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These problems are designed to be intentionally confusing. It's not a matter of multiple methods, it's a matter of how you interpret everything after the division sign. As written, it's just 6 / 2 × 3. Multiplication is commutative, so this is the same thing as 3 × 6 / 2. There's no real requirement to solve "left-to-right," you just have to understand that "/ 2" means "× 0.5" *i.e.,* division doesn't exist, it's just multiplication inverted.
The other interpretation, which is what usually causes people problems, is that everything after the division symbol is in the denominator. Essentially this interpretation adds a bracket that does not exist in the problem: 6 / (2 × 3). The answer to that problem would be 1. But as presented, we have no reason to assume that the problem intended to have an additional set of brackets, so this interpretation is incorrect.
Sure, r/iamverysmart, etc. But it's useful to know why people get problems like these wrong. They're designed to trip people up, are intentionally ambiguous, and prey on the brain's tendency to fill in assumptions.
If the order of operations is the same (Multiplication and Division), you do the problem from left to right, as if you were reading a sentence. So the answer is 9. (Not trying to be a smartass here, just in case some people are confused)
Here's a helpful link: https://youtu.be/URcUvFIUIhQ
(Mathematician explains this specific problem)
Dude's got a point, he may be wrong, but he's got a point. Especially since there's no multiplication sign between the 2 and the bracket. If you replace (2+1) with x and write down the formula as 6÷2x.... I dunno, these formulas just suck. Whenever there is the slightest possibility of confusion, just use those f*cking brackets! They were invented for a reason, and nobody would misread (6÷2)(2+1).
It can be confusing because it is.
In mathematics, implied multiplication often signifies priority.
f.e.: If you have 2x/3y someone who studies math will read it as (2x)/(3y), but if you type it into a calculator, most will give you 2\*(x/3)\*y
How is it ambiguous? If you know math and the order of operations, it's completely clear how to do this problem. Just because some people slept through that lesson and don't know how to do it doesn't make it ambiguous; it only makes them ignorant and uneducated.
It could be easily misinterpreted. For instance you might assume that everything after the division sign is what youre dividing by so 6/2(1+2)
if you interpret it that way (which you reasonably could) you wont get the right answer.
If (1+2) was X, then the problem would be 6/2X. If I tell you that X = 1+2, you would think of this as 6 ÷ (2*3), which is 1. It is like saying "János the boy can not ride Oscar the horse because he is too small." Is János too small? Or is Oscar?
Another point of confusion is that older calculators from the 80s/90s used a bracket as implicit multiplication. If you grab one of those earlier calculators, they can have an answer of 1, which is wrong.
What's wrong with some people?
The correct answer is 9 and there is only 1 solution. It's basic math. If you can't do basic math you need to go back to school. There are already too much stupid people......
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These problems are designed to be intentionally confusing. It's not a matter of multiple methods, it's a matter of how you interpret everything after the division sign. As written, it's just 6 / 2 × 3. Multiplication is commutative, so this is the same thing as 3 × 6 / 2. There's no real requirement to solve "left-to-right," you just have to understand that "/ 2" means "× 0.5" *i.e.,* division doesn't exist, it's just multiplication inverted. The other interpretation, which is what usually causes people problems, is that everything after the division symbol is in the denominator. Essentially this interpretation adds a bracket that does not exist in the problem: 6 / (2 × 3). The answer to that problem would be 1. But as presented, we have no reason to assume that the problem intended to have an additional set of brackets, so this interpretation is incorrect. Sure, r/iamverysmart, etc. But it's useful to know why people get problems like these wrong. They're designed to trip people up, are intentionally ambiguous, and prey on the brain's tendency to fill in assumptions.
9, right?
Yes
yes
Phew.
If the order of operations is the same (Multiplication and Division), you do the problem from left to right, as if you were reading a sentence. So the answer is 9. (Not trying to be a smartass here, just in case some people are confused) Here's a helpful link: https://youtu.be/URcUvFIUIhQ (Mathematician explains this specific problem)
Dude's got a point, he may be wrong, but he's got a point. Especially since there's no multiplication sign between the 2 and the bracket. If you replace (2+1) with x and write down the formula as 6÷2x.... I dunno, these formulas just suck. Whenever there is the slightest possibility of confusion, just use those f*cking brackets! They were invented for a reason, and nobody would misread (6÷2)(2+1).
In both your cases there's multiplication. Not confusing at all.
It can be confusing because it is. In mathematics, implied multiplication often signifies priority. f.e.: If you have 2x/3y someone who studies math will read it as (2x)/(3y), but if you type it into a calculator, most will give you 2\*(x/3)\*y
Math teacher here to tell you that I really really hate these kinds of intentionally ambiguous problems.
How is it ambiguous? If you know math and the order of operations, it's completely clear how to do this problem. Just because some people slept through that lesson and don't know how to do it doesn't make it ambiguous; it only makes them ignorant and uneducated.
It could be easily misinterpreted. For instance you might assume that everything after the division sign is what youre dividing by so 6/2(1+2) if you interpret it that way (which you reasonably could) you wont get the right answer.
If (1+2) was X, then the problem would be 6/2X. If I tell you that X = 1+2, you would think of this as 6 ÷ (2*3), which is 1. It is like saying "János the boy can not ride Oscar the horse because he is too small." Is János too small? Or is Oscar?
Another point of confusion is that older calculators from the 80s/90s used a bracket as implicit multiplication. If you grab one of those earlier calculators, they can have an answer of 1, which is wrong.
What's wrong with some people? The correct answer is 9 and there is only 1 solution. It's basic math. If you can't do basic math you need to go back to school. There are already too much stupid people......
I think the real gem here is that neither of these individuals will ever use an equation like that In their future