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The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression. We can remember the order using PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
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Why does BIMDAS work?
That is how the order of operations is defined.
What is the reason for the order of operations?
Those are conventions. Many people have gotten accustomed, over the years, to doing operations in a certain order. You can invent your own set of rules, but those would have to be clearly stated to avoid confusion... and it would serve no useful purpose. Having SOME order of operations defined is useful, to avoid having to write parentheses any time you have more than one operation.
Defined fraction and then the four fundamental operations?
[9+4]3
What do you call operations that undo each other like multiplication and division?
If defined, they are inverse operations. However, multiplication and division is a somewhat flawed example because division by 0 is not defined. So, if you have a number x, then x*0 = 0 but 0/0 is not x: it is not defined.
Why is it necessary to study order of operations and laws of operations before you solve equations?
Because if you did operations in an impermissible order, or violated laws of operations, then your solution to the equation is wrong.
