user338: This is a sandbox post for users to experiment with various Stack Exchange features. This question (and all answers) is a community wiki so that the reputation required to edit is lower. 
Also, the user who owns this post is set to Community, which is not a real user but a background process. So you needn't worry that some one might be notified by all your shenanigans here (do note that comments on others' answers will still notify them).
Feel free to post an answer (gibberish welcome), delete your answers as you wish, try out various formatting tricks, test out voting to close/delete, protect posts, test new privileges, whatever the hell you want (yes, really!). Of course, as always, offensive content/spam will not be tolerated. 
I merely request that you do not change the title of this post or add any new arbitrary tags. If you do cast the last close/delete vote or if it is not reopened, please let a ♦ moderator know so that we can reopen/undelete it. 
Test edit to test rollbacks stuff
Feel free to modify the question below this line

(This was copied from GL)

user338: .................................................................................................................................................................... ้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้

user25568: Heey Howdyyyyyyyyyyy Big big big thanks for your Witty post.
Some Abutilon indicum  (malvaceae) for you
 
 



user338: 
Thanks for your edit!
This edit will be visible only to you until it
is peer reviewed. Just kidding, your edit was horrible, and nobody cared enough to accept it.

This is my magic wand:- ้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้
It's a ball...http://upload.wikimedia.org/wikipedia/commons/4/4f/Soccer_ball_animated.svg ...Kick it.
Wow, this is fun!
rè̑ͧ̌aͨl̘̝̙̃ͤ͂̾̆ ZA̡͊͠͝LGΌ ISͮ̂҉̯͈͕̹̘̱ TO͇̹̺ͅƝ̴ȳ̳ TH̘Ë͖́̉ ͠P̯͍̭O̚​N̐Y̡
Messed up This is the smallest text you will ever see... there is no way you are reading this unless you viewed the page source or edited my answer or something. This is tiny! Impossibly tiny! Yay! I still haven't filled up a single line with all this text :/ I STILL haven't! Wow! Okay now I filled up a line finally. I will just keep typing okay I don't know what to say.
This is some very odd   formatting.
Loading, please wait... http://web.archive.org/web/20120111193542/http://files.quickmediasolutions.com/throbber.svg
Huh, didn't know this was possible.
rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr
ก็็็็็็็็็็็็็็็็็็็็ กิิิิิิิิิิิิิิิิิิิิ ก้้้้้้้้้้้้้้้้้้้้ ಠ_ಠ ก็็็็็็็็็็็็็็็็็็็็ กิิิิิิิิิิิิิิิิิิิิ ก้้้้้้้้้้้้้้้้้้้้

user25568: Learning Formatting
From Want to know commands (codes) for following formatting tasks 
Really I need this sandbox for that. 
ABCD
Underscore gave bold
https://www.latex-tutorial.com/symbols/text-formatting/ 
\texttt{Text}
\textbf{Text}   Oops
texttt{Text}  https://www.latex-tutorial.com/symbols/greek-alphabet/
B   \beta B    \epsilon E \theta \Theta  Oops their tutorial material doing nothing. Something tricky might be there which I'm missing.
Reading this one: https://www.latex-project.org/help/documentation/fntguide.pdf
°  
& d e g  ; option by Want to know commands (codes) for following formatting tasks  is working correctly.
α Α   β Β  γ Γ δ  Δ ε Ε ζ Ζ η Η η Η θ Θ ♦ •
                   &alpha; &Alpha;   &beta; &Beta;  &gamma; &Gamma; &delta;  &Delta; &epsilon; &Epsilon; &zeta; &Zeta; &eta; &Eta; &eta; &Eta; &theta; &Theta; &diams; &bull;

Several blank spaces at left side allow me quote the codes.

I'm doing an experiment which is known as titration. I'm finding how many blank spaces is required to become able to quote the code. 
Here I use the keyboard as a sort of burette and the screen as conical flask also known as Erlenmeyer flask
The analyte is the code inside (but excluding) quotation marks: 
          "&alpha; &Alpha;   &beta; &Beta;  &gamma; &Gamma; &delta;  &Delta; &epsilon; &Epsilon; &zeta; &Zeta; &eta; &Eta; &eta; &Eta; &theta; &Theta;"


Experiment result: in the following table (ladder?) the number of drops of pure raw space-bars ; and correspondent result is present: 

0 (Zero) Space:
α Α   β Β  γ Γ δ  Δ ε Ε ζ Ζ η Η η Η θ Θ
1 space:
α Α   β Β  γ Γ δ  Δ ε Ε ζ Ζ η Η η Η θ Θ
2 spaces
α Α   β Β  γ Γ δ  Δ ε Ε ζ Ζ η Η η Η θ Θ
3 spaces:
α Α   β Β  γ Γ δ  Δ ε Ε ζ Ζ η Η η Η θ Θ
4 spaces: 
&alpha; &Alpha;   &beta; &Beta;  &gamma; &Gamma; &delta;  &Delta; &epsilon; &Epsilon; &zeta; &Zeta; &eta; &Eta; &eta; &Eta; &theta; &Theta; 

grey coloration appears on 4 
5 spaces:
 &alpha; &Alpha;   &beta; &Beta;  &gamma; &Gamma; &delta;  &Delta; &epsilon; &Epsilon; &zeta; &Zeta; &eta; &Eta; &eta; &Eta; &theta; &Theta; 


Experiment discontinued

CONCLUSION:
It takes 4 drops (successive obviously) of space bars at left side (start) of the line to quote the code.
:)
---------
াাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাীীীীীীীীীীীীীীীীীুুুুুুুুুুুুুুুুুুুুুুুুুুুুুুু
trying to create that magic wand.
ঁঁঁঁঁঁঁঁঁঁঁঁঁঁ
(অীীীী)ীীীুুুুুুুুুুুুুুুুুূূূোো

Copy paste from Chat Reply

Q
      #Formatting Besides specialized command for chemistry equations like , 

      $\ce{HCl}$ dissociates in water as follows:   

      $$\ce{H2O + HCl <=> H3O+ + Cl-}$$ 

; is there any simple command for subscript and superscripts for general purpose?
@AlwaysConfused Yes:
          <sub>subscript</sub> and 
          <sup>superscript</sup> on the main site


User@Terdon

https://biology.stackexchange.com/editing-help#comment-formatting
https://en.wikipedia.org/wiki/Floater
that secret
that secret

user25568: $$LEARNING \quad  the \quad MATHJAX$$ 
$$(my \quad MathJax \quad notebook)$$ 

I've tried to write the things in a systematic manner; i.e, when the reader have a query about a plus-related problem, the visitor will find it on respective paragraph. Similarly when the user have a question about division, fraction and ratio; all the symbols would be found in the respective paragraph. 

Part-1 : Reference and resources.
Main Stack-Exchange Articles: 


MathJax basic tutorial and quick reference on Mathematics SE Meta


Formatting Chemistry equations with MathJax.  on Chemistry SE Meta 


Other useful Stack-exchange articles


What additional formatting features are available to MathJax? on Chemistry SE meta. 


Hidden points of editing you probably didn't know on chemistry SE meta. 


How to write physical units. on Chemistry SE Meta. 


How to render Angstrom and Parts-per notations in MathJax? on Chemistry SE Meta. 


How do I format a physical quantity (unit of measurement + numerical value)? on physics SE meta. 


Math and SI formatting on Physics SE meta. 


Rendering units in MathJaX in Electrical Engineering Stackexchange Meta. 


MathJax: How do I write matrices on the same line?


MathJax Official Website


MathJax official website. 


MathJax Documentation page. 


MathJax features and Test Page. 


Other Online Resources: 


MathJax Example pages and Test typing. 


Wikipedia Article on MathJax. 


Wikipedia Help:Displaying a formula and Wikipedia:Rendering math also mentions MathJax commands. 


List of mathematical symbols


Other quick references 

On a math expression formatted with MathJax; do a right-click (mouse secondary button). That would give following dropdown menu.   


.
  On this dropdown list; take help of "Show math as" (and then --> TeX commands) which will show the command prompt required to design the math expression. And also take help of "MathJax Help", which gives some help as well as gives a link to MathJax official site. 




Part-2 : The tutorial.
Content


Recognition of MathJax Commands. 


Most MathJax command involves Back-Slash.  


Special commands may not require in some cases. 


Writing punctuation marks, special characters, writing normal text, escaping execution. 


Subscript and Superscript lettering


Putting space. 


Grouping some characters as a single thing. 


Bracketing. 


Breaking into new lines. 


Writing Numbers. 


Writing variables. 


Writing Greek letters


Writing Physical Quantities. 


Writing Chemical formula. 


Writing relationships like equations and inequalities. 


Writing Chemical equations.


Addition, Subtraction, Positive, Negative and Plus-minus. 


Multiplication. 


Division, fraction, ratios. 


Power, Root, Logarithm.   


Trigonometric functions and inverse trigonometric functions.   


Modern algebra, Set- theory and logic.  


Geometry.  


Matrix, Tables, arrays.  


PHYSICS formatting 


CHEMISTRY Formatting.  


STATISTICS formatting.      



Inside :

$$Basic \quad Structure$$


Recognition of MathJax input: 

The Dollar sign ( $ ) works as a label or indicator of MathJax input. System will recognize the part text as Mathjax input with help of dollars used in input. 


To write math-expressions within line of normal text; cover the expression with single dollar sign at start and end. Such as
$2+2=4$ gives you $2+2=4$ within the line within normal text.
Similarly $2^2=4$ gives $2^2=4$ , within the line. 
To display mathematical expressions in a separate paragraph, cover the expression within double dollar (i.e. at start of expression a double dollar ($$), at end of expression again double dollar ($$).
Such as within line $$(x+y)^2=(x^2)+(2xy)+(y^2)$$ 
will give $$(x+y)^2=(x^2)+(2xy)+(y^2)$$ out of line.        


Don't Forget to use open and close the mathematical text with equal number of dollar sign. If the mathematical text starts with single dollar, close it with single dollar. If the math text start with double dollar, finish it with double dollar.        
In a continuous  mathematical text, normally you need not to introduce any extra dollar-signs (other than the starting and ending). Because that may be recognized as a close signal, or some other complication or error. In the following examples, where-ever, commands contain the dollars, it means the ultimate terminal dollars for an individual example of mathematical text. While applying them to a larger mathematical text, those extra dollars in commands to be discarded.          
To display a new line, it is NOT compulsory to end a mathjax text ($Math-text-1 $ or $$Math-text-1 $$) and again start a new mathJax Text ( $ Math-text-2$ or  $$ Math-text-2$$). The usage of \\ command for line break within a single continuous MathJax paragraph, has been discussed soon below. 




this section is about recognition of MathJax commands by system. The  detailed commands for specific purpose, has been discussed below


Most commands in MathJax requires 'back-Slash' (\) :

most commands in MathJax format, will require the special character back-slash or \, usually at the starting-end (left-hand end) of the command. For just some examples,
$\log_5{25}=2$ is obtained from $\log_5{25}=$.
$\sqrt[2]{25}=5$ is obtained from $\sqrt[2]{25}=2$.
Greek letter lowercase  alpha (α) (in markdown &alpha;), in MathJax obtained from \alpha and gives output as $\alpha$. 


Back-Slash (\) is not to be confused with forward-slash (/) , also known as front-slash, stroke-mark, oblique, etc. 
this section is about general structure of MathJax commands. The  detailed commands for specific purpose, has been discussed below


Special commands may NOT require for some common tasks. (!)     


Common numerals (0-9), English alphabet (Uppercase: A-Z, Lowercase: a-z), common mathematical signs plus (+), minus (-), equals (=), decimal point (.) does not require special commands. (Verification Required. Not based on reference; only based on observation). 
Some special characters could be entered directly from keyboard, but there are more safe commands for them.
Such as less than (<), $a<b$ gives output as $a<b$.
But with command it could be written as $a\lt b$ that gives output as $a\lt b$.
Similarly, greater than (>), $a>b$ gives output as $a<b$.
But in command prompt it would be $a\gt b$ that gives rise to $a\gt b$. 


this section is about when we need not a MathJax commands. The  detailed commands for specific purpose, has been discussed below
!Status: Verification and improvement required 


Writing punctuation marks, special characters, writing normal-text, escaping 
execution.



Subscript and Superscript lettering 



Putting Space.    


MathJax allows us to write normal sentence, but it does not show the blank spaces ( $\require{cancel}\cancel{_b}$ ) entered by users. so, both AB and A(space)B reads like AB.
Example: $a b c$ gives $a b c$ .
To avoid this situation, command or code for space required.       


To display a tiny little space, use \, (i.e. Backslash Comma).
Such as $a\,b\,c$ gives $a\,b\,c$
To display a larger space, use \; (i.e. Backslash Semicolon).
Such as $a\;b\;c$ gives to $a\;b\;c$. 
To display more larger space, use \quad.
Such as $a\quad b\quad c$ gives to $a\quad b\quad c$.      
To display even more larger space, use \qquad.
Such as $a\qquad b\qquad c$ gives to $a\qquad b\qquad c$. 



Note that; we can't output spacebar directly; but there is function of spacebar in input. Such as a\quad b does not work if we remove all the space i.e. do (a\quadb). between quad and b, the space is working as a separator. $a\quadb$ gives $a\quadb$ i.e.  
  Error message. 
this section is about usage of spaces in MathJax commands. The  detailed commands for specific purpose, has been discussed below


Grouping: Curly braces i.e. { } functions in 'grouping' of characters as a single value. It also indicates taking a value for a function        


For one example, while using the command for power (^), if we want to write x-to-the-power-Twenty-three (x23) and write $x^23$, it will give $x^23$ i.e. x 2 3.  


To avoid this circumstance, we need to group that 23 as a single value that we are giving as input.
i.e. $x^{23}$ gives $x^{23}$. 
Similarly,
To write ${x^{y}}^z$, type ${x^{y}}^z$ , or in more typographic sense $x^{yz}$(renders to $x^{yz}$).
But to write $x^{y^{z}}$ type $x^{y^{z}}$.  
Similarly, to write the command for trigonometric functions like sine (\sin), cosine (\cos) etc;
to render $\sin{90^\circ}=\cos{0^\circ}=1$, use $\sin{90^\circ}=\cos{0^\circ}=1$. To write $\sin{90}$ use $\sin{90}$.
To write $\sin{90^\circ}+\cos{90^\circ}$ use $\sin{90^\circ}+\cos{90^\circ}$

Some operations that require two values at a time; may seek to put one value in some other form. 


For example,
$\sqrt[123]{45678}$ is obtained from $\sqrt[123]{45678}$. Here the radicand is being taken within curly braces '{ }' but the index of the root is being taken by square braces or []. 
$\log_{10}{10000}$ is obtained by \log_{10}{10000}. 



this section is about grouping characters or part of an equation into a single value (with MathJax commands). The  detailed commands for specific purpose, has been discussed below


Bracketing



Breaking into new lines:

Double backslash is command for line break. 


example:
$a+b=10\\
\Rightarrow a=10-b\\
\Rightarrow -a=-10+b$.
To write this, we have to type the followings:
$a+b=10\\
\Rightarrow a=10-b\\
\Rightarrow -a=-10+b$
If we omit the line break sign, \\, i.e. write as:
$a+b=10
\Rightarrow a=10-b
\Rightarrow -a=-10+b$; it will render as:
$a+b=10
\Rightarrow a=10-b
\Rightarrow -a=-10+b$.
i.e. all in a continuous line. 



this section is about creating multiple lines (within a single continuous section written in MathJax). The  detailed commands for specific purpose, has been discussed below

$$Writing \quad mathematical \quad terms, \quad units \quad etc$$


Writing Numbers. 



Writing variables. 



Writing Greek Letters.  



Writing Physical Quantities. 

(Will be discussed again in physics notation section below. This is an introductory mention in writing things)


Writing chemical formulae

(Will be discussed again in chemistry notation section below. This is an introductory mention in writing things)


Writing relationships like equations and inequalities. 



Writing chemical Equations. 

(Will be discussed again in Chemistry notation below. This is an introductory mention about how to write things)

$$Applying \quad different \quad functions \quad and \quad operators$$ 


ADDITION, SUBTRACTION, POSITIVE, NEGATIVE, PLUS-MINUS

Simple Plus and Minus do not require any command.      


Plus obtained by + (plus) sign of keyboard.
Such as $5+2$=7 gives output as $5+2=7$.     
Same for positive sign,
such as, to write $+5.6 \; Coulomb$ , type $+5.6  Coulomb$ (!). 
Similarly, minus obtained by Dash (-) key of the keyboard.
Such as $5-2=3$ gives $5-2=3$. 
Same for Negative sign. 
Such as to write $-5.6 \; Coulomb$ , type $-5.6 Coulomb$ (!)         

To write Plus-minus, i.e. , use \pm.       


Such as
$\pm$ gives $\pm$.
$\pm 5.6$ gives $\pm5.6$.
$40\pm 0.5$ gives $40\pm 0.5$
$\sqrt{4}=\pm 2$ gives $\sqrt{4}=\pm 2$           

To use Minus-Plus, i. e. , use \mp.        


Such as
$\mp$ gives $\mp$.
$\mp 5.6$ gives $\mp 5.6$.
$40\mp 0.5$ gives $40\mp 0.5$.
$-\sqrt{4}=\mp 2$ gives $-\sqrt{4}=\mp 2$.           

To write the plus within a circle, use \oplus. It is basically sign of  direct sum  (Stackexchange). But it could also be used as positive or plus polarity sign as sometimes done in physics, chemistry and biochemistry.                        


Such as$\oplus$  gives $\oplus$.
Superscript form: $^\oplus$, gives to $^\oplus$.
Subscript form: $_\oplus$ gives $_\oplus$                    

To write minus within a circle, use \ominus . This is basically mathematical sign for Symmetric difference, the same sign could be use to show  negative or minus  polarity sign as sometimes done in physics, chemistry and biochemistry.                   


Such as $\ominus$ gives $\ominus$.
Similarly it works with superscript i.e.  $^\ominus$  gives $^\ominus$.
Subscript form: $_ominus$ gives $_\ominus$    



Summation: 
(for details about integration sign, see calculus section below)
!Requires review. If there exist more-formal commands to write Units,
 plz inform


Multiplication. 


Algebraic variables expressed as letters, normally can be write side-wise. 


e.g. $xyz$ renders $xyz$.
$5xy$ renders $5x$.
$5(a+b)(c+d)(e+f-g)$ renders $5(a+b)(c+d)(e+f-g)$.      

For a centered dot use \cdot.  


e. g. $x\cdot y$ gives $x\cdot y$.
$a\cdot b\cdot \cdot c$ gives $a\cdot b \cdot c$.
$5\cdot x\cdot y$ renders $5 \cdot x \cdot y$.         
The full-stop sign gives the dot at a lower portion of line. So it increase chances of confusion with decimal points. So it is better to use \cdot to mean multiplication.
Such as $21.67 \cdot x \cdot (a+b) \cdot (c-d)$gives $21.67 \cdot x \cdot (a+b) \cdot (c-d)$.
Or to further avoid clash, brackets could be used, such as
$(21.67) \cdot x \cdot (a+b) \cdot (c-d)$gives $(21.67) \cdot x \cdot (a+b) \cdot (c-d)$.     

To get Cross-sign, use \times.   


Such as $5\times 6=30$ gives $5\times 6=30$. 
On traditional or lower level math text it is okay to use either dot ($\cdot$) or cross ($\times$), any one, for the same purpose. But when dot product ($\cdot$) and cross product ($\times$) matters, the 2 signs have separate meaning. 

Cross sign could be also included into (covered by) a circle with the command $\otimes$ , that gives $\otimes$. (it is basically sign of tensor product, but also a notation of magnetic polarity down the plane. Likewise another symbol $\odot$ for magnetic polarity that could be obtained from \odot.)
They will be again discussed in physics symbols below. Here mentioned due to similarity with multiplication signs cross ($\times$) and dot($\cdot$).      
Serial multiplication  or product of a sequence sign could be obtained by \prod. 


$\prod$ This is obtained from $\prod$. 





Division, Fraction and ratios.

To use division sign (÷) use  \div,    


Such as
$\div$ gives $\div$ .
$10\div 2=5$ gives $10\div 2=5$ .
similarly $(x+3)\div y(z-5)$ gives $(x+3)\div y(z-5)$
And $x=(y\div 6)$ gives $x=(y\div 6)$        

There are several ways to deal fraction sign or line of division. 


One way is to use the Slash (or front-slash) sign or /.      
Examples-
$q=x/y$ gives $q=x/y$ .
$r={(a+b)}/{(x+y)}$ gives $t={(a+b)}/{(x+y)}$ .
$s={a}+{(b/x)}+{y} $ gives $s={a}+{(b/x)}+{y}$ .
$t={a}+{b/{(x+y)}}$ gives $t={a}+{(b/{(x+y)})}$ .
$u={{(a+b)}/x}+{b}$ gives $u={({(a+b)}/x)}+{b}$  .
However
$v={a+b}/{x+y}$ gives $v={a+b}/{x+y}$ which is ambiguous.
It can mean  either
(A) ${v_1}=a+{(b/x)}-y$ obtained from ${v_2}=a+{(b/x)}-y$.
(B) ${v_2}={(a+b)}/{(x+y)}$ obtained from ${v_2}={(a+b)}/{x-y}$.            

Another method is use of command \frac. This command draws a horizontal division line.
General format: \frac{numerator}{denominator}.            


Examples: $\frac{numerator}{denominator}$ gives $\frac{numerator}{denominator}$ .
$\frac{a}{b}$ gives $\frac{a}{b}$ .
$\frac{100a+200.5b}{5x-0.005yz}$ gives $\frac{100a+200.5b}{5x-0.005yz}$ .
$\frac{(a+b)}{(c+d)}$ gives $\frac{(a+b)}{(c+d)}$ .
$\frac{(a+b) (c+d) (e+f)}{(x+y-z)} gives $\frac{(a+b) (c+d) (e+f)}{(x+y-z)}$.
$p=\frac{(a+b)}{(m+n)} renders to $p=\frac{(a+b)}{(m+n)}$ .
$\frac{q+r}{s+t}=\frac{(a+b)}{(c+d+e+f)}$ displays $\frac{q+r}{s+t}=\frac{(a+b)}{(c+d+e+f)}$ .
It is also possible to write more complex fractions.
For example,
$m=\frac{(\frac{A}{B})}{C}$ is obtained from $m=\frac{(\frac{A}{B})}{C}$ .
Similarly $n=\frac{(\frac{a+b}{c+d})}{x+y-z}$
is obtained from $n=\frac{(\frac{a+b}{c+d})}{x+y-z}$
Also ,
$p=\frac{A}{(\frac{B}{C})}$ is obtained from
$p=\frac{A}{(\frac{B}{C})}$ .
Similarly $q=\frac{a+b+m+n}{(\frac{c+d}{e+f})}$ 
obtained from $q=\frac{a+b+m+n}{(\frac{c+d}{e+f})}$.        

There is another method to draw horizontal division lines, command \over. Its function is same as \frac command, but much easier to format, because its placement is is in between numerator and denominator (like the / and \div).
General format: {{numerator}\over {denominator}}
Note that, here requires an extra (outermost) pair of curly braces. Otherwise  a \over command will consider whatever  at the left (before) side of \over command, as a numerator; and whatever at the right (after) side of \over, as a denominator.        


Examples;
${{numerator}\over {denominator}}$ gives ${{numerator}\over {denominator}}$
Similarly $a\over b$ gives $a\over b$
And ${{a+b}\over {c+d}}$ gives ${{a+b}\over {c+d}}$ .
Also ${{(a+b)\times(c+d)}\over {(x+y+z)}}$ gives ${{(a+b)\times(c+d)}\over {(x+y+z)}}$ .
The command \over is more suitable to complex fractions. 
Such as
${{A\over B}\over C}$ obtained from ${{A\over B}\over C}$ .
Similarly ${{{(a+b)(c-d)}\over{(m+m)(p+q)}}\over {(a+b)}}$ obtained from ${{{(a+b)(c-d)}\over{(m+m)(p+q)}}\over {(a+b)}}$ .
Also, ${A\over {B\over C}}$ obtained from ${A\over {B\over C}}$ .
Similarly ${ {(a+b)(c-d)}\over { {(m+n)(p-q)}\over {(w+x)(y-z)} } }$ obtained from
${ {(a+b)(c-d)}\over { {(m+n)(p-q)}\over {(w+x)(y-z)} } }$ . 
Why that extra (outermost) curly-braces are important while using \over command?
Lets see the following expression.
$x={{2(a+b)}\over {(c-d)}}=c$.
it has been written with $x={{2(a+b)} \over {(c-d)}=c$ .
If it was mistakenly written as
$x={2(a+b)}\over {(c-d)}=c$, it would give output as 
$x={2(a+b)}\over{c+d}=c$. i.e. That is wrong and undeserved.  

There is way to use mixture of slash (oblique) type divisions and horizontal type divisions together.     


Example : Now we'll try to to tackle the following two fractions (A) and (B) using firstly with/  and \frac (harder method); and then \ and \over (easier method).

Expression-A:
Using / and \frac :
${x}=\frac{(a+b)}{(c-d)}=(a+b)/(c-d)$ gives
${x}=\frac{(a+b)}{(c-d)}=(a+b)/(c-d)$. 
Similarly using / and \over  :
${x}={(a+b)}\over {(c-d)}= {(a+b)}/{(c-d)}$  gives
${x}={{(a+b)}\over {(c-d)}}= {(a+b)}/{(c-d)}$. 



.   

A brief Summary is coming soon.
(for each sections).  

Update:
I am in a temporary pause from Stackexchange. Will be back few months latter. 
......................

338: <p>This is a sandbox post for users to experiment with various Stack Exchange features. This question (and all answers) is a community wiki so that the reputation required to edit is lower. </p>

<p>Also, the user who owns this post is set to <a href="https://gardening.meta.stackexchange.com/users/-1/community">Community</a>, which is not a real user but a background process. So you needn't worry that some one might be notified by all your shenanigans here (do note that comments on others' answers will still notify them).</p>

<p>Feel free to post an answer (gibberish welcome), delete your answers as you wish, try out various formatting tricks, test out voting to close/delete, protect posts, test new privileges, whatever the hell you want (<a href="https://meta.stackexchange.com/questions/3122/formatting-sandbox">yes, really!</a>). Of course, as always, offensive content/spam will not be tolerated. </p>

<p>I merely request that you do not change the title of this post or add any new arbitrary tags. If you do cast the last close/delete vote or if it is not reopened, please let a ♦ moderator know so that we can reopen/undelete it. </p>

<p>Test edit to test rollbacks stuff</p>

<p>Feel free to modify the question below this line</p>

<hr>

<p>(This was copied from GL)</p>
 338: <p>.................................................................................................................................................................... ้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้</p>
 25568: <p>Heey Howdyyyyyyyyyyy Big big big thanks for your Witty post.</p>

<p>Some <a href="https://en.wikipedia.org/wiki/Abutilon_indicum" rel="nofollow noreferrer"><em>Abutilon indicum</em></a>  (<a href="https://en.wikipedia.org/wiki/Malvaceae" rel="nofollow noreferrer">malvaceae</a>) for you</p>

<p><a href="https://i.stack.imgur.com/vebXQ.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/vebXQ.png" alt="enter image description here"></a> </p>

<p><a href="https://i.stack.imgur.com/cuBqg.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/cuBqg.png" alt="enter image description here"></a> </p>

<p><a href="https://i.stack.imgur.com/l9AY4.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/l9AY4.png" alt="enter image description here"></a></p>

<p><a href="https://i.stack.imgur.com/R3hEn.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/R3hEn.jpg" alt="enter image description here"></a></p>
 338: <blockquote>
<p><strong>Thanks for your edit!</strong><br />
This edit will be visible only to you until it
is peer reviewed. Just kidding, your edit was horrible, and nobody cared enough to accept it.</p>
</blockquote>
<p>This is my magic wand:- ้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้้</p>
<p><strong>It's a ball...</strong><a href="http://upload.wikimedia.org/wikipedia/commons/4/4f/Soccer_ball_animated.svg" rel="nofollow noreferrer">http://upload.wikimedia.org/wikipedia/commons/4/4f/Soccer_ball_animated.svg</a> <strong>...Kick it.</strong></p>
<p><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><kbd><code>Wow, this is fun!</code></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></kbd></p>
<p>rè̑ͧ̌aͨl̘̝̙̃ͤ͂̾̆ ZA̡͊͠͝LGΌ ISͮ̂҉̯͈͕̹̘̱ TO͇̹̺ͅƝ̴ȳ̳ TH̘<b>Ë͖́̉ ͠P̯͍̭O̚​N̐Y̡</p>
<h1><sup>M<sub>e</sub></sup><sub>s<sup>s</sup></sub><sup><sub>e</sub>d</sup> up <sup><sub><sup><sub><sup><sub><sup><sub><sup><sub><sup><sub><sup><sub><sup><sub><sup><sub>This is the smallest text you will ever see... there is no way you are reading this unless you viewed the page source or edited my answer or something. This is tiny! Impossibly tiny! Yay! I still haven't filled up a single line with all this text :/ I STILL haven't! Wow! Okay now I filled up a line finally. I will just keep typing okay I don't know what to say.</sup></sub></sup></sub></sup></sub></sup></sub></sup></sub></sup></sub></sup></sub></sup></sub></sup></sub></h1>
<p><em>T</em><code>h</code><strong>is</strong> i<em>s</em> <code>s</code><em>ome</b></em> v<strong>e<i>r</i></strong><code>y</code> <a href="https://biology.stackexchange.com/questions/tagged/od" class="post-tag" title="show questions tagged &#39;od&#39;" rel="tag">od</a><kbd>d</kbd>   <sup><a href="https://biology.stackexchange.com/questions/tagged/f" class="post-tag" title="show questions tagged &#39;f&#39;" rel="tag">f</a><kbd>o</kbd></sup><sub><a href="https://biology.stackexchange.com/questions/tagged/r" class="post-tag" title="show questions tagged &#39;r&#39;" rel="tag">r</a><kbd>m</kbd></sub><sup>at</sup>ti<sub>ng.</sub></p>
<p><strong>Loading, please wait...</strong> <a href="http://web.archive.org/web/20120111193542/http://files.quickmediasolutions.com/throbber.svg" rel="nofollow noreferrer">http://web.archive.org/web/20120111193542/http://files.quickmediasolutions.com/throbber.svg</a></p>
<h1>Huh, didn't know this was possible.</h1>
<p>rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr</p>
<p>ก็็็็็็็็็็็็็็็็็็็็ กิิิิิิิิิิิิิิิิิิิิ ก้้้้้้้้้้้้้้้้้้้้ ಠ_ಠ ก็็็็็็็็็็็็็็็็็็็็ กิิิิิิิิิิิิิิิิิิิิ ก้้้้้้้้้้้้้้้้้้้้</p>
 25568: <p>Learning Formatting</p>

<p>From <a href="https://biology.meta.stackexchange.com/questions/3466/want-to-know-commands-codes-for-following-formatting-tasks">Want to know commands (codes) for following formatting tasks</a> </p>

<p>Really I need this sandbox for that. </p>

<p><strong>AB<em>C</em>D</strong></p>

<p>Underscore gave bold</p>

<p><a href="https://www.latex-tutorial.com/symbols/text-formatting/" rel="nofollow noreferrer">https://www.latex-tutorial.com/symbols/text-formatting/</a> </p>

<p>\texttt{Text}</p>

<p>\textbf{Text}   Oops</p>

<p>texttt{Text}  <a href="https://www.latex-tutorial.com/symbols/greek-alphabet/" rel="nofollow noreferrer">https://www.latex-tutorial.com/symbols/greek-alphabet/</a></p>

<p>B   \beta B    \epsilon E \theta \Theta  Oops their tutorial material doing nothing. Something tricky might be there which I'm missing.</p>

<p>Reading this one: <a href="https://www.latex-project.org/help/documentation/fntguide.pdf" rel="nofollow noreferrer">https://www.latex-project.org/help/documentation/fntguide.pdf</a></p>

<p>&deg;  </p>

<p>&amp; d e g  ; option by <a href="https://biology.meta.stackexchange.com/questions/3466/want-to-know-commands-codes-for-following-formatting-tasks">Want to know commands (codes) for following formatting tasks</a>  is working correctly.</p>

<p>&alpha; &Alpha;   &beta; &Beta;  &gamma; &Gamma; &delta;  &Delta; &epsilon; &Epsilon; &zeta; &Zeta; &eta; &Eta; &eta; &Eta; &theta; &Theta; &diams; &bull;</p>

<pre><code>                   &amp;alpha; &amp;Alpha;   &amp;beta; &amp;Beta;  &amp;gamma; &amp;Gamma; &amp;delta;  &amp;Delta; &amp;epsilon; &amp;Epsilon; &amp;zeta; &amp;Zeta; &amp;eta; &amp;Eta; &amp;eta; &amp;Eta; &amp;theta; &amp;Theta; &amp;diams; &amp;bull;
</code></pre>

<p>Several blank spaces at left side allow me quote the codes.</p>

<hr>

<p>I'm doing an experiment which is known as <a href="https://en.wikipedia.org/wiki/Titration" rel="nofollow noreferrer">titration</a>. I'm finding how many blank spaces is required to become able to quote the code. </p>

<p>Here I use the keyboard as a sort of <a href="https://en.wikipedia.org/wiki/Burette" rel="nofollow noreferrer">burette</a> and the screen as <a href="https://en.wikipedia.org/wiki/Erlenmeyer_flask" rel="nofollow noreferrer">conical flask</a> also known as Erlenmeyer flask</p>

<p>The analyte is the code inside (but excluding) quotation marks: </p>

<pre><code>          "&amp;alpha; &amp;Alpha;   &amp;beta; &amp;Beta;  &amp;gamma; &amp;Gamma; &amp;delta;  &amp;Delta; &amp;epsilon; &amp;Epsilon; &amp;zeta; &amp;Zeta; &amp;eta; &amp;Eta; &amp;eta; &amp;Eta; &amp;theta; &amp;Theta;"
</code></pre>

<hr>

<p>Experiment result: in the following table (ladder?) the number of drops of pure raw space-bars ; and correspondent result is present: </p>

<hr>

<p>0 (Zero) Space:</p>

<p>&alpha; &Alpha;   &beta; &Beta;  &gamma; &Gamma; &delta;  &Delta; &epsilon; &Epsilon; &zeta; &Zeta; &eta; &Eta; &eta; &Eta; &theta; &Theta;</p>

<p>1 space:</p>

<p>&alpha; &Alpha;   &beta; &Beta;  &gamma; &Gamma; &delta;  &Delta; &epsilon; &Epsilon; &zeta; &Zeta; &eta; &Eta; &eta; &Eta; &theta; &Theta;</p>

<p>2 spaces</p>

<p>&alpha; &Alpha;   &beta; &Beta;  &gamma; &Gamma; &delta;  &Delta; &epsilon; &Epsilon; &zeta; &Zeta; &eta; &Eta; &eta; &Eta; &theta; &Theta;</p>

<p>3 spaces:</p>

<p>&alpha; &Alpha;   &beta; &Beta;  &gamma; &Gamma; &delta;  &Delta; &epsilon; &Epsilon; &zeta; &Zeta; &eta; &Eta; &eta; &Eta; &theta; &Theta;</p>

<p>4 spaces: </p>

<pre><code>&amp;alpha; &amp;Alpha;   &amp;beta; &amp;Beta;  &amp;gamma; &amp;Gamma; &amp;delta;  &amp;Delta; &amp;epsilon; &amp;Epsilon; &amp;zeta; &amp;Zeta; &amp;eta; &amp;Eta; &amp;eta; &amp;Eta; &amp;theta; &amp;Theta; 
</code></pre>

<p><em>grey coloration</em> appears on 4 </p>

<p>5 spaces:</p>

<pre><code> &amp;alpha; &amp;Alpha;   &amp;beta; &amp;Beta;  &amp;gamma; &amp;Gamma; &amp;delta;  &amp;Delta; &amp;epsilon; &amp;Epsilon; &amp;zeta; &amp;Zeta; &amp;eta; &amp;Eta; &amp;eta; &amp;Eta; &amp;theta; &amp;Theta; 
</code></pre>

<hr>

<p>Experiment discontinued</p>

<hr>

<p>CONCLUSION:</p>

<p>It takes 4 drops (successive obviously) of space bars at left side (start) of the line to quote the code.</p>

<p>:)</p>

<h2>---------</h2>

<p>াাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাাীীীীীীীীীীীীীীীীীুুুুুুুুুুুুুুুুুুুুুুুুুুুুুুু</p>

<p>trying to create that magic wand.</p>

<p>ঁঁঁঁঁঁঁঁঁঁঁঁঁঁ</p>

<p>(অীীীী)ীীীুুুুুুুুুুুুুুুুুূূূোো</p>

<blockquote>
  <p>Copy paste from Chat Reply</p>
</blockquote>

<h2>Q</h2>

<pre><code>      #Formatting Besides specialized command for chemistry equations like , 

      $\ce{HCl}$ dissociates in water as follows:   

      $$\ce{H2O + HCl &lt;=&gt; H3O+ + Cl-}$$ 
</code></pre>

<p>; is there any simple command for subscript and superscripts for general purpose?</p>

<p>@AlwaysConfused Yes:</p>

<pre><code>          &lt;sub&gt;subscript&lt;/sub&gt; and 
          &lt;sup&gt;superscript&lt;/sup&gt; on the main site
</code></pre>

<ul>
<li>User@Terdon</li>
</ul>

<p><a href="https://biology.stackexchange.com/editing-help#comment-formatting">https://biology.stackexchange.com/editing-help#comment-formatting</a></p>

<p><a href="https://en.wikipedia.org/wiki/Floater" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Floater</a>
<a href="https://en.wikipedia.org/wiki/Floater" rel="nofollow noreferrer">that secret</a>
<a href="https://en.wikipedia.org/wiki/Floater" rel="nofollow noreferrer">that secret</a></p>
 25568: <p>$$LEARNING \quad  the \quad MATHJAX$$ </p>

<p>$$(my \quad MathJax \quad notebook)$$ </p>

<hr>

<p>I've tried to write the things in a systematic manner; i.e, when the reader have a query about a plus-related problem, the visitor will find it on respective paragraph. Similarly when the user have a question about division, fraction and ratio; all the symbols would be found in the respective paragraph. </p>

<hr>

<h2><strong>Part-1 : Reference and resources.</strong></h2>

<p>Main Stack-Exchange Articles: </p>

<ul>
<li><ol>
<li><a href="https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference">MathJax basic tutorial and quick reference</a> on <a href="https://math.meta.stackexchange.com">Mathematics SE Meta</a></li>
</ol></li>
<li><ol start="2">
<li><a href="https://chemistry.meta.stackexchange.com/questions/86/how-can-i-format-math-chemistry-expressions-here">Formatting Chemistry equations with MathJax.</a>  on <a href="https://chemistry.meta.stackexchange.com">Chemistry SE Meta</a> </li>
</ol></li>
</ul>

<p>Other useful Stack-exchange articles</p>

<ul>
<li><ol start="3">
<li><a href="https://chemistry.meta.stackexchange.com/questions/3540/what-additional-formatting-features-are-available-to-mathjax-possibly-via-requ">What additional formatting features are available to MathJax?</a> on Chemistry SE meta. </li>
</ol></li>
<li><ol start="4">
<li><a href="https://chemistry.meta.stackexchange.com/questions/3044/hidden-points-of-editing-you-probably-didnt-know">Hidden points of editing you probably didn't know</a> on chemistry SE meta. </li>
</ol></li>
<li><ol start="5">
<li><a href="https://chemistry.meta.stackexchange.com/questions/3286/how-to-write-physical-units/3287#3287">How to write physical units</a>. on Chemistry SE Meta. </li>
</ol></li>
<li><ol start="6">
<li><a href="https://chemistry.meta.stackexchange.com/questions/3738/how-to-render-angstrom-and-parts-per-notations-in-mathjax">How to render Angstrom and Parts-per notations in MathJax?</a> on Chemistry SE Meta. </li>
</ol></li>
<li><ol start="7">
<li><a href="https://physics.meta.stackexchange.com/questions/4233/how-do-i-format-a-physical-quantity-unit-of-measurement-numerical-value">How do I format a physical quantity (unit of measurement + numerical value)?</a> on physics SE meta. </li>
</ol></li>
<li><ol start="8">
<li><a href="https://physics.meta.stackexchange.com/questions/1233/math-and-si-formatting-buttons">Math and SI formatting</a> on Physics SE meta. </li>
</ol></li>
<li><ol start="9">
<li><a href="https://electronics.meta.stackexchange.com/questions/3164/rendering-units-in-mathjax">Rendering units in MathJaX</a> in Electrical Engineering Stackexchange Meta. </li>
</ol></li>
<li><ol start="10">
<li><a href="https://physics.meta.stackexchange.com/questions/6463/mathjax-how-do-i-write-matrices-on-the-same-line">MathJax: How do I write matrices on the same line?</a></li>
</ol></li>
</ul>

<p>MathJax Official Website</p>

<ul>
<li><ol start="11">
<li>MathJax <a href="https://www.mathjax.org/" rel="nofollow noreferrer">official website</a>. </li>
</ol></li>
<li><ol start="12">
<li>MathJax <a href="https://docs.mathjax.org/en/latest/" rel="nofollow noreferrer">Documentation page</a>. </li>
</ol></li>
<li><ol start="13">
<li>MathJax <a href="https://www.mathjax.org/#features" rel="nofollow noreferrer">features</a> and <a href="https://www.mathjax.org/#modal-livedemo" rel="nofollow noreferrer">Test Page</a>. </li>
</ol></li>
</ul>

<p>Other Online Resources: </p>

<ul>
<li><ol start="14">
<li><a href="https://cdn.rawgit.com/mathjax/MathJax/2.7.1/test/examples.html" rel="nofollow noreferrer">MathJax Example pages</a> and <a href="https://cdn.rawgit.com/mathjax/MathJax/2.7.1/test/sample-dynamic.html" rel="nofollow noreferrer">Test typing</a>. </li>
</ol></li>
<li><ol start="15">
<li>Wikipedia Article on <a href="https://en.wikipedia.org/wiki/MathJax" rel="nofollow noreferrer">MathJax</a>. </li>
</ol></li>
<li><ol start="16">
<li>Wikipedia <a href="https://en.wikipedia.org/wiki/Help:Displaying_a_formula" rel="nofollow noreferrer">Help:Displaying a formula</a> and <a href="https://en.wikipedia.org/wiki/Wikipedia:Rendering_math" rel="nofollow noreferrer">Wikipedia:Rendering math</a> also mentions MathJax commands. </li>
</ol></li>
<li><ol start="17">
<li><a href="https://en.wikipedia.org/wiki/List_of_mathematical_symbols" rel="nofollow noreferrer">List of mathematical symbols</a></li>
</ol></li>
</ul>

<p><strong>Other quick references</strong> </p>

<ul>
<li>On a math expression formatted with MathJax; do a right-click (mouse secondary button). That would give following dropdown menu.   

<blockquote>
  <p><a href="https://i.stack.imgur.com/1mvBy.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/1mvBy.png" alt="Dropdown menu"></a>.<br>
  On this dropdown list; take help of "Show math as" (and then --> TeX commands) which will show the command prompt required to design the math expression. And also take help of "MathJax Help", which gives some help as well as gives a link to MathJax <a href="https://www.mathjax.org/" rel="nofollow noreferrer">official site</a>. </p>
</blockquote></li>
</ul>

<hr>

<hr>

<h2>Part-2 : The tutorial.</h2>

<p><strong>Content</strong></p>

<ul>
<li><ol>
<li>Recognition of MathJax Commands. </li>
</ol></li>
<li><ol start="2">
<li>Most MathJax command involves Back-Slash.  </li>
</ol></li>
<li><ol start="3">
<li>Special commands may not require in some cases. </li>
</ol></li>
<li><ol start="4">
<li>Writing punctuation marks, special characters, writing normal text, escaping execution. </li>
</ol></li>
<li><ol start="5">
<li>Subscript and Superscript lettering</li>
</ol></li>
<li><ol start="6">
<li>Putting space. </li>
</ol></li>
<li><ol start="7">
<li>Grouping some characters as a single thing. </li>
</ol></li>
<li><ol start="8">
<li>Bracketing. </li>
</ol></li>
<li><ol start="9">
<li>Breaking into new lines. </li>
</ol></li>
<li><ol start="10">
<li>Writing Numbers. </li>
</ol></li>
<li><ol start="11">
<li>Writing variables. </li>
</ol></li>
<li><ol start="12">
<li>Writing Greek letters</li>
</ol></li>
<li><ol start="13">
<li>Writing Physical Quantities. </li>
</ol></li>
<li><ol start="14">
<li>Writing Chemical formula. </li>
</ol></li>
<li><ol start="15">
<li>Writing relationships like equations and inequalities. </li>
</ol></li>
<li><ol start="16">
<li>Writing Chemical equations.</li>
</ol></li>
<li><ol start="17">
<li>Addition, Subtraction, Positive, Negative and Plus-minus. </li>
</ol></li>
<li><ol start="18">
<li>Multiplication. </li>
</ol></li>
<li><ol start="19">
<li>Division, fraction, ratios. </li>
</ol></li>
<li><ol start="20">
<li>Power, Root, Logarithm.   </li>
</ol></li>
<li><ol start="21">
<li>Trigonometric functions and inverse trigonometric functions.   </li>
</ol></li>
<li><ol start="22">
<li>Modern algebra, Set- theory and logic.  </li>
</ol></li>
<li><ol start="23">
<li>Geometry.  </li>
</ol></li>
<li><ol start="24">
<li>Matrix, Tables, arrays.  </li>
</ol></li>
<li><ol start="25">
<li>PHYSICS formatting </li>
</ol></li>
<li><ol start="26">
<li>CHEMISTRY Formatting.  </li>
</ol></li>
<li><ol start="27">
<li>STATISTICS formatting.      </li>
</ol></li>
</ul>

<hr>

<p><strong>Inside :</strong></p>

<hr>

<p>$$Basic \quad Structure$$</p>

<hr>

<ol>
<li><p><strong>Recognition of MathJax input</strong>: </p>

<ul>
<li>The <strong>Dollar sign</strong> ( <code>$</code> ) works as a label or indicator of MathJax input. System will recognize the part text as Mathjax input with help of dollars used in input. 

<ul>
<li>To write math-expressions within line of normal text; cover the expression with <strong>single dollar</strong> sign at start and end. Such as<br>
<code>$2+2=4$</code> gives you $2+2=4$ within the line within normal text.<br>
Similarly <code>$2^2=4$</code> gives $2^2=4$ , within the line. </li>
<li>To display mathematical expressions in a separate paragraph, cover the expression within <strong>double dollar</strong> (i.e. at start of expression a double dollar (<code>$$</code>), at end of expression again double dollar (<code>$$</code>).<br>
Such as within line <code>$$(x+y)^2=(x^2)+(2xy)+(y^2)$$</code> 
will give $$(x+y)^2=(x^2)+(2xy)+(y^2)$$ out of line.        

<ul>
<li>Don't Forget to use open and close the mathematical text with equal number of dollar sign. If the mathematical text starts with single dollar, close it with single dollar. If the math text start with double dollar, finish it with double dollar.        </li>
<li>In a continuous  mathematical text, normally you need not to introduce any extra dollar-signs (other than the starting and ending). Because that may be recognized as a close signal, or some other complication or error. <em>In the following examples, where-ever, commands contain the dollars, it means the ultimate terminal dollars for an individual example of mathematical text.</em> While applying them to a larger mathematical text, those extra dollars in commands to be discarded.          </li>
<li>To display a new line, it is NOT compulsory to end a mathjax text (<code>$</code>Math-text-1 <strong><code>$</code></strong> or <code>$$</code>Math-text-1 <strong><code>$$</code></strong>) and again start a new mathJax Text ( <strong><code>$</code></strong> Math-text-2<code>$</code> or  <strong><code>$$</code></strong> Math-text-2<code>$$</code>). The usage of <code>\\</code> command for line break within a single continuous MathJax paragraph, has been discussed soon below. </li>
</ul></li>
</ul></li>
</ul></li>
</ol>

<p><sub><sub>this section is about recognition of MathJax commands by system. The  detailed commands for specific purpose, has been discussed below</sub></sub></p>

<hr>

<ol start="2">
<li><strong>Most commands in MathJax requires 'back-Slash' (<code>\</code>) :</strong> 

<ul>
<li>most commands in MathJax format, will require the special character <a href="https://en.wikipedia.org/wiki/Backslash" rel="nofollow noreferrer">back-slash</a> or <code>\</code>, usually at the <strong>starting-end</strong> (left-hand end) of the command. For just some examples,<br>
$\log_5{25}=2$ is obtained from <code>$\log_5{25}=$</code>.<br>
$\sqrt[2]{25}=5$ is obtained from <code>$\sqrt[2]{25}=2$</code>.<br>
Greek letter lowercase  alpha (&alpha;) (in markdown <code>&amp;alpha;</code>), in MathJax obtained from <code>\alpha</code> and gives output as $\alpha$. </li>
</ul></li>
</ol>

<p>Back-Slash (<code>\</code>) is not to be confused with <a href="https://en.wikipedia.org/wiki/Slash_(punctuation)" rel="nofollow noreferrer">forward-slash</a> (<code>/</code>) , also known as front-slash, stroke-mark, oblique, etc. </p>

<p><sub><sub>this section is about general structure of MathJax commands. The  detailed commands for specific purpose, has been discussed below</sub></sub></p>

<hr>

<ol start="3">
<li><strong>Special commands may NOT require for some common tasks.</strong> (<code>!</code>)     

<ul>
<li>Common numerals (<code>0-9</code>), English alphabet (Uppercase: <code>A-Z</code>, Lowercase: <code>a-z</code>), common mathematical signs plus (<code>+</code>), minus (<code>-</code>), equals (<code>=</code>), decimal point (<code>.</code>) does not require special commands. <strong>(<em>Verification Required</em>. Not based on reference; only based on observation)</strong>. </li>
<li>Some special characters could be entered directly from keyboard, but there are more safe commands for them.<br>
Such as less than (<code>&lt;</code>), <code>$a&lt;b$</code> gives output as $a&lt;b$.<br>
But with command it could be written as <code>$a\lt b$</code> that gives output as $a\lt b$.<br>
Similarly, greater than (<code>&gt;</code>), <code>$a&gt;b$</code> gives output as $a&lt;b$.<br>
But in command prompt it would be <code>$a\gt b$</code> that gives rise to $a\gt b$. </li>
</ul></li>
</ol>

<p><sub><sub>this section is about when we need not a MathJax commands. The  detailed commands for specific purpose, has been discussed below</sub></sub></p>

<p><code>!</code><sub><sub>Status: Verification and improvement required </sub></sub></p>

<hr>

<ol start="4">
<li><strong>Writing punctuation marks, special characters, writing normal-text, escaping 
execution.</strong></li>
</ol>

<hr>

<ol start="5">
<li><strong>Subscript and Superscript lettering</strong> </li>
</ol>

<hr>

<ol start="6">
<li><strong>Putting Space</strong>.    

<ul>
<li>MathJax allows us to write normal sentence, but it does not show the blank spaces ( $\require{cancel}\cancel{_b}$ ) entered by users. so, both AB and A(space)B reads like AB.<br>
Example: <code>$a b c$</code> gives $a b c$ .<br>
To avoid this situation, command or code for space required.       

<ul>
<li>To display a tiny little space, use <code>\,</code> (i.e. Backslash Comma).<br>
Such as <code>$a\,b\,c$</code> gives $a\,b\,c$</li>
<li>To display a larger space, use <code>\;</code> (i.e. Backslash Semicolon).<br>
Such as <code>$a\;b\;c$</code> gives to $a\;b\;c$. </li>
<li>To display more larger space, use <code>\quad</code>.<br>
Such as <code>$a\quad b\quad c$</code> gives to $a\quad b\quad c$.      </li>
<li>To display even more larger space, use <code>\qquad</code>.<br>
Such as <code>$a\qquad b\qquad c$</code> gives to $a\qquad b\qquad c$. </li>
</ul></li>
</ul></li>
</ol>

<p>Note that; we can't output spacebar directly; but there is function of spacebar in input. Such as <code>a\quad b</code> does not work if we remove all the space i.e. do (<strike><code>a\quadb</code></strike>). between quad and b, the space is working as a separator. <strike><code>$a\quadb$</code></strike> gives $a\quadb$ i.e.  </p>

<p><a href="https://i.stack.imgur.com/6A27m.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/6A27m.png" alt="error message"></a>  Error message. </p>

<p><sub><sub>this section is about usage of spaces in MathJax commands. The  detailed commands for specific purpose, has been discussed below</sub></sub></p>

<hr>

<ol start="7">
<li><strong>Grouping: Curly braces i.e. <code>{ }</code> functions in <em>'grouping'</em> of characters as a <em>single</em> value.</strong> It also indicates <strong>taking a value</strong> for a function        

<ul>
<li>For one example, while using the command for power (<code>^</code>), if we want to write x-to-the-power-Twenty-three (x<sup>23</sup>) and write <code>$x^23$</code>, it will give $x^23$ i.e. x <sup>2</sup> 3.  

<ul>
<li>To avoid this circumstance, we need to group that 23 as a single value that we are giving as input.<br>
i.e. <code>$x^{23}$</code> gives $x^{23}$. </li>
<li>Similarly,<br>
To write ${x^{y}}^z$, type <code>${x^{y}}^z$</code> , or in more typographic sense <code>$x^{yz}$</code>(renders to $x^{yz}$).<br>
But to write $x^{y^{z}}$ type <code>$x^{y^{z}}$</code>.  </li>
<li>Similarly, to write the command for trigonometric functions like sine (<code>\sin</code>), cosine (<code>\cos</code>) etc;<br>
to render $\sin{90^\circ}=\cos{0^\circ}=1$, use <code>$\sin{90^\circ}=\cos{0^\circ}=1$</code>. To write $\sin{90}$ use <code>$\sin{90}$</code>.<br>
To write $\sin{90^\circ}+\cos{90^\circ}$ use <code>$\sin{90^\circ}+\cos{90^\circ}$</code></li>
</ul></li>
<li>Some operations that require two values at a time; may seek to put one value in some other form. 

<ul>
<li>For example,<br>
$\sqrt[123]{45678}$ is obtained from <code>$\sqrt[123]{45678}$</code>. Here the radicand is being taken within curly braces '{ }' but the index of the root is being taken by square braces or <code>[]</code>. </li>
<li>$\log_{10}{10000}$ is obtained by <code>\log_{10}{10000}</code>. </li>
</ul></li>
</ul></li>
</ol>

<p><sub><sub>this section is about grouping characters or part of an equation into a single value (with MathJax commands). The  detailed commands for specific purpose, has been discussed below</sub></sub></p>

<hr>

<ol start="8">
<li><strong>Bracketing</strong></li>
</ol>

<hr>

<ol start="9">
<li><strong>Breaking into new lines:</strong> 

<ul>
<li>Double backslash is command for line break. 

<ul>
<li>example:<br>
$a+b=10\\
\Rightarrow a=10-b\\
\Rightarrow -a=-10+b$.<br>
To write this, we have to type the followings:<br>
<code>$a+b=10\\</code><br>
<code>\Rightarrow a=10-b\\</code><br>
<code>\Rightarrow -a=-10+b$</code>
If we omit the line break sign, <code>\\</code>, i.e. write as:<br>
<strike><code>$a+b=10</code></strike><br>
<strike><code>\Rightarrow a=10-b</code></strike><br>
<strike><code>\Rightarrow -a=-10+b$</code></strike>; it will render as:<br>
$a+b=10
\Rightarrow a=10-b
\Rightarrow -a=-10+b$.<br>
i.e. all in a continuous line. </li>
</ul></li>
</ul></li>
</ol>

<p><sub><sub>this section is about creating multiple lines (within a single continuous section written in MathJax). The  detailed commands for specific purpose, has been discussed below</sub></sub></p>

<hr>

<p>$$Writing \quad mathematical \quad terms, \quad units \quad etc$$</p>

<hr>

<ol start="10">
<li><strong>Writing Numbers</strong>. </li>
</ol>

<hr>

<ol start="11">
<li><strong>Writing variables</strong>. </li>
</ol>

<hr>

<ol start="12">
<li><strong>Writing Greek Letters</strong>.  </li>
</ol>

<hr>

<ol start="13">
<li><strong>Writing Physical Quantities.</strong>  </li>
</ol>

<p><sub>(Will be discussed again in physics notation section below. This is an introductory mention in writing things)</sub></p>

<hr>

<ol start="14">
<li><strong>Writing chemical formulae</strong></li>
</ol>

<p><sub>(Will be discussed again in chemistry notation section below. This is an introductory mention in writing things)</sub></p>

<hr>

<ol start="15">
<li><strong>Writing relationships like equations and inequalities.</strong>   </li>
</ol>

<hr>

<ol start="16">
<li><strong>Writing chemical Equations.</strong> </li>
</ol>

<p>(Will be discussed again in Chemistry notation below. This is an introductory mention about how to write things)</p>

<hr>

<p>$$Applying \quad different \quad functions \quad and \quad operators$$ </p>

<hr>

<ol start="17">
<li><strong>ADDITION, SUBTRACTION, POSITIVE, NEGATIVE, PLUS-MINUS</strong>         

<ul>
<li>Simple Plus and Minus do not require any command.      

<ul>
<li>Plus obtained by <code>+</code> (plus) sign of keyboard.<br>
Such as <code>$5+2$=7</code> gives output as $5+2=7$.     </li>
<li>Same for positive sign,<br>
such as, to write $+5.6 \; Coulomb$ , type <code>$+5.6  Coulomb$</code> (<code>!</code>). </li>
<li>Similarly, minus obtained by Dash (<code>-</code>) key of the keyboard.<br>
Such as <code>$5-2=3$</code> gives $5-2=3$. </li>
<li>Same for Negative sign. 
Such as to write $-5.6 \; Coulomb$ , type <code>$-5.6 Coulomb$</code> (<code>!</code>)         </li>
</ul></li>
<li>To write Plus-minus, i.e. <a href="https://i.stack.imgur.com/M2nhc.gif" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/M2nhc.gif" alt="plus-minus"></a>, use <code>\pm</code>.       

<ul>
<li>Such as<br>
<code>$\pm$</code> gives $\pm$.<br>
<code>$\pm 5.6$</code> gives $\pm5.6$.<br>
<code>$40\pm 0.5$</code> gives $40\pm 0.5$<br>
<code>$\sqrt{4}=\pm 2$</code> gives $\sqrt{4}=\pm 2$           </li>
</ul></li>
<li>To use Minus-Plus, i. e. <a href="https://i.stack.imgur.com/fvUtz.gif" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/fvUtz.gif" alt="minus-plus"></a>, use <code>\mp</code>.        

<ul>
<li>Such as<br>
<code>$\mp$</code> gives $\mp$.<br>
<code>$\mp 5.6$</code> gives $\mp 5.6$.<br>
<code>$40\mp 0.5$</code> gives $40\mp 0.5$.<br>
<code>$-\sqrt{4}=\mp 2$</code> gives $-\sqrt{4}=\mp 2$.           </li>
</ul></li>
<li>To write the plus within a circle, use <code>\oplus</code>. It is basically sign of  <a href="https://en.wikipedia.org/wiki/Direct_sum" rel="nofollow noreferrer">direct sum</a>  (<a href="https://math.stackexchange.com/questions/340637/what-does-the-plus-sign-contained-in-a-circle-oplus-mean-in-this-case">Stackexchange</a>). But it could also be used as <em>positive or plus polarity</em> sign as sometimes done in physics, chemistry and biochemistry.                        

<ul>
<li>Such as<code>$\oplus$</code>  gives $\oplus$.<br>
Superscript form: <code>$^\oplus$</code>, gives to $^\oplus$.<br>
Subscript form: <code>$_\oplus$</code> gives $_\oplus$                    </li>
</ul></li>
<li>To write minus within a circle, use <code>\ominus</code> . This is basically mathematical sign for <a href="https://en.wikipedia.org/wiki/Symmetric_difference" rel="nofollow noreferrer">Symmetric difference</a>, the same sign could be use to show  <em>negative or minus  polarity</em> sign as sometimes done in physics, chemistry and biochemistry.                   

<ul>
<li>Such as <code>$\ominus$</code> gives $\ominus$.<br>
Similarly it works with superscript i.e.  <code>$^\ominus$</code>  gives $^\ominus$.<br>
Subscript form: <code>$_ominus$</code> gives $_\ominus$    </li>
</ul></li>
</ul></li>
</ol>

<p>Summation: </p>

<p>(for details about integration sign, see calculus section below)</p>

<p><code>!</code><sub>Requires review. If there exist more-formal commands to write Units,
 plz inform</sub></p>

<hr>

<ol start="18">
<li><strong>Multiplication</strong>. 

<ul>
<li>Algebraic variables expressed as letters, normally can be write side-wise. 

<ul>
<li>e.g. <code>$xyz$</code> renders $xyz$.<br>
<code>$5xy$</code> renders $5x$.<br>
<code>$5(a+b)(c+d)(e+f-g)$</code> renders $5(a+b)(c+d)(e+f-g)$.      </li>
</ul></li>
<li>For a centered dot use <code>\cdot</code>.  

<ul>
<li>e. g. <code>$x\cdot y$</code> gives $x\cdot y$.<br>
<code>$a\cdot b\cdot \cdot c$</code> gives $a\cdot b \cdot c$.<br>
<code>$5\cdot x\cdot y$</code> renders $5 \cdot x \cdot y$.         </li>
<li>The full-stop sign gives the dot at a lower portion of line. So it increase chances of confusion with decimal points. So it is better to use <code>\cdot</code> to mean multiplication.<br>
Such as <code>$21.67 \cdot x \cdot (a+b) \cdot (c-d)$</code>gives $21.67 \cdot x \cdot (a+b) \cdot (c-d)$.<br>
Or to further avoid clash, brackets could be used, such as<br>
<code>$(21.67) \cdot x \cdot (a+b) \cdot (c-d)$</code>gives $(21.67) \cdot x \cdot (a+b) \cdot (c-d)$.     </li>
</ul></li>
<li>To get Cross-sign, use <code>\times</code>.   

<ul>
<li>Such as <code>$5\times 6=30$</code> gives $5\times 6=30$. </li>
<li>On traditional or lower level math text it is okay to use either dot ($\cdot$) or cross ($\times$), any one, for the same purpose. But when <a href="https://en.wikipedia.org/wiki/Dot_product" rel="nofollow noreferrer">dot product</a> ($\cdot$) and <a href="https://en.wikipedia.org/wiki/Cross_product" rel="nofollow noreferrer">cross product</a> ($\times$) matters, the 2 signs have separate meaning. </li>
</ul></li>
<li>Cross sign could be also included into (covered by) a circle with the command <code>$\otimes$</code> , that gives $\otimes$. (it is basically sign of <a href="https://en.wikipedia.org/wiki/Tensor_product" rel="nofollow noreferrer">tensor product</a>, but also a notation of magnetic polarity down the plane. Likewise another symbol $\odot$ for magnetic polarity that could be obtained from <code>\odot</code>.)<br>
<sub>They will be again discussed in physics symbols below. Here mentioned due to similarity with multiplication signs cross ($\times$) and dot($\cdot$)</sub>.      </li>
<li>Serial multiplication  or <a href="https://en.wikipedia.org/wiki/Multiplication#Products_of_sequences" rel="nofollow noreferrer">product of a sequence</a> sign could be obtained by <code>\prod</code>. 

<ul>
<li>$\prod$ This is obtained from <code>$\prod$</code>. </li>
</ul></li>
</ul></li>
</ol>

<hr>

<ol start="19">
<li><strong>Division, Fraction and ratios.</strong> 

<ul>
<li>To use division sign (÷) use  <code>\div</code>,    

<ul>
<li>Such as<br>
<code>$\div$</code> gives $\div$ .<br>
<code>$10\div 2=5$</code> gives $10\div 2=5$ .<br>
similarly <code>$(x+3)\div y(z-5)$</code> gives $(x+3)\div y(z-5)$<br>
And <code>$x=(y\div 6)$</code> gives $x=(y\div 6)$        </li>
</ul></li>
<li>There are several ways to deal fraction sign or line of division. 

<ul>
<li>One way is to use the Slash (or front-slash) sign or <code>/</code>.      </li>
<li>Examples-<br>
<code>$q=x/y$</code> gives $q=x/y$ .<br>
<code>$r={(a+b)}/{(x+y)}$</code> gives $t={(a+b)}/{(x+y)}$ .<br>
<code>$s={a}+{(b/x)}+{y} $</code> gives $s={a}+{(b/x)}+{y}$ .<br>
<code>$t={a}+{b/{(x+y)}}$</code> gives $t={a}+{(b/{(x+y)})}$ .<br>
<code>$u={{(a+b)}/x}+{b}$</code> gives $u={({(a+b)}/x)}+{b}$  .<br>
However<br>
<strike><code>$v={a+b}/{x+y}$</code></strike> gives $v={a+b}/{x+y}$ which is ambiguous.<br>
It can mean  either<br>
(A) ${v_1}=a+{(b/x)}-y$ obtained from <code>${v_2}=a+{(b/x)}-y$</code>.<br>
(B) ${v_2}={(a+b)}/{(x+y)}$ obtained from <code>${v_2}={(a+b)}/{x-y}$</code>.            </li>
</ul></li>
<li>Another method is use of command <code>\frac</code>. This command draws a horizontal division line.<br>
<strong>General format</strong>: <code>\frac{numerator}{denominator}</code>.            

<ul>
<li>Examples: <code>$\frac{numerator}{denominator}$</code> gives $\frac{numerator}{denominator}$ .<br>
<code>$\frac{a}{b}$</code> gives $\frac{a}{b}$ .<br>
<code>$\frac{100a+200.5b}{5x-0.005yz}$</code> gives $\frac{100a+200.5b}{5x-0.005yz}$ .<br>
<code>$\frac{(a+b)}{(c+d)}$</code> gives $\frac{(a+b)}{(c+d)}$ .<br>
<code>$\frac{(a+b) (c+d) (e+f)}{(x+y-z)}</code> gives $\frac{(a+b) (c+d) (e+f)}{(x+y-z)}$.<br>
<code>$p=\frac{(a+b)}{(m+n)}</code> renders to $p=\frac{(a+b)}{(m+n)}$ .<br>
$\frac{q+r}{s+t}=\frac{(a+b)}{(c+d+e+f)}$ displays $\frac{q+r}{s+t}=\frac{(a+b)}{(c+d+e+f)}$ .<br>
It is also possible to write more complex fractions.<br>
For example,<br>
$m=\frac{(\frac{A}{B})}{C}$ is obtained from <code>$m=\frac{(\frac{A}{B})}{C}$</code> .<br>
Similarly $n=\frac{(\frac{a+b}{c+d})}{x+y-z}$<br>
is obtained from <code>$n=\frac{(\frac{a+b}{c+d})}{x+y-z}$</code><br>
Also ,<br>
$p=\frac{A}{(\frac{B}{C})}$ is obtained from
<code>$p=\frac{A}{(\frac{B}{C})}$</code> .<br>
Similarly $q=\frac{a+b+m+n}{(\frac{c+d}{e+f})}$ 
obtained from <code>$q=\frac{a+b+m+n}{(\frac{c+d}{e+f})}$</code>.        </li>
</ul></li>
<li>There is another method to draw horizontal division lines, command <strong><code>\over</code></strong>. Its function is same as <code>\frac</code> command, but much easier to format, because its placement is is in between numerator and denominator (like the <code>/</code> and <code>\div</code>).<br>
<strong>General format</strong>: <code>{{numerator}\over {denominator}}</code><br>
Note that, here requires an extra (outermost) pair of curly braces. Otherwise  a <code>\over</code> command will consider whatever  at the left (before) side of <code>\over</code> command, as a numerator; and whatever at the right (after) side of <code>\over</code>, as a denominator.        

<ul>
<li>Examples;<br>
<code>${{numerator}\over {denominator}}$</code> gives ${{numerator}\over {denominator}}$<br>
Similarly <code>$a\over b$</code> gives $a\over b$<br>
And <code>${{a+b}\over {c+d}}$</code> gives ${{a+b}\over {c+d}}$ .<br>
Also <code>${{(a+b)\times(c+d)}\over {(x+y+z)}}$</code> gives ${{(a+b)\times(c+d)}\over {(x+y+z)}}$ .<br>
The command <code>\over</code> is more suitable to complex fractions. 
Such as<br>
${{A\over B}\over C}$ obtained from <code>${{A\over B}\over C}$</code> .<br>
Similarly ${{{(a+b)(c-d)}\over{(m+m)(p+q)}}\over {(a+b)}}$ obtained from <code>${{{(a+b)(c-d)}\over{(m+m)(p+q)}}\over {(a+b)}}$</code> .<br>
Also, ${A\over {B\over C}}$ obtained from <code>${A\over {B\over C}}$</code> .<br>
Similarly ${ {(a+b)(c-d)}\over { {(m+n)(p-q)}\over {(w+x)(y-z)} } }$ obtained from<br>
<code>${ {(a+b)(c-d)}\over { {(m+n)(p-q)}\over {(w+x)(y-z)} } }$</code> . </li>
<li>Why that extra (outermost) curly-braces are important while using <code>\over</code> command?<br>
Lets see the following expression.<br>
$x={{2(a+b)}\over {(c-d)}}=c$.<br>
it has been written with <code>$x={{2(a+b)} \over {(c-d)}=c$</code> .<br>
If it was mistakenly written as<br>
<strike><code>$x={2(a+b)}\over {(c-d)}=c$</code></strike>, it would give output as 
$x={2(a+b)}\over{c+d}=c$. i.e. <a href="https://i.stack.imgur.com/k8Sej.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/k8Sej.png" alt="erroneous"></a>That is wrong and undeserved.  </li>
</ul></li>
<li>There is way to use mixture of slash (oblique) type divisions and horizontal type divisions together.     

<ul>
<li>Example : Now we'll try to to tackle the following two fractions (A) and (B) using firstly with<code>/</code>  and <code>\frac</code> (harder method); and then <code>\</code> and <code>\over</code> (easier method).<br>
<a href="https://i.stack.imgur.com/tY5EA.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/tY5EA.png" alt="Two expressions"></a><br>
Expression-A:<br>
Using <code>/</code> and <code>\frac</code> :<br>
<code>${x}=\frac{(a+b)}{(c-d)}=(a+b)/(c-d)$</code> gives<br>
${x}=\frac{(a+b)}{(c-d)}=(a+b)/(c-d)$. 
Similarly using <code>/</code> and <code>\over</code>  :<br>
<code>${x}={(a+b)}\over {(c-d)}= {(a+b)}/{(c-d)}$</code>  gives<br>
${x}={{(a+b)}\over {(c-d)}}= {(a+b)}/{(c-d)}$. </li>
</ul></li>
</ul></li>
</ol>

<p>.   </p>

<hr>

<h2>A brief Summary is coming soon.</h2>

<p>(for each sections).  </p>

<hr>

<h2>Update:</h2>

<p>I am in a temporary pause from Stackexchange. Will be back few months latter. </p>

<p>......................</p>
