Viral Math Problem

New York Post ^ | August 1, 2019 | Frank Miles

[Renkluaf]

“8÷2(2+2).” Can you solve this math problem? The equation went viral online this week on Twitter causing major confusion over the right answer. Mathematicians and physicists went nuts about it. Mike Breen, the Public Awareness Officer for the American Mathematical Society, told popular Mechanics: “The way it’s written, it’s ambiguous. In math, a lot of times there are ambiguities. Mathematicians try to make rules as precise as possible.” Depending on where in the world you learned math, as Mashable reported, determines how you can solve the problem.

[HartleyMBaldwin]

I’m a geologist. DON’T call me an engineer, please!

[central_va]

c = 3
o = 15
v = 22
f = 6
e = 5
f = 6
e = 5
--------
62

[rlmorel]

In my 12 years of primary schooling, the best grade I ever got in any math course was a “C”...once. I failed nearly every class and had to go to summer school for several years.

My schooling took place through the sixties and mid-seventies and in counting I went to 12 different schools.

Taught one way in Catholic schools. Differently in military schools on one base. Again differently on another base. Then differently again back in one school system. And differently in another school system in another state.

All this overlaid with a least three major changes in society attitudes of teaching math from traditional math, to New Math, back so some non-New Math method...

No damn wonder I struggled. I nearly had a nervous breakdown trying to pass Physical Chemistry, but I did it on my own two feet.

Then I saw this absolutely totally insane Common Core approach to math, and thought “If this ever goes through, we are screwed as a country. We will never have competent engineers again.”

Bottom line for me-I think there are multiple ways math can be taught, but one method will work great for one person and not for another, and that is the way it is. Using one approach rigidly will always leave some people behind.

[cymbeline]

“E.g. if I want to say that a times b, is divided by c times d I would write

ab / cd”

To start with your sentence is ambiguous. You realize that now, don’t you?

The “ab/cd” means a * b / c * d which is evaluated left to right:

multiply a by b
divide that result by c
multiply that result by d

[Ingtar]

16, but many will get the loneliest number... 1.

[bankwalker]

math is weight lifting for the mind ... and ya gotta start light and be patient ...

[Little Ray]

It is not ambiguous.

The order in which operations should be done is abbreviated as PEMDAS:
Parentheses.
Exponents.
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)

So:

8÷2(2+2)

That means “2+2” goes first. So

8÷2(4)

Next, you take 8÷2. So

4(4)

So the answer is 16.

But that is the reason I prefer to group operations in parentheses, anyway:

(8/2)*(2+2)

There are no questions about what that means. That way I don’t have to care about “PEMDAS.”

[Notthemomma]

“8/2(2+2)
8/2(4)
4(4)

Result 16”

Wrong.
Even if you choose to do operations from left to right, the multiplication or division is against EVERYTHING AFTER THE OPERATION SIGN until you get to addition or subtraction signs outside of brackets or parentheses (or powers)

8/2(4) = (8/2)/4 = 4/4 = 1
That’s the same as
8/2(4) = 8/[(2)(4)] = 8/8 = 1
but the brackets are understood not to be needed.

In contrast, 8/2+4 = (8/2) + 4 = 4 + 4 = 8
and
8/(2+4) = 8/6 = 1 1/3

Or, go backward, and remember that division is the same as multiplication by 1 over the item you’re dividing by:

1 = 8/8 = 8/(2)(4) = (8/1)[1/{(2)(4)}] = (8/1)(1/2)(1/4)

To write it they way you’re implying it should be interpreted would be
(8/2)(4).

[rlmorel]

I never had any aptitude for it, but when I made up my mind after I got out of the USN that I was going to college as a Chemistry major, I knew I would have to work hard to make up for my lack of aptitude.

That took me where I needed to go, but I admit to not enjoying it. You simply cannot BS your way through math. You have to do it.

That is why I laugh derisively when I see people say math is “racist”. It is simply the single most OBJECTIVE thing out there I can envision.

The math either works...or it doesn’t. No middle ground.

[nuconvert]

Sounds terrible

[GnuThere]

Oh, now it makes sense. ;)

[Big Red Badger]

Agreed,
I figured 16 too.

[Gil4]

It’s parentheses and powers, then multiplication and division, then addition and subtraction.

Multiplication and division are done at the same time (left to right.) It’s usually presented as a list, but it’s three tiers.

[democratsaremyenemy]

You proles are all wrong.

[fproy2222]

This is fun if you are only talking about numbers.
Lets say all those numbers are dollars and your bank has to figure out how much interest to pay you.

[Gil4]

This would be correctly written as

8
-— (2+2) = 16
2

The whole issue is whether or not multiplication is a higher precedence than division. It isn’t; they are at the same level and are done left to right.

[mjp]

The answer is 1, by the way I learned math. I am not going to change my math rules now, and I am not going to change the pronouns I use. So There!

[Ancesthntr]

1

[Gil4]

8/2(2+2) = 8/2*4 = 4*4 = 16

8/2*4 = (8/2)*4, not 8/(2*4)

Multiplication and division are at the same priority and are done left to right if written left to right.

[metmom]

the way it’s written, according to the rules of math, it’s 8 divided by 2 which equals 4.

Then it’s four times (2+2), which makes it 16.

If the 2(2+2) were to be taken as one unit, then it would have been written as [2(2+2)] which would make it 8 divided by 8 equaling one.