Template:Frac/doc

This documentation subpage contains instructions, categories, or other information for Template:Frac. [<Edit> Template:Frac]

[⧼Purge⧽ Template:Frac/doc]

Note: the former {{frac}} template is now {{fraction}}. (It displays either mixed fractions or simple fractions, though the presentation style is not suitable for mathematics documents!)

Note: to get a smaller fraction, the {{tfrac}} (tiny fraction) template should be used, e.g. within {{frac}}, {{root}}, {{sqrt}}, etc.

The {{frac}} mathematical formatting template and/or mathematical function template gives an HTML+CSS or a $L a T e X$ formatted rational expression and/or the numerical result of the rational expression.

Usage

{{frac|numerator|denominator}}

or

{{frac|numerator|denominator|format}}

where format is taken from

htm: text style HTML+CSS rational expression (default);
HTM: display style HTML+CSS rational expression;
tex: text style $L a T e X$ rational expression;
TEX: display style $L a T e X$ rational expression;
#: numerical result.

As an alternative to using $L a T e X$ rendered as PNG images (with either tex or TEX options), the html or HTML options will render the rational expression as HTML+CSS. You must use the {{frac}} template within the {{math}} template, which completes the formatting for mathematical expressions. (Do not use this option inside <math>...</math> tags.)

NOTE: To get rendered $L a T e X$ , you must use the {{math}} template, since you cannot evaluate templates, parser functions or magic words inside <math>...</math> tags.

Minus sign issue

Use {{op|-}} for minus sign (instead of -, the hyphen, hyphus or hyphen minus sign {{dash|hyphus}}) in the provided mathematical expression (because the border-top used to make the vinculum of radicals in the {{root}} template turns out to be made out of hyphens -, and we need to convert the {{dash|hyphus}} into proper {{dash|minus}} − signs for the HTML+CSS renderings).

The {{op|-}} is replaced by a proper minus sign {{sym|-}} (i.e. {{dash|minus}}) in the {{math}} template for the HTML+CSS renderings (for $L a T e X$ renderings, the {{dash|hyphus}} is properly turned into {{dash|minus}} by the $L a T e X$ software).

Examples

Value of `\frac{22}{7}`

: before {{math|{{frac|22|7|#}}{{...|ldots}}|&}} after yields the text style HTML+CSS

before 

3.1428571428571…

after

: before {{math|{{frac|22|7|#}}{{...|ldots|tex}}|$}} after yields the text style $L a T e X$

before

\textstyle {3.1428571428571\ldots }

after

: {{math|{{frac|22|7|#}}{{...|ldots}}|&&}} yields the display style HTML+CSS

3.1428571428571…

: {{math|{{frac|22|7|#}}{{...|ldots|tex}}|$$}} yields the display style $L a T e X$

{\begin{array}{l}\displaystyle {3.1428571428571\ldots }\end{array}}

`\frac{22}{7}`

: before {{math|{{tfrac|22|7}}|&}} after yields the text style HTML+CSS

before 

22

7

after

: before {{math|{{tfrac|22|7|tex}}|$}} after yields the text style $L a T e X$

before

\textstyle {\tfrac {22}{7}}

after

: {{math|{{frac|22|7|HTM}}|&&}} yields the display style HTML+CSS

22

7

: {{math|{{frac|22|7|TEX}}|$$}} yields the display style $L a T e X$

{\begin{array}{l}\displaystyle {\frac {22}{7}}\end{array}}

`\frac{22}{7} =` value of `\frac{22}{7}`

: before {{math|{{tfrac|22|7}} {{=}} {{frac|22|7|#}}{{...|ldots}}|&}} after yields the text style HTML+CSS

before 

22

7

= 3.1428571428571…

after

: before {{math|{{frac|22|7|tex}} {{=}} {{frac|22|7|#}}{{...|ldots|tex}}|$}} after yields the text style $L a T e X$

before

\textstyle {{\frac {22}{7}}=3.1428571428571\ldots }

after

: {{math|{{frac|22|7|HTM}} {{=}} {{frac|22|7|#}}{{...|ldots}}|&&}} yields the display style HTML+CSS

22

7

= 3.1428571428571…

: {{math|{{frac|22|7|TEX}} {{=}} {{frac|22|7|#}}{{...|ldots|tex}}|$$}} yields the display style $L a T e X$

{\begin{array}{l}\displaystyle {{\frac {22}{7}}=3.1428571428571\ldots }\end{array}}

`\frac{\pi + 1}{ \tfrac{22}{7} + 1 }`

: before {{math|{{frac|{{Gr|pi}} + 1|{{tfrac|22|7}} + 1}}|&}} after yields the text style HTML+CSS

before 

π + 1

22

7

+ 1

after

: before {{math|{{frac|{{Gr|pi|tex}} + 1|{{frac|22|7|tex}} + 1|tex}}|$}} after yields the text style $L a T e X$

before

\textstyle {\frac {\pi +1}{{\frac {22}{7}}+1}}

after

: {{math| {{frac|{{Gr|pi}} + 1|{{tfrac|22|7}} + 1|HTM}}|&&}} yields the display style HTML+CSS

π + 1

22

7

+ 1

: {{math| {{frac|{{Gr|pi|TEX}} + 1|{{frac|22|7|tex}} + 1|TEX}}|$$}} yields the display style $L a T e X$

{\begin{array}{l}\displaystyle {\frac {\pi +1}{{\frac {22}{7}}+1}}\end{array}}

`1 + \frac{22}{60} + \frac{7}{60^2} + \frac{42}{60^3} + \frac{33}{60^4} + \frac{4}{60^5} + \frac{40}{60^6}`

: before {{math|1 + {{tfrac|22|60}} + {{tfrac|7|60{{^|2}}}} + {{tfrac|42|60{{^|3}}}} + {{tfrac|33|60{{^|4}}}} + {{tfrac|4|60{{^|5}}}} + {{tfrac|40|60{{^|6}}}}|&}} after yields the text style HTML+CSS

before 

1 +

22

60

+

7

60 2

+

42

60 3

+

33

60 4

+

4

60 5

+

40

60 6

after

: before {{math|1 + {{frac|22|60|tex}} + {{frac|7|60{{^|2|tex}}|tex}} + {{frac|42|60{{^|3|tex}}|tex}} + {{frac|33|60{{^|4|tex}}|tex}} + {{frac|4|60{{^|5|tex}}|tex}} + {{frac|40|60{{^|6|tex}}|tex}}|$}} after yields the text style $L a T e X$

before

\textstyle {1+{\frac {22}{60}}+{\frac {7}{60^{2}}}+{\frac {42}{60^{3}}}+{\frac {33}{60^{4}}}+{\frac {4}{60^{5}}}+{\frac {40}{60^{6}}}}

after

{{math|1 + {{frac|22|60}} + {{frac|7|60{{^|2}}}} + {{frac|42|60{{^|3}}}} + {{frac|33|60{{^|4}}}} + {{frac|4|60{{^|5}}}} + {{frac|40|60{{^|6}}}}|&&}} yields the display style HTML+CSS

1 +

22

60

+

7

60 2

+

42

60 3

+

33

60 4

+

4

60 5

+

40

60 6

{{math|1 + {{frac|22|60|tex}} + {{frac|7|60{{^|2|tex}}|tex}} + {{frac|42|60{{^|3|tex}}|tex}} + {{frac|33|60{{^|4|tex}}|tex}} + {{frac|4|60{{^|5|tex}}|tex}} + {{frac|40|60{{^|6|tex}}|tex}}|$$}} yields the display style $L a T e X$

{\begin{array}{l}\displaystyle {1+{\frac {22}{60}}+{\frac {7}{60^{2}}}+{\frac {42}{60^{3}}}+{\frac {33}{60^{4}}}+{\frac {4}{60^{5}}}+{\frac {40}{60^{6}}}}\end{array}}

`\frac{j_2}{k^2}`

: before {{math|{{frac|''j''{{sub|2}}|''k''{{^|2}}}}|&}} after yields the text style HTML+CSS

before 

j2

k 2

after

: before {{math|{{frac|''j''{{sub|2|tex}}|''k''{{^|2|tex}}|tex}}|$}} after yields the text style $L a T e X$

before

\textstyle {\frac {j_{2}{\!\,\!}}{k^{2}}}

after

: {{math|{{frac|''j''{{sub|2}}|''k''{{^|2}}|HTM}}|&&}} yields the display style HTML+CSS

j2

k 2

: {{math|{{frac|''j''{{sub|2|TEX}}|''k''{{^|2|TEX}}|TEX}}|$$}} yields the display style $L a T e X$

{\begin{array}{l}\displaystyle {\frac {j_{2}{\!\,\!}}{k^{2}}}\end{array}}

`\frac{p}{q}`

: before {{math|{{frac|''p''|''q''}}|&}} after yields the text style HTML+CSS

before 

p

q

after

: before {{math|{{frac|''p''|''q''|tex}}|$}} after yields the text style $L a T e X$

before

\textstyle {\frac {p}{q}}

after

: {{math|{{frac|''p''|''q''|HTM}}|&&}} yields the display style HTML+CSS

p

q

: {{math|{{frac|''p''|''q''|TEX}}|$$}} yields the display style $L a T e X$

{\begin{array}{l}\displaystyle {\frac {p}{q}}\end{array}}

`\frac{d}{q}`

: before {{math|{{frac|''d''|''q''}}|&}} after yields the text style HTML+CSS

before 

d

q

after

: before {{math|{{frac|''d''|''q''|tex}}|$}} after yields the text style $L a T e X$

before

\textstyle {\frac {d}{q}}

after

: {{math|{{frac|''d''|''q''|HTM}}|&&}} yields the display style HTML+CSS

d

q

: {{math|{{frac|''d''|''q''|TEX}}|$$}} yields the display style $L a T e X$

{\begin{array}{l}\displaystyle {\frac {d}{q}}\end{array}}

`\frac{q}{d}`

: before {{math|{{tfrac|''q''|''d''}}|&}} after yields the text style HTML+CSS

before 

q

d

after

: before {{math|{{tfrac|''q''|''d''|tex}}|$}} after yields the text style $L a T e X$

before

\textstyle {\frac {q}{d}}

after

: {{math|{{frac|''q''|''d''|HTM}}|&&}} yields the display style HTML+CSS

q

d

: {{math|{{frac|''q''|''d''|TEX}}|$$}} yields the display style $L a T e X$

{\begin{array}{l}\displaystyle {\frac {q}{d}}\end{array}}

`\frac{x^2 + 1}{3}`

: before {{math|{{tfrac|''x''{{^|2}} {{op|+}} 1|3}}|&}} after yields the text style HTML+CSS

before 

x 2 + 1

3

after

: before {{math|{{frac|''x''{{^|2|tex}} {{op|+|tex}} 1|3|tex}}|$}} after yields the text style $L a T e X$

before

\textstyle {\frac {x^{2}+1}{3}}

after

: {{math|{{frac|''x''{{^|2}} {{op|+}} 1|3|HTM}}|&&}} yields the display style HTML+CSS

x 2 + 1

3

: {{math|{{frac|''x''{{^|2|tex}} {{op|+|tex}} 1|3|TEX}}|$$}} yields the display style $L a T e X$

{\begin{array}{l}\displaystyle {\frac {x^{2}+1}{3}}\end{array}}

`\frac{x^2 + 1}{y^3 - 1}`

: before {{math|{{frac|''x''{{^|2}} {{op|+}} 1|''y''{{^|3}} {{op|-}} 1}}|&}} after yields the text style HTML+CSS

before 

x 2 + 1

y 3 − 1

after

: before {{math|{{frac|''x''{{^|2|tex}} {{op|+|tex}} 1|''y''{{^|3|tex}} {{op|-|tex}} 1|tex}}|$}} after yields the text style $L a T e X$

before

\textstyle {\frac {x^{2}+1}{y^{3}{\,}-{\,}1}}

after

: {{math|{{frac|''x''{{^|2}} {{op|+}} 1|''y''{{^|3}} {{op|-}} 1|HTM}}|&&}} yields the display style HTML+CSS

x 2 + 1

y 3 − 1

: {{math|{{frac|''x''{{^|2|tex}} {{op|+|tex}} 1|''y''{{^|3|tex}} {{op|-|tex}} 1|TEX}}|$$}} yields the display style $L a T e X$

{\begin{array}{l}\displaystyle {\frac {x^{2}+1}{y^{3}-1}}\end{array}}

`\frac{x^2 + xy + 1}{y^3 - 1}`

: before {{math|{{tfrac|''x''{{^|2}} {{op|+}} ''x''{{sp|1}}''y'' {{op|+}} 1|''y''{{^|3}} {{op|-}} 1}}|&}} after yields the text style HTML+CSS

before 

x 2 + x y + 1

y 3 − 1

after

: before {{math|{{frac|''x''{{^|2|tex}} {{op|+|tex}} xy {{op|+|tex}} 1|''y''{{^|3|tex}} {{op|-|tex}} 1|tex}}|$}} after yields the text style $L a T e X$

before

\textstyle {\frac {x^{2}+xy+1}{y^{3}{\,}-{\,}1}}

after

: {{math|{{frac|''x''{{^|2}} {{op|+}} ''x''{{sp|1}}''y'' {{op|+}} 1|''y''{{^|3}} {{op|-}} 1|HTM}}|&&}} yields the display style HTML+CSS

x 2 + x y + 1

y 3 − 1

: {{math|{{frac|''x''{{^|2|tex}} {{op|+|tex}} xy {{op|+|tex}} 1|''y''{{^|3|tex}} {{op|-|tex}} 1|TEX}}|$$}} yields the display style $L a T e X$

{\begin{array}{l}\displaystyle {\frac {x^{2}+xy+1}{y^{3}-1}}\end{array}}

`\frac{x^2 + \sqrt{xy} + 1}{y^3 - 1}`

: before {{math|{{frac|''x''{{^|2}} {{op|+}} {{sqrt|''xy''}} {{op|+}} 1|''y''{{^|3}} {{op|-}} 1}}|&}} after yields the text style HTML+CSS

before 

x 2 +

2√ xy

+ 1

y 3 − 1

after

: before {{math|{{frac|''x''{{^|2|tex}} {{op|+|tex}} {{sqrt|xy|tex}} {{op|+|tex}} 1|''y''{{^|3|tex}} {{op|-|tex}} 1|tex}}|$}} after yields the text style $L a T e X$

before

\textstyle {\frac {x^{2}+{\sqrt {xy}}+1}{y^{3}{\,}-{\,}1}}

after

: {{math|{{frac|''x''{{^|2}} {{op|+}} {{sqrt|''xy''}} {{op|+}} 1|''y''{{^|3}} {{op|-}} 1|HTM}}|&&}} yields the display style HTML+CSS

x 2 +

2√ xy

+ 1

y 3 − 1

: {{math|{{frac|''x''{{^|2|tex}} {{op|+|tex}} {{sqrt|xy|tex}} {{op|+|tex}} 1|''y''{{^|3|tex}} {{op|-|tex}} 1|TEX}}|$$}} yields the display style $L a T e X$

{\begin{array}{l}\displaystyle {\frac {x^{2}+{\sqrt {xy}}+1}{y^{3}-1}}\end{array}}

`\frac{x^2 + \sqrt{xy} + 1}{ \sqrt[3]{y^3 - 1} }`

: before {{math|{{frac|''x''{{^|2}} {{op|+}} {{sqrt|''x''{{sp|1}}''y''}} {{op|+}} 1|{{root|''y''{{^|3}} {{op|-}} 1|3}}}}|&}} after yields the text style HTML+CSS

before 

x 2 +

2√ x y

+ 1

3√ y 3 − 1

after

: before {{math|{{frac|''x''{{^|2|tex}} {{op|+|tex}} {{sqrt|xy|tex}} {{op|+|tex}} 1|{{root|''y''{{^|3|tex}} {{op|-|tex}} 1|3|tex}}|tex}}|$}} after yields the text style $L a T e X$

before

\textstyle {\frac {x^{2}+{\sqrt {xy}}+1}{\sqrt[{3}]{y^{3}{\,}-{\,}1}}}

after

: {{math|{{frac|''x''{{^|2}} {{op|+}} {{sqrt|''x''{{sp|1}}''y''}} {{op|+}} 1|{{root|''y''{{^|3}} {{op|-}} 1|3}}|HTM}}|&&}} yields the display style HTML+CSS

x 2 +

2√ x y

+ 1

3√ y 3 − 1

: {{math|{{frac|''x''{{^|2|tex}} {{op|+|tex}} {{sqrt|xy|tex}} {{op|+|tex}} 1|{{root|''y''{{^|3|tex}} {{op|-|tex}} 1|3|tex}}|TEX}}|$$}} yields the display style $L a T e X$

{\begin{array}{l}\displaystyle {\frac {x^{2}+{\sqrt {xy}}+1}{\sqrt[{3}]{y^{3}-1}}}\end{array}}

HTML compared with rendered $L a T e X$

: {{math|{{tfrac|''x''{{^|2}} {{op|+}} ''x''{{sp|1}}''y'' {{op|+}} 1|''y''{{^|3}} {{op|-}} 1}}|&}}, {{math|{{frac|''x''{{^|2|tex}} {{op|+|tex}} xy {{op|+|tex}} 1|''y''{{^|3|tex}} {{op|-|tex}} 1|tex}}|$}}

yields the text style HTML+CSS, the text style $L a T e X$

x 2 + x y + 1

y 3 − 1

,

\textstyle {\frac {x^{2}+xy+1}{y^{3}{\,}-{\,}1}}

: {{math|{{frac|''x''{{^|2}} {{op|+}} ''x''{{sp|1}}''y'' {{op|+}} 1|''y''{{^|3}} {{op|-}} 1|HTM}}|&&}}, {{math|{{frac|''x''{{^|2|tex}} + xy + 1|''y''{{^|3|tex}} {{op|-|tex}} 1|TEX}}|$$}}

yields the display style HTML+CSS, the display style $L a T e X$

x 2 + x y + 1

y 3 − 1

,

{\begin{array}{l}\displaystyle {\frac {x^{2}+xy+1}{y^{3}-1}}\end{array}}

Euler’s number

The code

: {{math|''e'' {{=|sp}} {{lim|''n''->infty|HTM}} {{(|{{sp|-1}}{{frac|''n''{{^|''n''}}|''n''!|HTM}}|)|Big}}{{^|{{^|{{^|1{{op|/}}''n''|100%}}|100%}}}} {{=|sp}} <!--
-->{{lim|''n''->infty|HTM}} {{frac|''n''|{{root|''n''!|<big>''n''</big>{{sp|1}}}}|HTM}}{{sp|1}},
|tex = e = \lim_{n \to \infty} { \left( \frac{n^n}{n!} \right) }^{1/n} = \lim_{n \to \infty} \frac{n}{ \sqrt[n]{n!} },|&&}}

yields the display style HTML+CSS

e =

⎛

⎝

n n

n!

⎞

⎠

1 / n =

n

n √ n!

,

and with the $$ option, yields the display style $L a T e X$

{\begin{array}{l}\displaystyle {e=\lim _{n\to \infty }{\left({\frac {n^{n}}{n!}}\right)}^{1/n}=\lim _{n\to \infty }{\frac {n}{\sqrt[{n}]{n!}}},}\end{array}}

Examples (improper usage)

These rational expressions cannot be [numerically] evaluated:

{{frac|1|x^2 + 1|#}} yields Expression error: Unrecognized word "x".

{{frac|x|x^2 + 1|#}} yields Expression error: Unrecognized word "x".

$L a T e X$ cannot render HTML+CSS formatted expressions:

{{frac|1|''x''{{^|2}} + 1|TEX}} yields \frac{ 1 }{ x 2 + 1 }

whereas

{{frac|1|''x''{{^|2|tex}} + 1|TEX}} yields \frac{ 1 }{ x^{ 2 } + 1 }

and thus {{math|{{frac|1|''x''{{^|2}} + 1|TEX}}|$$}} yields Error: Failed to parse!

Template:Frac/doc

Contents

Usage

Minus sign issue

Examples

Value of `\frac{22}{7}`

`\frac{22}{7}`

`\frac{22}{7} =` value of `\frac{22}{7}`

`\frac{\pi + 1}{ \tfrac{22}{7} + 1 }`

`1 + \frac{22}{60} + \frac{7}{60^2} + \frac{42}{60^3} + \frac{33}{60^4} + \frac{4}{60^5} + \frac{40}{60^6}`

`\frac{j_2}{k^2}`

`\frac{p}{q}`

`\frac{d}{q}`

`\frac{q}{d}`

`\frac{x^2 + 1}{3}`

`\frac{x^2 + 1}{y^3 - 1}`

`\frac{x^2 + xy + 1}{y^3 - 1}`

`\frac{x^2 + \sqrt{xy} + 1}{y^3 - 1}`

`\frac{x^2 + \sqrt{xy} + 1}{ \sqrt[3]{y^3 - 1} }`

HTML compared with rendered $L a T e X$

Euler’s number

Examples (improper usage)

See also

Navigation menu

Views

Personal tools

Navigation

Search

Tools

Template:Frac/doc

Contents

Usage

Minus sign issue

Examples

Value of \frac{22}{7}

\frac{22}{7}

\frac{22}{7} = value of \frac{22}{7}

\frac{\pi + 1}{ \tfrac{22}{7} + 1 }

1 + \frac{22}{60} + \frac{7}{60^2} + \frac{42}{60^3} + \frac{33}{60^4} + \frac{4}{60^5} + \frac{40}{60^6}

\frac{j_2}{k^2}

\frac{p}{q}

\frac{d}{q}

\frac{q}{d}

\frac{x^2 + 1}{3}

\frac{x^2 + 1}{y^3 - 1}

\frac{x^2 + xy + 1}{y^3 - 1}

\frac{x^2 + \sqrt{xy} + 1}{y^3 - 1}

\frac{x^2 + \sqrt{xy} + 1}{ \sqrt[3]{y^3 - 1} }

HTML compared with rendered LaTeX

Euler’s number

Examples (improper usage)

See also

Navigation menu

Search

Value of `\frac{22}{7}`

`\frac{22}{7}`

`\frac{22}{7} =` value of `\frac{22}{7}`

`\frac{\pi + 1}{ \tfrac{22}{7} + 1 }`

`1 + \frac{22}{60} + \frac{7}{60^2} + \frac{42}{60^3} + \frac{33}{60^4} + \frac{4}{60^5} + \frac{40}{60^6}`

`\frac{j_2}{k^2}`

`\frac{p}{q}`

`\frac{d}{q}`

`\frac{q}{d}`

`\frac{x^2 + 1}{3}`

`\frac{x^2 + 1}{y^3 - 1}`

`\frac{x^2 + xy + 1}{y^3 - 1}`

`\frac{x^2 + \sqrt{xy} + 1}{y^3 - 1}`

`\frac{x^2 + \sqrt{xy} + 1}{ \sqrt[3]{y^3 - 1} }`

HTML compared with rendered $L a T e X$