The Math Question that's Breaking the Internet! Can You Solve It? 8 ÷ 2 (2+2)

Have you seen that math problem floating around the internet that no one can seem to agree on? In this video, we're going to solve the infamous question: 8 ÷ 2 (2+2) once and for all.

Or....maybe we won't.

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Music:

[rolandocabrera]

People: SAT math isn’t even that difficult
First question on the SAT:

[Jay]

Is it really BREAKING the internet though? Or are some people just dumb?

[dgkcpa]

Simple problem of division. a÷b, where a=8, b=2(2+2), which is also 8. 8÷8=1

Key point, not addressed in video: When changing from implicit to explicit multiplication, you must do more than just add the multiplication symbol (x).
You must add brackets around the factors involved, in this case, 2 and (2+2).
In this problem, 8÷2(2+2) = 8÷(2 x (2+2)) not 8÷2 x (2+2)

Key point, not addressed in the video: if we do the problem as stated, we can solve the problem without using multiplication at all.
Division by a product, in this case 2(2+2), is the same as division by each of its factors, i.e., 2 and (2+2)

8÷2(2+2) Step 1: Start by adding the 2+2 within the parentheses.
8÷2(4) Step 2: Divide 8 by the first factor, 2
4÷(4) Step 3: Divide the quotient of 8÷2, or 4, by the second factor (4), to get the answer.
=1

If we present these same steps in fractional form, we get:

8 8 4
= = = 1
2(2+2) 2(4) (4)

If you want to input the problem into a calculator or math enginge, you should enter 8/2/(2+2), because the division symbol, (÷) in this instance. applies to both the 2 and the (2+2).
alternatively, you can add () and enter 8÷(2(2+2)) so that your calculator will know how you want it to handle the problem.
Remember, it is your tool, not vice versa. It won't do your thinking for you.

[iyslaalicecastelo]

i'm from canada and we use BEDMAS (brackets, exponents, divison, multiplication, addition, subtraction)

[nfpnone]

This question only stumped people who use calculators and spreadsheets to do math, anyone who learned to do it by hand isn’t stumped at all, they all know the answer is 1!

The problem with this problem is that the “P” in PEMDAS doesn’t just mean what’s inside the parenthesis, it means the whole parenthetical statement which includes any implied operators and exponents.

An implied operator is not a fixed operator, and you definitely can’t change an implied multiplication to a fixed division, which is what you are doing if you separate the 2 from the parenthesis, instead of 2*(4) it becomes 4/2, and you can check this very easily. 8/2*4=(8*4)/2=8*(4/2)=16, therefore if you separate the coefficient from the parenthesis by replacing the implied operator with a fixed operator it changes the whole meaning of the problem and converts the implied multiplication into a fixed division. Which is mathematically impossible.

[kennyprocacci]

Think about it like this:
8÷2(2+2)
=8÷2(4)
=8÷2*4
=4*4
=16
In my school we learned
P
E
MD
AS
Multiplication and division are on the same level so in that case you just go left to right when those are the only operations left to perform.

[shubhankardasgupta]

As an Indian and though totally learned the British way of learning maths, we are taught about to follow BODMAS from class 5th. Also, the full abbreviation of the BODMAS is {Brackets; Order(Exponents); Division; Multiplication; Addition; Subtraction}

[cellocoversimprov]

I mean... technically with PEMDAS it would be 16. But arguably with standard notation it would be 1. So that’s where the confusion is coming from

[XRyXRy]

no pranking dude, that's 16 lol
PEMDAS isn't really a perfect rule in the first place, but the issue here is that PEMDAS doesn't clarify that Multiplication and Division should be done from left to right regardless of order, along with Addition and Subtraction.

[avedsodah]

O = order. Two to the order of two would be 2^2. Basically same as E

[johnsciara]

I look at a(b+c) and how that is solved. It appears that once you substitute numbers for the variables, for some people, the rules change. I agree with you that the expression was written so that you could argue either way what you believe the answer to be. I like your solution. I also like that you stated that this would not be expressed this way on a SAT exam.

[themusicguy]

The original order of operations in most countries was BODMAS, which stands for Brackets, Orders or powers, Division, Multiplication, Addition, Subtraction. The O is sometimes associated with Of. This mnemonic was common until exponentials were added into the mnemonic.
so according to it the answer should be 16

[OAS]

also the person who created this is laughing because they know the expression is flawed

[СултанРзагалиев]

From Kazakhstan
And I think the answer should be 16
In my country division & multiplication have a same priority, and we solving from left to right

[RustyCas]

Answer is 1. The distributive property is implied. Instead of 2(2+2) if it was written with a variable, A(2+2) you’d instantly think “4A”

[lubnaabdulrehman]

O stands for "of" as in when you say "to the power of ..."
but the new way is BIDMAS where "i" stands for "indices"
.

[MichaelA]

Dividing by 2 is the same as multiplying by 0.5. 8 * .5(2+2) = 8 * .5 * 4 = 16. It's definitely 16!!

[raikiri]

Congrats on hitting the 150K subscribers!! :)

[kaushaljha]

Bodmas stands for "brackets, orders, division, multiplication, addition, subtraction". It is the order of how Microsoft Excel works out how to perform the order of calculations.

[robinramchander]

Please read this article: The Fallacy around Inserting Brackets to Evaluate Expressions Involving Multiplication and Division (waset.org)