Horizontal Lines in Math

Introduction to Horizontal Lines in Math:
              
              Horizontal lines in math are used for arithmetic operations which denotes the next step in this operations. Generally it does not have any meaning or symbols or notation or formula but it is expressed for easy understanding of the problems. In every math problems horizontal lines are present especially with the dividing symbol. In fraction, horizontal lines divides numerator and denominator in math. A horizontal line in math separates the equations when substituting the equation steps.



Applications of Horizontal lines in math:


             In all math problems we denote horizontal lines.Some of the applications are,

• In addition we are using horizontal lines when we adding numbers we expressed the horizontal lines for sum answers

            Example 12
                          +14
                            26

• In subtraction we apply as same as addition for the subtracted answers

             Example 20
                            -12
                              8  

• In multiplication horizontal lines express for the multiply value with the multiplicand

             Examples  12
                              ` xx ` 14    
                                  48 
                                12    
                                168   

• In division horizontal lines are shows the divide symbols which denotes quotient and steps involved in the division.

             Example 12 by 3
                             `12/3` =4  

• In fraction we denotes the horizontal lines for separations of numerator and denominator by use of  horizontal lines.

              Example` 5/3, 4/3` here 5 is the numerator and 4 is denominator.

• In algebraic equations when we equating two equations horizontal lines express the next step for equations in both elimination and substitution method we have horizontal lines for equations.

              Example 2x+y =5 .........(1)
                                 x-y  =4........(2)
                                3x =9
                                  x=`9/3 `
                                  x=3
                       substitute x=3  in (2)
                            3-y =4
                                y=`4/3`
                           



Example Problems for Horizontal lines in math:


Example 1:
      Add 24 and 10.

Solution:
          24
       + 10
         34 

Example 2:
    Subtract  -24 and 10

Solution:
          24
        - 10
          14

Example 3:
         Multiply 10  ` xx`

Solution:
           
       10
    `xx`      4
        40
Example 4:
      Divide 25 ÷ 5

Solution:
         `25/5` = 5

Example 5:
      Simplify `4/3+ 2/3`

Solution:

      `4/3+2/3= 6/3`

Example 6:
           solve x+y =3
                   2x-y  =0

Solution:
                        x+y =3 .........(1)
                      2x-y  =0........(2)
                                3x =3
                                  x=`3/3 `
                                  x=1
                       substitute x=1  in (2)
                            1-y =4
                                y=`4/1`
                                y=4