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DrWatson · 70-79, M
The problem with PEMDAS is that many students ( and, sadly, a few teachers) misunderstand it's meaning. They mistakenly think multiplications should be performed before divisions, and that additions likewise precede subtractions.
So, for example, when presented with
10 - 5 + 1,
they incorrectly get 10 - 6 = 4, rather than 5 + 1 = 6.
I tell students to think of it as PE(MD)(AS).
Of course, there would be no confusion at all if we simply said there are only two operations: addition and multiplication, and we replace subtraction with adding a negative number, and replace division by multiplying by the reciprocal
Then the problem above becomes
10 + (-5) + 1
This gives 6 no matter how you group it, since addition, unlike subtraction, is associative.
So, for example, when presented with
10 - 5 + 1,
they incorrectly get 10 - 6 = 4, rather than 5 + 1 = 6.
I tell students to think of it as PE(MD)(AS).
Of course, there would be no confusion at all if we simply said there are only two operations: addition and multiplication, and we replace subtraction with adding a negative number, and replace division by multiplying by the reciprocal
Then the problem above becomes
10 + (-5) + 1
This gives 6 no matter how you group it, since addition, unlike subtraction, is associative.