# On Multiplication,Division,Addition,Subtraction

I was asked if what is the basis of MDAS rule. (multiplication, division, addition, subtraction). Will these operations be followed at all times, or can it be changed in some cases?

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Subtraction is just addition with negation on the second element and division is just multiplication with inverse on the second element. Then, multiplication follows addition from the distributive property of fields: $a(b+c)=ab+ac$. Real numbers with addition and multiplications form a field and one of the properties of fields is the distributive property. If you wanted to switch them around, you would have to change the operations fundamentally. – fhyve Dec 14 '12 at 9:55

## 1 Answer

It equally can be DMAS, DMSA and MDAS. The point is multiplication and division always have higher precedence over addition and subtraction unless there are parantheses. Evaluating a subtraction before or after an addition doesn't change the value of the result. Same thing for multiplication and division.

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