. Why would anyone here think otherwise.

Thumbs-down on your second sentence. I have already read the strong opinions of
certain others on here, so your comment of your second sentence does not follow
that you would have everyone align with you.

My choice of an answer could align with yours, but I would never write your second
sentence, given what I have already read of certain opinions elsewhere in this thread.

 

[khansaheb]

If the "stated problem is:
9/3 * (1+2) then the answer is 3*3 = 9 ..........................No argument there.

If the "stated problem is:
9/{3 * (1+2)} then the answer is 9/9 = 1 ..........................No argument there.

If the problem is stated in "Neither" of those form (Like your problem is ) - then the problem is "non-sense" - like giving a problem to a Greek written Sanskrit.

 

[Agent Smith]

I assume you saw this somewhere and saw people give different answers.

The solution to this sort of problem is never to write ambiguous expressions, and not to take the bait when people ask about them.

Different people have different opinions about this sort of thing; some will say 9, and some (who I think are more reasonable) will say 1. Arguing about it gains nothing.

Doktor, bullseye!!

It's a matter of convention, nothing to do with logic, except in that rules have to "make sense".