fundamental laws of algebra

Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics and number theory, algebra is one of the main branches of pure mathematics.Source: Wikipedia

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Fundamental Laws of Algebra:

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 laws for addition.

a + b = b + a

Example:

5+2=2+5

Commutative laws for multiplication.

a * b = b * a

Example:

6*5=5*6

Associative laws for addition.

(a + b) + c = a + (b + c)

Example:

(6+2)+5=6+(2+5)

Associative laws for multiplication.

(a * b) * c = a * (b * c)

Example:


(5*4)*2=5*(4*2)

Distributive laws of addition over multiplication.

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


And


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

Example:
2*(5+3)=2*3+2*5

Fundamental Laws of addition in algebra:

For the addition of positive and negative number, the follow rules, established in the First Course, apply make easy to solve algebra equation:

A number represented by a letter is called a literal number, and any number expression in which more than numbers of symbols are variable is called a literal expression.

Laws for fundamental addition in algebra:

1)  To add two numbers with similar signs, find the sum of their total values, and prefix the sign common to both.

2)  To add two numbers with different signs, find the diversity of their total values, and prefix the sign of the one with the larger total value.
Order of Operations for Fundamental Laws of Algebra:

In long math problems with +,-,x,%,(), and exponents in them, you have to know 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. You need to do operation in side parentheses first.

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

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

Mice             “M” means multiply

And               “A” means addition.

Snails           “S” means subtract. Always on the left hand side and perform all additions and subtractions.


Example for fundamental laws of algebra:

Solve 12%2(10-6)-2+4 using order of operations.

Solution:

Big                 reduce brackets. 10-6=4                                                                          12%2*4-2+4

Elephants       reduce exponents. We do not have any exponents.                             12%2*4-2+4

Destroy           make divide operation in order from left to right     12%2=6                 6*4-2+4

Mice                carry out multiply operation in order from left to right 6*4=24                24-2+4

And                 do addition operation in order from left to right 24-2+4=24+2=26        26



Answer is 26.