Quote:
Originally Posted by Noah930
What is 56 - 24 / 3 + 12?
My child's math teacher said 36.
I say 60, as does a friend who was formerly a schoolteacher.
Essentially, in PEMDAS, do you literally do all the operations according to P-E-M-D-A-S? So that all addition gets done before all subtraction? Or are addition/subtraction considered equivalent in priority so that you then do the equation left-to-right?
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These 2 are the same
56 - 24 / 3 + 12 = 60
56 - 24 ÷ 3 + 12
this is not allowed, you can't put a parentheses into an expression in any ole place that you want, in this case it does not change the answer though but it is only serandipity that the answer doesn't change
56 - (24 / 3 + 12) = 36
you can put parenthesis where it does not change the problem
56-(24/3) +12 is allowed, because you would need to do the division first anyway
56+(-24/3) +12 is also allowed, here you added a parenthesis that didn't change any thing and used the unary minus in place of the binary minus, also allowed, in the original, this does not change the problem, adding a negative is the same as subtracting the same positive . It does change what is possible as a next step. because now the minus is inside the parentheses leaving only addition outside
56+12+(-24/3)here the above expression which is the same as the original used the commutative property of addition to change the order of processing, the answer does not change. Only addition and multiplication(of the common binary operations) are commutative. Neither subtraction nor division is commutative.
(-24/3) +12+56 or 12+56+ (-24/3) are also possible rewrites because of CPA
This changes the meaning of the original and is not allowed as a transformation of the original, it may or may not have been what was intended, but this was a math test not a ESP test.
(56-24) / (3+12)
this also changes the meaning of the original, it is the same as the one above and is not allowed as a transformation of the original
56 - 24
3 + 12