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

Step Functions In Math

Introduction to step function:

     A step function in math is one of the concepts of functions in math. The line is the collection of x and y points. At the same time x and y value can be increased values. We can plot this points on the graph we can get the equation of the line. That forms the step figure. So these functions are known as step functions.


Definition of Step functions in math
Definition of Step function:
    A function in the real analysis R can be defined as the step function it can be written as linear combination of semi open intervals. Open interval can be defined as [a, b) in R.  Then the step function f(x) can be described as,

f(x) =a1 f1(x) + a2 f2(x) + …………………… + an fn(x)

Brief Description of the Heaviside Step functions in math

This involves the following steps.

They are,

Step 1: First we can form the equation into y = m x + b form.

Step 2: Substitute any value for x we can get the y values.

Step 3: Plot the (x, y) points on the graph.

Step 4: This line plot increases sequentially.

Step 5: It look like as a step format.

These are the main steps used in math step functions.

Consider the equation of the line y = x -1

Substitute the values for x we can get the y values.

Substitute x=1 in the given equation y = x -1.

That is y= 1 – 1 = 0

Therefore the (x, y) co-ordinate is (1, 0)

Substitute x=2 in the given equation y = x -1.

That is y= 2 – 1 = 1

Therefore the (x, y) co-ordinate is (2, 1)

Substitute x=0 in the given equation y = x -1.

That is y= 0 – 1 = -1

Therefore the (x, y) co-ordinate is (0, -1)

Substitute x=-1 in the given equation y = x -1.

That is y= =-1 – 1 = -2

Therefore the (x, y) co-ordinate is (-2, -2)

Substitute x=-2 in the given equation y = x -1.

That is y= -2 – 1 = -3

Therefore the (x, y) co-ordinate is (-1, -3)

We can tabulate these points

X: -2 -1  0 1 2

Y: -3 -2 -1 0 1

Here the x and y values are correspondingly varies. So this function is namely known as step function.

The graph of the step function in math described as



This is also known as Heaviside step functions in math.

Live Online Chat About Math

Introduction to live online chat about math:

Live online chat about math is nothing but the help to students by tutors of  live tutoring website through online. Many students find difficult in doing the math homework problems. Parents also don't find time to help their students with homework problems. So they were in need of a website that provide live online chat about math. Tutor vista is a website to get help in math anytime. Many students find maths help vista website with the highly qualified tutors live at any time.  Below are some of the model problems solved by tutors for live online chat about math.


Live online chat about math:


1. Add 322 + 343 + 346

Solution

The given is an addition problem with three 3 digit numbers. Addition is the basic arithmetic operations

3 2 2
3 4 3
3 4 6 +
---------
10 1 1
---------
2.     Subtract the numbers given 444 – 240
Solution

Similar to add start the subtract with the ones digit first

4 4 4
2 4 0 –
----------
2 0 4
---------
3.  Solve and find the value of b  7b+3 = 24
Solution

This is an algebra problem. Here we have to find the value of b.

7b + 3 = 24

Subtract 3 on both sides

7b+3 -3 = 24 – 3

7b = 21

Divide by 7 on both sides to find the value of b

`(7b)/7` =`21/7`

b= 3

4. Solve 10 + 4 x 3 + 22-(1x4)

Solution

Here more than one arithmetic operation is given in the problem. So we perform this problem by using arithmetic operation.

10 + 4x3+22 - 4-------Parenthesis

10 + 4x3 + 4 – 4 -----Exponents

10 + 12 + 4 - 4 ------Multiplication

22+ 4 - 4   ------------No division so we do addition

22 ------------Subtraction

So the answer is 22


Live online chat about math:

Add 868 + 325 + 110
Subtract 875-340
Find the value of s in the equation shown below 4s – 6 = 26
By using PEMDAS rule perform 14 + 2 – 3 +(4x5) – 20
5. Find the value of u in the equation 3p = 42

Answers:

1303
535
s = 8
13
p = 14