SOLUTION: What operation should be perfermided first in this expression? 8 - 3 + 12 / 3 x 2 Division correct? 12/3 would be the first operation? Thank you

Question 1108615: What operation should be perfermided first in this expression?
8 - 3 + 12 / 3 x 2
Division correct? 12/3 would be the first operation?
Thank you
Found 2 solutions by Alan3354, KMST:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
What operation should be perfermided first in this expression?
8 - 3 + 12 / 3 x 2
Division correct? 12/3 would be the first operation?
==============
IDK.
It's ambiguous.
It is ?
Or ?
Or ?
Or ?
Or ?
===========
Notice I use * (Shift 8) for multiply.
Use that, not x. x will be used for other things.

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
I agree, and so would almost all calculators.
8 - 3 + 12 / 3 * 2 = .
My Casio fx-260SOLAR calculates it that way. It knows order of operations. When I am entering the operation as listed, right after the second 3, the display shows the result of 12/3=4.
The calculator app in the computer I am using, when using the "scientific" version, does the same thing.
Those two options follow algebra rules about order of operations.
The calculator app in my cell phone also knows algebra. It writes the whole string of operations, showing no result until the end, and after I press "=" it display "=13" in red on a second line.

My old-fashioned (accountant type) Cannon LS-82Z calculates each operation as a 4th grader. After I enter "8-3+" it shows the result 8-3=5. As I continue typing "12/", it gives me the result 15+12=17. As I continue typing "3x", it gives me the result 17/3=5.6666666. Then, as i enter the final "2=", it gives me the result 5.6666666=11.333333.
When using the "standard" version, the calculator app in the computer I am currently using does the same thing as the Cannon LS-82Z. They are options for people who do not use algebra, and do one calculation at a time.

NOTE: The thing about PEMDAS is that multiplication and division are the same operation and so are addition and subtraction. So, one face of the operation does not have priority over the other. In the realm of the real numbers, there is no such thing as division; dividing by a number is really multiplying times its multiplicative inverse (called its reciprocal). When you think you are dividing by 2, you are really multiplying by 1/2. When proctoring a 12th grader physics final exam, a student was concerned that she was making a mistake in her calculations. She said she was dividing by 0.5, and was getting a result that was "a bigger number", which contradicted her belief that when you divide you must always get a smaller number. The reason why a teacher once told you about division, is that they had not yet introduced you to fractions. When you were told about subtraction they had not yet taught you about negative numbers. It is not the teachers' fault. They were misled too, and so was I, all the way until a few years into college.
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