My thought process: if I had 8÷(4+4) = 1 and factored out a 2, I get 8÷2(2+2) = 1. However, if I say 2(2+2) = 2*(2+2), then 8÷2(2+2) = 8÷2*(2+2) = 1, BUT 8÷2*(2+2) = 16.
Please help I’m feeling dumber by the second
In: Mathematics
÷ is an antiquated symbol and should no longer be used in this context.
This is where ALL of the issues with these problems come from.
The problem is irrelevant, the whole point of these is to use a math symbol “÷” in a shitty way to confuse people. Especially because that symbol is absolutely NOT meant to be used in this type of more complex equation. It’s not meant for this type of equation and is specifically regarded that it should no longer be used in this type of equations.
In other words, whomever gave you this equation you should tell them to suck your balls
Edit: because other morons are calling out PEMDAS, this does do PEMDAS, but you misinterpret the ÷ symbol and just call out PEMDAS without understand what that symbol means or why there would be confusion. The ÷ means all items to the right of it are in the divisor, ALL of them, no matter what. It’s a shitty symbol, it should not be used like this, its only to screw with people. You’ll quickly notice all of these “confusing” problems are ones that incorporate the ÷, specifically because its a symbol that is not meant to be used, and only leads to confusion
so
8÷2(2+2) = 8 / (2*(2+2))
[see ALL of the numbers to the right of ÷ are in the divisor, and this is a more understandable and equal equation, and the equation should NEVER have been written the other way!]
It’s easy to see there that you get
8 / (2*4) = 8 / 8 = 1
Order of operations: PEMDAS.
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
Always in this order
First do the parentheses.
(2+2)=4
But the first 2 is connected to the parentheses, so we follow through.
2(2+2)=2×4=8 or 2(2+2)=(4+4)=8
Now we have 8÷8=1.
It’s the order of operations. Stuff in parentheses is done first. Then, you do any multiplication or division, and finally any addition or subtraction. If there are multiple addition/subtraction or multiplication/division operations, work them rightmost to leftmost. For your example, here’s how it goes:
8÷2(2+2)
Do the stuff in parentheses, and you get:
8÷2(4)
Do the first multiplication (that is, 2*4):
8÷8
And the last division (8÷8) gives you:
1
Figure out the sum to the right of the divided symbol first. So, 2+2 =4, take 4 and times it by 2, now you have 8. So it is 8 divided by 8 which equals 1.
For those who keeping spouting PEMDAS, you’re missing something huge with order of operations. The correct interpretation of PEMDAS is:
-Parentheses
-Exponents
-Multiplication AND Division from left to right
-Addiction AND Subtraction from left to right
Lemme say it again: multiplication is not ALWAYS performed before division—it MUST be calculated from left to right. The same applies to addition and subtraction.
If the division symbol were actually a /, then the original equation would be: 8 / 2 * (2 + 2). Following order of operations (which is what is being stressed here, NOT the division symbol vs /)…
Parentheses: 8 / 2 * (2 + 2) = 8 / 2 * (4)
Multiplication/Division from left to right: 8 / 2 * (4) = 4 * (4) = 16
Why is this so complicated for people to understand? I blame Common Core math…
Edits: rewording my statements to better explain myself.
This factoring …
8÷(4+4) == 8÷2*(2+2)
is faulty. Taking just 4+4 (without the parens)…
4+4 = 2(2+2) – this is correct, factoring out the 2, creates a NEW set of parens. You must ALSO preserve the original set of parens in the whole equation…
(4+4) = (2*(2+2))…
So the whole thing is …
8÷(2*(2+2)) = 8÷(2*(4)) = 8÷(8) = 1
Yes, the ÷ symbol is often confusing, but the / symbol just means the exact same thing and can be just as confusing.
This is easier…
8 8 8 8
—– = ———- = ———- = ——– = 1
4+4 2*(2+2) 2*(4) 8
It equals 1 because you chose to follow a criteria that gives you 1. If you decided and we all adopted the idea that we’d do the operations from left to right, treating the division symbol as applying to the numbers immediately next to it then it wouldn’t equal 1. But the same way as you can read this text in English because we chose to use these sequence of letters and words as English, we chose the language where the equation equals 1.
It’s not, it’s 16.
First, I don’t think anyone debates that we should do the parentheses first, so we have 8÷2(4).
So let’s just make that last operation an explicit multiplication, 8÷2*4
So then you remember pemdas from elementary school. But then you remember later in elementary school that multiplication and division are the same operation, in the same way that addition and subtraction are the same. ie division by 2 is multiplication by 0.5 and subtracting 1 is adding -1.
For this reason, multiplication and division are performed as they come from left to right, neither taking priority over the other. If you had 8-2+4 you do the subtraction and then the addition and get 10, not 2.
So here we do the division to get 4 and then the multiplication to get 16.
Use the method called BODMAS, the mathematical equations are solved in this manner.
Brackets >Of >Division >Multiplication >Addition >Subtraction
Brackets- (2+2) = (4)
Of- 2(4) = 8
Division – 8÷8 = 1
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