can you solve it?

9 

7

9

4.5

Hmm, I’m going to say with 70% confidence it is anywhere from 2 to 2.4 billion.

 

but actually it’s 

Spoiler

9.  Obviously 

 

9

9

nope 

Problems written this way are intentionally designed to create arguments.

 

It's 1, because the implicit multiplication of 2(1+2) with the 2 directly adjacent to the parentheses takes priority over the division sign despite multiplication and division traditionally having equal priority under PEMDAS. But it's also 9, because implicit multiplication isn't universally agreed to take priority - many modern calculators (but not all) would evaluate this as 9.

 

In a serious textbook situation, either the answer would be 1 or this would be written as a fraction instead of with the ÷ symbol. They avoid this form because of the ambiguity.

 

6 minutes ago, Cruel Summer said:

Problems written this way are intentionally designed to create arguments.

 

It's 1, because the implicit multiplication of 2(1+2) with the 2 directly adjacent to the parentheses takes priority over the division sign despite multiplication and division traditionally having equal priority under PEMDAS. But it's also 9, because implicit multiplication isn't universally agreed to take priority - many modern calculators (but not all) would evaluate this as 9.

 

In a serious textbook situation, either the answer would be 1 or this would be written as a fraction instead of with the ÷ symbol. They avoid this form because of the ambiguity.

I'm confused by this understanding of "implicit multiplication priority".  I'm actually not sure why it matters.  The question is asking 6*(1/2)*(1+2).  [Note division and multiplication are identical functions so writing it out like this is the same to the above]  It does not matter which one you multiply first. You get the same answer.  

16 minutes ago, Cruel Summer said:

Problems written this way are intentionally designed to create arguments.

 

It's 1, because the implicit multiplication of 2(1+2) with the 2 directly adjacent to the parentheses takes priority over the division sign despite multiplication and division traditionally having equal priority under PEMDAS. But it's also 9, because implicit multiplication isn't universally agreed to take priority - many modern calculators (but not all) would evaluate this as 9.

 

In a serious textbook situation, either the answer would be 1 or this would be written as a fraction instead of with the ÷ symbol. They avoid this form because of the ambiguity.

Mathematically, in general, we first have to evaluate the parentheses. In programing languages and calculators after the parentheses are evaluated it continues from "there" in terms of multiplication. (Speaking only of the example in the OP)

 

So we will end up with 6/6 which is 1.

 

Those type of problems, written in this confusing form, are not in any "serious" math textbooks unless it's related to programming and computers.

19 minutes ago, byzantium said:

I'm confused by this understanding of "implicit multiplication priority".  I'm actually not sure why it matters.  The question is asking 6*(1/2)*(1+2).  [Note division and multiplication are identical functions so writing it out like this is the same to the above]  It does not matter which one you multiply first. You get the same answer.  

This is why I mentioned that this would never be written this way in a serious setting. The ambiguity is the point - the fact that you see it differently than I see it is the point. I see it as a fraction with 6 as the numerator and 2(1+2), all together, as the denominator. You don't. Neither of us is really right or wrong because it 1) depends on what we learned from likely entirely different sources and 2) is more a question of ambiguous notation and style than of actual simple mathematics that we both already understand.

 

Here's someone who is of the opinion that they'd evaluate it simply left to right, as you would, who explains nicely why it's ambiguous and should never actually be written that way in a serious context:

 

https://www.themathdoctors.org/order-of-operations-implicit-multiplication/

9

Let’s go back to school, ATRL

the image isnt even loading but it's probably one of those dumb ambiguous problems. Stop being a [redacted] and use fractions

with PEMDAS it's 1

[Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).]

Edited June 3, 20232 yr by Vixen Eyes
PEMDAS

This is why fractions exist. No one math would write an equation like that down like this

its 1 

It's 1. Everyone who said 9 needs to go back to school?

As far as I’m concerned it’s 9 but this isn’t really a question of mathematical ability so much as it is a question of what version of PEMDAS you were taught

 

Getting heated over this is silly

1

4 hours ago, Aristotle said:

Mathematically, in general, we first have to evaluate the parentheses. In programing languages and calculators after the parentheses are evaluated it continues from "there" in terms of multiplication. (Speaking only of the example in the OP)

 

So we will end up with 6/6 which is 1.

 

Those type of problems, written in this confusing form, are not in any "serious" math textbooks unless it's related to programming and computers.

Programming languages would output 9. You’d have to add in additional parentheses to get it to output 1.

 

OT: The answer is 9.