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Glitch in the matrix (ani.social)

submitted 9 months ago by [email protected] to c/[email protected]

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[–] [email protected] 23 points 9 months ago* (last edited 9 months ago) (34 children)

spoiler

For anyone like me who has math as their worst subject: PEMDAS.

PEMDAS is an acronym used to mention the order of operations to be followed while solving expressions having multiple operations. PEMDAS stands for P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction.

So we gotta do it in the proper order. And remember, if the number is written like 2(3) then its multiplication, as if it was written 2 x 3 or 2 * 3.

So we read 8/2(2+2) and need to do the following;

Read the Parentheses of (2 + 2) and follow the order of operations within them, which gets us 4.
Then we do 2(4) which is the same as 2 x 4 which is 8
8 / 8 is 1.

The answer is 1. The old calculator is correct, the phone app which has ads backed into it for a thing that all computers were invented to do is inaccurate.

EDIT: Turns out I'm wrong, but I haven't been told how or why. I'm willing to learn if people actually tell me, instead of call me wrong and keep it at that. I was told PEMDAS and did PEMDAS.

[–] [email protected] 33 points 9 months ago* (last edited 9 months ago) (3 children)

Well that's just wrong... Multiplication and division have equal priorities so they are done from left to right. So: 8 / 2 * (2 + 2)=8 / 2 * 4=4 * 4=16

[–] [email protected] 8 points 9 months ago

This but unironically

[–] [email protected] 5 points 9 months ago (1 children)

Not quite, pemdas can go either from the left or right (as long as you are consistent) and division is the same priority as multiplication because dividing by something is equal to multiplying by the inverse of that thing... same as subtraction being just addition but you flip the sign.

8×1/2=8/2 1-1=1+(-1)

The result is 16 if you rewrite the problem with this in mind: 8÷2(2+2)=8×(1/2)×(2+2)

[–] [email protected] 9 points 9 months ago (1 children)

I've never had anyone tell me operations with the same priority can be done either way, it's always been left to right.

[–] [email protected] 4 points 9 months ago (1 children)

I've always heard it that way too but I think it is for consistency with students, imo Logically, if you are looking at division = multiplying by inverse and subtraction = adding the negative, you should be able to do it both ways. Addition and multiplication are both associative, so we can do 1+2+3 = (1+2)+3 = 1+(2+3) and get the same answer.

[–] [email protected] 1 points 9 months ago (1 children)

But subtraction and division are not associative. Any time you work on paper, 2 - 2 - 2 would equal -2. That is, (2-2)-2=0-2=-2. If you evaluate right to left, you get 2-2-2=2-(2-2)=2-0=2

[–] [email protected] 2 points 9 months ago

Correct, subtraction and division are not associative. However, what is subtraction if not adding the opposite of a number? Or division if not multiplying the inverse? And addition and multiplication are associative.

2-2-2 can be written as 2 + (-2) + (-2) which would equal -2 no matter if you solve left to right, or right to left.

In your example with the formula from right to left, distributing the negative sign reveals that the base equation was changed, so it makes sense that you saw a different answer.

2 - (2 - 2) = 2 + ((-2) + 2) = 2

[–] [email protected] 5 points 9 months ago

Implicit multiplication takes priority over explicit multiplication or division. 2(2+2) is not the same thing as 2*(2+2).

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