Well now that you have the answer, Now what???
LA is cake. VC was covered in our normal calculus curriculum. That's crap like gauss, stokes and greens theorem, right?
This. LA was one of my favorite classes because it was fun and super easy (and super applicable to computing)
My favorite courses were the applied ones like numerical analysis and mathematical image processing (Fourier transforms, partial differential equations, wavelet transforms). I was a math minor and went to grad school for ECE, so i'm a glutton for math punishment, lol
Calc 3 introduced it. VC was way more in depth.
Diff EQ was my least favorite math class. It wasn't hard, it was just stupid. Figure out how to get an equation into a known solvable pattern and solve. Damn it was boring.
Well, I don't eat bacon so that's no problem.
As far as the math, I am satisfied memorizing the mil dot drop/windage rates on my 2 favorite sniper rifles. I will depend on my high dollar ($4.99) Casio calculator for balancing my checkbook.
Proud member of the Obama Sucks Clan!!!
As far as the math, I am satisfied memorizing the mil dot drop/windage rates on my 2 favorite sniper rifles. I will depend on my high dollar ($4.99) Casio calculator for balancing my checkbook.
Proud member of the Obama Sucks Clan!!!
a) x÷2y = x / ( 2*y )
b) x÷2(y) = (x / 2) * y
OP is written is b - can't ignore the parenthesis.
b) x÷2(y) = (x / 2) * y
OP is written is b - can't ignore the parenthesis.
Well Its been 25 years since I studies algebra in school and I rely on an HP calculator and computer now so I went and looked it up and I found this. It makes good sense as best I can remember from 25 years ago.
The answer is 288. Anyone who thinks the answer is 2 is doing their order of operations incorrectly. this is how i learned it:
1) Parenthesis
2) Exponents
3) Multiplication and Division (from left to right)
4) Addition and Subtraction (from left to right)
First you evaluate whats in the parenthesis
48÷2(9+3) = 48÷2(12)
Now you do multiplication and division from left to right. In this case, the division comes first since it is more to the left.
48÷2(12) = 24(12)
Now you multiply
24(12) = 288
"What are the order of operations anyway?"
They are a convention used in math to clarify ambiguous problems such as this one.
"Well it depends wheather you use PEMDAS or BEDMAS"
No it doesnt. Multiplication and division are treated with equal precedence regardless of acronym you choose to use. Multiplication and division are evaluated from left to right. Google "order of operations" or read any algebra textbook and it will say the same thing.
"But usually when theres a division sign, everything to the left is the numerator and everything to the right is the denomenator..."
No that is not true. There is no math property that says that everything on the right is naturally the denomenator.
"But some calculators say 2"
This is true. Not all calculators evaluate the order of operations correctly. In general, newer calculators/computer programs will get the order of operations correctly. For example, C++, Python, MATLAB, Maple, Wolframalpha, and my TI-89 all say 288 whereas many older calculators that dont do the order of operations correctly may say 2.
"But wait! The denomenator says 2(9+3), not 2*(9+3)"
The presence an "x" or "*" for multiplication (and similarly the presence of "/" or "÷" for division) makes no difference. Either way, it indicates the multiplication of 2 and (9+3), regardless of notation. The manner in which multiplication is notated has no impact on the order of operations. You still do multiplication and division from left to right
"but you can use the distributive property to determine that 2(9+3)=24, and 48/24=2!"
Mathmatically, the distributive property is exactly the same as multiplying 2 and (9+3). By doing it before the division of 48 and 2, you are violating the order of operations, and therefore you are wrong. The distributive property in no way takes precedence over normal multiplication (and in fact has no effect at all on the order of operations). That logic is faulty and the answer is 288.
"Ok, I understand that if you use BEDMAS you get 288, but what if I choose not to use BEDMAS?"
Then you are doing the problem wrong. BEDMAS is the math convention and there is no choice of wheather or not to use BEDMAS.
"Both answers are correct; it just depends on how you interpret/see the question!"
No you are also wrong. There is only one right answer and its 288. The idea that both answers are correct is also wrong. Like I said before, this problem is not ambiguous at all when you use the order of operations. Essentially, there is only one correct way of interpreting this problem.
"But we cant be sure if there are implied brackets around the denomenator like this 48÷(2(9+3)), therefore we can't be sure if the answer is 2 or 288!"
Yes, we can be sure that there are no implied brackets. The reason we know this is because the original problem was given like this: 48÷2(9+3). In math, you cannot imply brackets. The only brackets are the ones that are written in the equation.
I hope this clarifies things.
Word. Interpretation requires adding parentheses and thus changes the equation.
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