Numbers and Operation in Mathmatics

NUMBERS:

Algebra as a generalization of arithmetic in which we can use letters such as a, b, c, x,y to represent numbers.

OPERATIONS:

Operations are bases of algebra. Without operations algebra is uncompleted. In algebra we solve all problems by using operations. The symbols used in algebra to represent operations of addition, subtraction, multiplication and division are ±, ·, and /. The words used to describe the results of these operations are sum, difference, product and quotient.

Operation                                 symbol                                                       words

addition                                           a+b                                                                     sum: a plus bsubtraction                                      a-b                                                                    difference: a less bmultiplication                               a.b, (a).b, a.(b), (a).(b)                                       product: a time bdivision                                            a/b                                                                   quotient: a divide bIn algebra, we generally avoid to use the multiplication sign “ ×” and the division sign “÷”.We must note that when two expression are placed next to each other without an operation symbol, as in ab, or in parentheses as in (a)(b) , these expressions are called factors, are to be multiplied.The four operations addition, subtraction, multiplication and division are called binary operations.
Each is performed on a pair of numbers. The symbol “ =” called an equal sign and read as equals.

Writing statements using symbols:

1:The sum of 4 and 5 equals 9.In symbol, this statement is written as  4+5=9.
2:The product of 2 and 5 is 10. In symbols, this statement is written as 2·5=10.
3:The difference between 6 and 4 is 2.  In symbols, this statement is written as 6-4=2.
4:The division of 9 and 3 is 3. In symbols, this statement is written as 9/3 =3.

Equality:

 we use equal sign to convey the idea that one expression is equivalent to another.
           Important Properties of equality are given below.1: Reflexive property: It states that a number always equals itself i.e x=x2: Symmetric property: It states that if x=y, then y=x.3: Principle of substitution: It states that, if a=b, then we may substitute “b”, for “a” in any expression containing “a 

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