Real Numbers Math Arithmetic

Real Numbers Math Arithmetic

The  Real numbers includes  all  whole ( 0 ,1 , 2, 3, ,4 ,5 ,6 ….) rational (-5, -6, -9 , 3/5/ 7/8 ……) and   irrational ( √2 =1.41421356 , √3 = 1.7320508 , π = 3.1415)  numbers. It can be positive,  negative and zero. 

The real numbers can be represented on number line known as Real Number Line.

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The infinite  and imaginary  numbers are not real numbers like √ -1  = Imaginary or (No value ) .

 

Greater than  ‘>’

If any real number ‘a’ is  greater than another real number ‘b’ than ‘a’ will be on the right side of the ‘b’ on the number line . a>b.

Ex. 1

If  a=5   and b = 1

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Lesser than  ‘<’

If any real number ‘a’ is  lesser than another real number ‘b’ than ‘a’ will be on the right side of the ‘b’ on the number line . a < b

Ex. 1

If  a= -3   and b = 1

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Interval

When we write like 2 < x < 6 that means ‘x’ is having the value in between 2 and 6.

As we all know that there are four intervals with one end point.

<     Less than

>     Greater than

≤     Less than or equal to

≥     Greater than or equal to

 

Absolute Value

The absolute value of any number ‘a’  is  its distance from zero. The symbol is “│ │”  .   

Whether number is on positive side of number line or negative side of number line . The result will always be positive.

│a│ = a  and │-a│ = a

If a = 4  than  │4│ = 4  and │- 4 │ = 4

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But when  the negative sign is outside the absolute symbol than  

     -│a│  = – a

Some More Rules

  1. │a + b │ ≤ │a│ + │ b │

     2.  │a│ x │b│ = │a x b│

 

 

Examples

  • │5│  = 5
  • │-5│ = 5
  • -│5│ = -5
  • -│- 5│= – (5) = -5
  • │0│ = 0
  • │-2 x 7│ = 14
  • -│ 8 – 3│ = -5

                                                                                         

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