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Imgonnatrythis@sh.itjust.works 4 weeks agoNot a genius. But if subtraction is last, why isn’t it 9-4?
Parenthesis, exponents, multiplication, division, addition, subtraction.
should actually be
Parenthesis, exponents, (multiplication and division), (addition and subtraction).
Addition and subtraction are given the same priority, and are done in the same step, from left to right.
It’s not a great system of notation, it could be made far clearer (and parenthesis allow you to make it as clear as you like), but it’s essentially the universal standard now and it’s what we’re stuck with.
No, it should simply be "Parenthesis, exponents, multiplication, addition.
A division is defined as a multiplication, and a substraction is defined as an addition. I am so confused everytime I see people arguing about this, as this is basic real number arithmetics that every kid in my country learns at 12 yo, when movong on from the simplified version you learn in elementary school.
A division is defined as a multiplication
No it isn’t. Multiplication is defined as repeated addition. Division isn’t repeated subtraction. They just happen to have opposite effects if you treat the quotient as being the result of dividing.
Yes, it is. The division of a by b in the set of real numbers and the set of rational numbers (which are, de facto, the default sets used in most professions) is defined as the multiplication of a by the multiplicative inverse of b. Alternative definitions are also based on a multiplication.
That’s why divisions are called an auxilliary operation.
You want PEMA with knowledge of what is defined, when people can’t even understand PEMDAS. You wish for too much.
I hate most math eduction because it’s all about memorizing formulas and rules, and then memorizing exceptions. The user above’s system is easier to learn, because there’s no exceptions or weirdness. You just learn the rule that division is multiplication and subtraction is addition. They’re just written in a different notation. It’s simpler, not more difficult. It just requires being educated on it. Yes, it’s harder if you weren’t obviously, as is everything you weren’t educated on.
I’m just confused as to how that is not common knowledge. The country I speak of is France, and we’re not exactly known for our excellent maths education.
Addition/subtraction work out the dame regardless of how you order the operations. If you do subtraction last you have:
9-1+3
and you are adding 3 to the result of (9-1). Since you are trying to perform it before the (9-1) operation is carried out, you can add 3 to the 9:
12-1 = 11
or you can add three to the -1 and get:
9+2 = 11
You only end up with 9-4 if you were subtracting 3 rather than adding three. It all becomes more obvious if you read the original as:
9 + (-1) + 3
It’s multiplication or division from left to right followed by addition or subtraction, also from left to right.
That’s where a lot of people fuck up.
aliceblossom@lemmy.world 4 weeks ago
Because its not really “1 plus 3”, its negative 1 plus 3 which is two. I know it seems a little weird but the minus sign is " tied" to the thing following it.