Infamous Internet Math Problem

[mrhtutoring]

Here's another take on the topic.

[SB-Boi]

Perfect example of why you NEVER use the division symbol

[tom_something]

But let's also appreciate that in industry, the "division symbol" pretty much never comes up. There's right, and then there's unambiguous. Professional settings don't use notation that leave things to chance.

Expressions are only written this way to cause disagreements on the internet.

[xr_xharprazoraxtra]

This is the vague part when it comes to syntax, to me :
K / a(b) ≠ K / a * b
Because
K / a(b) = K / (ab)
K / a * b = (K/a) * b

Quick example :
K / (fa + fb + fc) = K / f(a+b+c)

But anyway, one rule : use enough parentheses to make the order and meaning clear enough to avoid confusion.

[AliceSkurpski-retv]

Rule states parenthesis first. Just because you want to separate 3(3) into 3 x (3) doesn't mean it isn't a part of the parenthesid portion. Answer is 1.

[Fireatank]

We learned a catch phrade when I was young to figure the order of operations.... BODMAS
Brackets
Of .... ie 1/3 of 9
Division
Multiplication
Addition
Subtraction
Worked then, works now.
You're Welcome.

[SusiloAdi]

Division symbol is so good for dividing people.. 😂

[Robin-fgmo]

Everyone thinks 2+1 is in denominator

[arjay]

Solid reminder that distribution = multiplication in the PEMDAS model

[virtuoz_virti]

9/3(2+1)= 9/ (6+3)= 9/9 =1 the parentheses have priority and you need to get rid of them first. when there is a number in front of the parentheses without a sign, then it is calculated as multiplication.and those who write that the number 3 stands alone in parentheses have no idea. The number alone cannot stand in parentheses. That's a simple rule.

[sparshsharma]

The reason why usage of parentheses is crucial in simplification of expressions.

[davideesposito]

I met a few people don't care about parantesis and just do the operations from left to right, 9 : 3 * (2+1) = 3 * 2 + 1 = 6 + 1 = 7

[Monkey_Luffy]

Robert Troncoso

Jake Jacobs PEMDAS:
-Parenthesis
-Exponents
-Multiplication & Division (at the same time), from left to right
-Addition & Subtraction (at the same time), from left to right
9/3(2+1)=
9/3(3)=
3(3)=
9

[john]

I haven't had a math class in decades but I can't stop watching these videos!

[mr.fahrenheit]

Others here thougt that the teacher didnt use BODMAS/PEMDAS. Actually he used it, many of us here just didnt know that there is Left-to-Right rule inside PEMDAS and BODMAS. Im already sick and tired of this dumb society!

[beru]

All one need to do is acquaint oneself with the international standards governing this precise topic: ISO 80000-2. "If there is any risk of confusion, parentheses should always be inserted." (By the way ISO 80000-2.9-6 also states that "The symbol ÷ should not be used.")
Also NIST's "Guide for the Use of the International System of Units (SI)" acknowedges that there is an AMBIGUITY where those who believe in the left to right rule would see no problems, and advices to use parentheses. I so wonder who is right here, NIST or those who belive in the left to right rule. (A small hint: the S stands for "standards".)
Oh, and what would 2^2^2^2 be, you believers in the left to right rule?
256 or 65536?
This is why there is no INTERNATIONAL consensus on that left to right-rule.
ISO says use parentheses. NIST also. And they explain why.
I guess many universities have style guides governing this. But it is NOT an international ageement.
Also: Many tables for specific heat have the units J/gK or kJ/kgK NOT J/(gK) or kJ/(kgK) or J×g^-1×K^-1 or kJ×kg^-1×K^-1.
The explanation is of course not that the publishers of these tables are unaware of the left to right-rule but rather that no such rule exists in INTERNATIONALLY agreed upon standards.

[RedGallardo]

That's an incorrect way of writing an equation. Because you need to strictly define what's in divisor and what's in dividend. We don't know if they meant 9\3 or 9\(3(2+1)). Always use the line. And always have only 1 line per 1 dividend and 1 divisor. No towers, no "divide" sign. It's from elementary school where kids are taught simple equations of 2 numbers.

It's not about the order, division by x is multiplication by 1\x. It can go in any order. 9\3 = 9 x 1\3 = 1\3 x 9. So the only problem is defining the divisor.

[MrMisticZ]

That is true for arithmetic. But in algebra 3(3) is treated differently from 3×(3).

Same way 2X is not the same as 2×X, 3(3) will be treated as one uniform number and not an equasion.
Compare 2÷2X vs 2÷2×X, and don't forget that 2X is also often written as X(1+2÷2) or w/e else


This is also why on some (generic) calculators you get an answer of 9 and in others (scientific calculators) you get 1 (unless you write × before parenthesis, then the answer will be 9 in both cases).

[zwivhuyamavhidula]

The answer is 1, we can't argue this, 9÷3(3) = 1 you have to deal with the bracket 1st every if you try to expand it like what you did 9÷3x(3) =1 because if you start by dividing you are ignoring the bracket which is wrong.. also write the problem this way, 9/3(3) if you are confused

[aucourant]

When I was in school in the 1950s, we were taught that the brackets were put there for a reason. The number outside (and touching the bracket) was multiplied by the numbers inside the brackets and was to be carried out as a separate and self-contained function. He re-wrote the function 3(3) = 3X(3), whereas we were taught that 3(3) =(3X3). So we would have got 1 as the answer. The way we were taught makes more logical sense.