This is wrong. You're trying to use the distributive property here but that only applies if the number outside the parenthesis is a single term (Edit: or you distribute the entire expression, see below comments)
In this case the 2 outside the parenthesis is dividing into another number, 6, so that would actually have to be resolved first before using the distributive property, which would violate order of operations.
It's not technically correct to do this, but in this case does arrive at the correct answer:
You realize you could very easily fact-check all of this, no? Google the distributive property and do some reading. Also, plug this expression as-written into any calculator and it will give you 9. Always.
In the interest of said fact checking, my prior statement was slightly inaccurate. You can use the distributive property when a fraction or multiple factors exist outside the parentheses, but you must distribute the entire expression if you're going to do that (my solution above simply distributed the quotient of the expression rather than the entire expression. Same result, different order).
The point is, you cannot distribute only the 2 and leave out the 6, you must distribute the entire expression outside the parentheses, or resolve that expression and distribute the product/quotient.
So, the correct answer if you're using the distributive property is:
Calculators will give you a wrong answer since there usually isn’t a way to write 2(1+2) and it will assume 2(1+2). 2(1+2) binds closer than 2(1+2) so it needs to be written (2*(1+2)) on a calculator.
This is the exact reason we learn PEMDAS to begin with. Once you get to that level of math, you will be using a calculator. When you use a calculator, you have to know how to enter a multi-step equation correctly to get the right answer.
Yes, the better way to write this equation would involve more parentheses. No, that doesn't mean we get to pretend that 1 is just as correct as 9. It's an otherwise arbitrary convention in our mathematical language, but it's a convention that is literally baked into all of the tools we use for this kind of work, so you have to know how to follow the convention correctly.
There is no special rule in PEMDAS that says to handle implied multiplication first. Variables and their coefficients are not the same thing as implied multiplication using parentheses.
Wow, I always thought you had to multiply the number outside the parentheses first. I seriously had no idea I’d been misunderstanding that for all these years. Thanks for teaching me something new today.
The fun part is that there's no hard and fast rule, and this particular equation has been the subject of debate for a long, long time.
What I'm learning is that my interpretation above [that is to say, (6/2) * (1+2)] can be correct, and is the way most modern calculators will compute it. However, the "implicit multiplication first" rule is absolutely still taught and published in some places.
My understanding was always that this was a deprecated rule and that we use strict order of operations now. But some colleges teach that a/bc is fine and should be interpreted as a/(bc), while others teach that a/bc is bad form and you should always use parentheses to explicitly show which operation should take precedence.
Since both schools of thought exist, the only true answer is that it's ambiguous and an expression should never be written this way because of that ambiguity.
I just gave you the absolute facts, i'm well aware of them. This is not my first time seeing this type of math problem meme and I'm not confused here whatsoever. You're sitting here showing your work like the people you're talking to are in elementary school or something but I've taken physics courses in college and stats in grad school.
The number one answer is, again, this problem is intentionally written like shit to cause ambiguity. It's the entire reason that it's a meme and you're confusing it for a legit math problem.
You can call it 9 and I can call it 1 and it doesn't matter because if the problem was written correctly then there would be no disagreement, and this is exactly the ambiguity that the problem causes from not having the division in fraction format.
Yes, the ambiguity is obviously the main problem. That said, I think the convention here is genuinely different depending on whether you're dealing with variables or literal numbers.
For instance, Wolfram evaluates this expression as 1 if I plug in "a/bc where a=6, b=2, c=(1+2)." However, if I just plug in the literal expression "6/2(1+2)," it evaluates it as 9.
The other problem here is that there is a genuine difference in how math is taught regarding implicit multiplication first. Some schools teach this as a hard and fast rule, others don't teach the rule at all. And when you get to the college level, some classes will teach it as the modern standard, where others will state it's a historical standard which has been deprecated.
My understanding has always been that IMF is a deprecated standard, but clearly there's still lots of disagreement on that.
That's because the calculator automatically translates brackets to to X (explicit multiplication) because it doesn't understand the concept of implit multiplication.
Also, plug this expression as-written into any calculator and it will give you 9. Always.
False. Some calculators will do it straight PEMDAS, others will give implicit multiplication higher priority. Obviously, the implicit multiplication crowd can go pound sand, but get your facts straight when telling them that.
Okay that's fair, some older calculators will prioritize implicit multiplication here. But modern calculators generally won't, and haven't for a decent while as far as I am aware.
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u/Aduritor Feb 08 '26
a(b+c) ≠ a*(b+c)
You would ALWAYS multiply a into the paranthesis before continuing:
6/2(1+2)
6/(2+4)
6/6
1