6/2 (1+2) had the world stumped but we finally have an answer! #shorts #maths #mathstricks

[gunthegoldminer]

There are 2 main reasons why people get 1

1. They think parenthesis takes priority no matter what. In reality, parenthesis no longer serves a purpose once everything inside it is at its simplest form.
2. Some people think that multiplication takes priority over division when in reality they have the same amount of priority. Meaning its from left to right instead of a specific order.

[allozovsky]

From Quora: “When writing mathematical formulas, what you are trying to do is _communicate._ That means that you should make it easy for your reader to understand what you’re trying to say“.

[davidduncan]

I would have to disagree upon PEMDAS being wrong. The problem we have is evaluating 6/2(1+2), which can also be written as 6÷2(1+2), 6÷2×(1+2) or 6/2×(1+2). Either way, it's still the same problem that we are arguing over. Of course, we can all agree that we take care of the parenthesis first, so 6/2(1+2) turns into 6/2(3). We basically have 6/2×3, which means we have a division and a multiplication to deal with. If both of these were multiplication, we would be evaluating from left to right. My side of the argument why we sometimes do division before multiplication is based on the fact that division is literally another form of multiplication. When you divide, you are multiplying times the reciprocal fraction of the number that is shown. 6/2 is the same as 6×(1/2). 6÷2 in fraction form is this: 6/1×1/2. When dividing in fraction form, we keep the first fraction, change the opperation to multiplication, and flip the second fraction. We can cancel out the 2 and reduce the 6 to 3, so we have 3/1×1/1, which we can simplify down to just 3, so we have third grade basic multiplication: 3×3=9, therefore, 6/2(1+2)=9. Note that the parenthesis is only grouping the 1+2 and nothing else, therefore, when we see 6/2(3), we are not multiplying 2×3 before taking care of the division. Instead, we are multiplying 6/2×3. 6/2 is a single factor in this multiplication that can be simplified as 3, therefore giving us 9 as the product. If you want to divide six by everything else to get one as the quotient, you would have to add more parenthesis or brackets to group everything together as the denominator like this: 6/[2(1+2)]. In this case, I would start with addition and work my way out like this: 6/[2(1+2)], 6/[2(3)], 6/6, which equals 1. Be careful with these problems because 6/2(1+2) does not equal 6/[2(1+2)]. We can also look at 6/2(1+2) this way: multiply 6/2×1, then 6/2×2 and add these products. Let's check to see if 6/2 can be simplified...yes, it can! 6/2=3, therefore we can multiply 3×1, which equals 3 and 3×2, which equals 6. Add these numbers up and we get 9. I actually would agree with your evaluation of juxtaposition multiplication except for this one thing: when we see 6/2(1+2), it's the fraction of 6/2 that we need to multiply, not the integer of 2 before doing division.

[Valerius]

It's that people think division and fractions operators (÷ and /) are identical. When using a fraction you are splitting your expression into a numerator and denominator which groups the order of operations in a way like brackets. When only using ÷ it doesn't do this. This is where everyone is confused. So 6÷2(1+2) is all in the numerator and 6/2(1+2) has 6 in the numerator and 2(1+2) in the denominator. One of these gives the answer 9 and one of them gives the answer 1.

[c.jishnu]

As a professional mathematician and a professional philosopher(both self proclaimed(i am 13)), the question is wrong as having two answers is failure at the side of the examinar and not the atudent.

[HardKnght]

Its 1. The multiplication sign has been removed between the 2 and the brackets the juxtaposition of the 2 to the brackets implies this is one term. 6÷(2(1+2)). If the multiplication sign was left explicitly in place. 6÷2×(1+2) then the answer is 9.

[mr.getrighhttt]

Multiplication by juxtaposition takes precedence over division. This has been the standard for a long time by engineers, scientists, and physicists. PEMDAS is only used in America but in reality PEJMDAS is the actual acronym used across the world, and even for some scientific calculators like modern day Calcios.

[bakonandsonicfamily]

Well, here in Vietnam, from Secondary education forward, we no longer have to put a times sign? “x” to refer to the equation as a multiplication. For example, (a+b)c is (a+b)xc, so my answer is 9 :)

[GanonTEK]

100%
It's ambiguous notation as there are two common interpretations for juxtaposition.

Academically, juxtaposition implies grouping and multiplication (1).

Literally/programming-wise, juxtaposition implies multiplication only (9)

The division symbol doesn't matter. It's ambiguous either way with ÷ or /.

÷ and / are synonymous in most cases.
Both are one line division operators.
Not fraction notation.
½ and
1
--
2
are fraction operators. Two different symbols to ÷ and /.

Even over in America, the American Mathematical Society stated it was ambiguous notation and modern international standards like ISO-80000-1 mentions about writing division on one line with multiplication or division directly after and that brackets are required to remove ambiguity.

Even scientific calculators don't agree on one answer.

It's obvious it's ambiguous notation but there seems to be a lot of stubborn people out there wanting their opinion to be the only correct one, which won't happen as their opinion doesn't change the evidence of what's in use.

[lucasbusselen]

There are rules you have to follow and according to the rules 2( 2+1) = 2×(2+1) and the answer to the question is 9

[qdycvfc]

Your first statement sets the wrong tone. Math doesn’t have opinions . It has proofs, theorems, hypothesis, and rules. One rule being conveniently ignored is that parens come first and simply performing the operation contained within the parens does not clear the parens. If the expression was: 6/2(3), what would be the first operation performed? Clear the parens to get 6/6. There should be no confusion!

[pandu]

Answer is 1
It's just simple arithmetic problem where we have to give first preference to bracket
a÷b(c+d) = a÷(bc+cd)
So, 6÷2(1+2) = 6÷2(3) =6÷6=1
Mathematicians always write like this

[andrewmcmillan]

Wrong. This problem takes the form of a/b*c; that's why the Commutative Property works. We can flip the order of the operands and still maintain the same solution.

[JackieRodriguez-uigp]

Let me tell you why I know it's 9 1+2=3 then we have 23 so we do 23+23=46 now we add 6 bc it's there and that's 52 and then we add 2 bc it's there it's 54 and 54 ÷ 6 = 9 so that's how I got 9

[meiter]

If you got 4/2x you do the 2x part first right? Then why does it have to be different with 2(1+2)
Answer is 1.

[andrewmcmillan]

The problem is separated by multiplication

[AmritGrewal]

Because it doesn’t use brackets properly.

[ogostrich]

This guy is trying to say that division comes before parenthesis lmao

[kmusic]

Pemdas.... 9.. i dont get what so confusing..growing up. We wouldnt even give this equation a second thought...ir did they chnage math over the 3 decades

[andrewmcmillan]

This problem is just like saying

2 × 3 = 6 or 3 × 2 = 6