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?
On Multiplication,Division,Addition,Subtraction
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3Subtraction 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. – 2012-12-14
2 Answers
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.
If you are trying to compare MDAS against DMAS then they are both equivalent as long as you replace division with inverse of multiplication i.e. replace $x/y$ with $x \times\frac{1}{y}$
For instance: $4/2\times3$ using MDAS rule AND (not replacing $x/y$ with $x \times\frac{1}{y}$) , would be like $4/2\times3 = 4/6 = 2/3$ which is not equal to the answer obtained by using DMAS rule $4/2\times3 = 2\times3 = 6$
But if you replace $x/y$ with $x \times\frac{1}{y}$ then solving $4/2\times3$ would be like $4/2\times3 = 4\times\frac{1}{2}\times3 = \frac{12}{2} = 6$ which is the answer obtained by using DMAS rule i.e. $6$
same goes for Addition and Subtraction operations, that is considering Subtraction as inverse of Addition $a-b = a+({-x})$