Algebra i

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Algebra is the branch of mathematics which deals with numbers, variables and their operations and relations.
Numbers are categories in different types, such as –

1.The natural numbers are represented by N; Counting numbers are called natural numbers.Example - 1, 2, 3, 4, 5…

2.Real numbers are represented by R; a number which can place on a number line is called real numbers.

3. Integers are denoted by Z, both positive and negative numbers, includes zero are known as integers.Example - Positive integers : 1,2,3,4… and Negative integers : -1,-2,-3,…

4 Rational numbers are denoted by Q, numbers which can be represented in the form of p/q where q is not equal to zero.
Example - 1, 1/3, 0.4 and -6/7 etc.

5 Variables or literals- representations of numbers by symbols (non-numerical). Whose value can change?
Example - a, b, c etc.

Relations of numbers- different symbols like “=", ">", "<", etc. are used to compare mathematical expressions and numbers.
Example
·16>3
· 9<15
Example 1:  Solve: - 5+ [2 (4 – 2)] 2
 
Solution:  In the equation, the rule of PEMDAS is used
 - 5 + [2 (4 – 2)] 2
  
  = 5+ [2(2)] 2  

   = 5 + [4]2  

   = 5 + 16 

    = 21

Example 2:  Solve: - 6 + (4 + 3)3.

Solution: -  In the equation, the rule of PEMDAS is used. The steps are shown below:-

   6 + (4 + 3)3 

= 6 + (7)3 

= 6 + 343

= 349
 

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