Operation of Law

Introduction of law of operation:


In mathematics, an expression of symbols intended to represent a numerical value must follow commonly accepted and unambiguous rules. For example, the rule for evaluate 2 + 3 * 4 in mathematics and in most computer languages is to do the multiplication first, so the correct answer is 14. Which have their own rules, may be used to avoid confusion, the convention needed to clarify which operator should be applied first is known as a law of operation. 


Source: Wikipedia 


Law of Operation: 

We list the fundamental rules and properties for useful algebra and give examples on they may be used. 

Suppose that a, b and c are variables or applied algebraic expressions. 

Commutative law for addition. 

 a + b = b + a 

 Example:7+2=2+7 


Commutative law for multiplication:a * b = b * a

 Example:10*4=4*10 

 Associative law for addition.(a + b) + c = a + (b + c)

 Example:(12+4)+5=12+(4+5) 

 Associative law for multiplication.(a * b) * c = a * (b * c) 

 Example:(6*2)*5=6*(2*5) 

 Distributive law of addition over multiplication. 

 a * (b + c) = a * b + a * cAnd(a + b) * c = a * c + b * c

 Example:7*(3+9)=7*3+7*9 


Law of Operations in Order Operation

 In long math problems with +,-,x,%,(), and exponents in them, you have to identify what to do first. Without follow the same rules, you may get unlike answers. 

You can easily keep in mind the silly sentence, Big Elephants Destroy Mice And Snails, you can commit to memory the order of operations, and you must follow. 


Big “B” means Brackets. We need to carry out operation in side parentheses first. 

Elephants “E” means an exponent, you must calculate exponents next.

Destroy “D” means division. Begin on the left of the equation and perform all multiplication and divisions in the order in which they appear. 

 Mice “M” means multiplyAnd “A” means addition. 

 Snails “S” means subtract. For all time on the left hand side and complete all additions and subtractions. 


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Example for Law of operations in order operation: 

 To simplify 25`-:`5(8-3)+10-5 in law of operations in order operation. 

Solution:=25`-:`5(8-3)+10-5

=25`-:`5(5)+10-5 where 25`-:`5 are `25/5

=`25/5``xx`5+10-5 

= 5 `xx` 5+10-5 

=25+10-5 

=35-5 

=30Answer is 30.