This site is supported by donations to The OEIS Foundation.
Template:Frac
[⧼Purge⧽ Template:Frac]
- 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 LaTeX formatted rational expression and/or the numerical result of the rational expression.
Contents
- 1 Usage
- 2 Examples
- 2.1 Value of \frac{22}{7}
- 2.2 \frac{22}{7}
- 2.3 \frac{22}{7} = value of \frac{22}{7}
- 2.4 \frac{\pi + 1}{ \tfrac{22}{7} + 1 }
- 2.5 1 + \frac{22}{60} + \frac{7}{60^2} + \frac{42}{60^3} + \frac{33}{60^4} + \frac{4}{60^5} + \frac{40}{60^6}
- 2.6 \frac{j_2}{k^2}
- 2.7 \frac{p}{q}
- 2.8 \frac{d}{q}
- 2.9 \frac{q}{d}
- 2.10 \frac{x^2 + 1}{3}
- 2.11 \frac{x^2 + 1}{y^3 - 1}
- 2.12 \frac{x^2 + xy + 1}{y^3 - 1}
- 2.13 \frac{x^2 + \sqrt{xy} + 1}{y^3 - 1}
- 2.14 \frac{x^2 + \sqrt{xy} + 1}{ \sqrt[3]{y^3 - 1} }
- 2.15 HTML compared with rendered LaTeX
- 2.16 Euler’s number
- 3 Examples (improper usage)
- 4 See also
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 LaTeX rational expression;
- TEX: display style LaTeX rational expression;
- #: numerical result.
As an alternative to using LaTeX 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 LaTeX, 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 LaTeX renderings, the {{dash|hyphus}} is properly turned into {{dash|minus}} by the LaTeX software).
Examples
Value of \frac{22}{7}
: before {{math|{{frac|22|7|#}}{{...|ldots}}|&}} after
yields the text style HTML+CSS
- before
after3.1428571428571…
: before {{math|{{frac|22|7|#}}{{...|ldots|tex}}|$}} after
yields the text style LaTeX
- before after
: {{math|{{frac|22|7|#}}{{...|ldots}}|&&}}
yields the display style HTML+CSS
3.1428571428571…
: {{math|{{frac|22|7|#}}{{...|ldots|tex}}|$$}}
yields the display style LaTeX
\frac{22}{7}
: before {{math|{{tfrac|22|7}}|&}} after
yields the text style HTML+CSS
- before
after22 7
: before {{math|{{tfrac|22|7|tex}}|$}} after
yields the text style LaTeX
- before after
: {{math|{{frac|22|7|HTM}}|&&}}
yields the display style HTML+CSS
22 7
: {{math|{{frac|22|7|TEX}}|$$}}
yields the display style LaTeX
\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
after
= 3.1428571428571…22 7
: before {{math|{{frac|22|7|tex}} {{=}} {{frac|22|7|#}}{{...|ldots|tex}}|$}} after
yields the text style LaTeX
- before after
: {{math|{{frac|22|7|HTM}} {{=}} {{frac|22|7|#}}{{...|ldots}}|&&}}
yields the display style HTML+CSS
= 3.1428571428571…22 7
: {{math|{{frac|22|7|TEX}} {{=}} {{frac|22|7|#}}{{...|ldots|tex}}|$$}}
yields the display style LaTeX
\frac{\pi + 1}{ \tfrac{22}{7} + 1 }
: before {{math|{{frac|{{Gr|pi}} + 1|{{tfrac|22|7}} + 1}}|&}} after
yields the text style HTML+CSS
- before
afterπ + 1
+ 122 7
: before {{math|{{frac|{{Gr|pi|tex}} + 1|{{frac|22|7|tex}} + 1|tex}}|$}} after
yields the text style LaTeX
- before after
: {{math| {{frac|{{Gr|pi}} + 1|{{tfrac|22|7}} + 1|HTM}}|&&}}
yields the display style HTML+CSS
π + 1
+ 122 7
: {{math| {{frac|{{Gr|pi|TEX}} + 1|{{frac|22|7|tex}} + 1|TEX}}|$$}}
yields the display style LaTeX
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
after1 +
+22 60
+7 60 2
+42 60 3
+33 60 4
+4 60 5 40 60 6
: 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 LaTeX
- before 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}}|$$}}
yields the display style LaTeX
\frac{j_2}{k^2}
: before {{math|{{frac|''j''{{sub|2}}|''k''{{^|2}}}}|&}} after
yields the text style HTML+CSS
- before
afterj2 k 2
: before {{math|{{frac|''j''{{sub|2|tex}}|''k''{{^|2|tex}}|tex}}|$}} after
yields the text style LaTeX
- before after
: {{math|{{frac|''j''{{sub|2}}|''k''{{^|2}}|HTM}}|&&}}
yields the display style HTML+CSS
j2 k 2
: {{math|{{frac|''j''{{sub|2|TEX}}|''k''{{^|2|TEX}}|TEX}}|$$}}
yields the display style LaTeX
\frac{p}{q}
: before {{math|{{frac|''p''|''q''}}|&}} after
yields the text style HTML+CSS
- before
afterp q
: before {{math|{{frac|''p''|''q''|tex}}|$}} after
yields the text style LaTeX
- before after
: {{math|{{frac|''p''|''q''|HTM}}|&&}}
yields the display style HTML+CSS
p q
: {{math|{{frac|''p''|''q''|TEX}}|$$}}
yields the display style LaTeX
\frac{d}{q}
: before {{math|{{frac|''d''|''q''}}|&}} after
yields the text style HTML+CSS
- before
afterd q
: before {{math|{{frac|''d''|''q''|tex}}|$}} after
yields the text style LaTeX
- before after
: {{math|{{frac|''d''|''q''|HTM}}|&&}}
yields the display style HTML+CSS
d q
: {{math|{{frac|''d''|''q''|TEX}}|$$}}
yields the display style LaTeX
\frac{q}{d}
: before {{math|{{tfrac|''q''|''d''}}|&}} after
yields the text style HTML+CSS
- before
afterq d
: before {{math|{{tfrac|''q''|''d''|tex}}|$}} after
yields the text style LaTeX
- before after
: {{math|{{frac|''q''|''d''|HTM}}|&&}}
yields the display style HTML+CSS
q d
: {{math|{{frac|''q''|''d''|TEX}}|$$}}
yields the display style LaTeX
\frac{x^2 + 1}{3}
: before {{math|{{tfrac|''x''{{^|2}} {{op|+}} 1|3}}|&}} after
yields the text style HTML+CSS
- before
afterx 2 + 1 3
: before {{math|{{frac|''x''{{^|2|tex}} {{op|+|tex}} 1|3|tex}}|$}} after
yields the text style LaTeX
- before after
: {{math|{{frac|''x''{{^|2}} {{op|+}} 1|3|HTM}}|&&}}
yields the display style HTML+CSS
x 2 + 1 3
: {{math|{{frac|''x''{{^|2|tex}} {{op|+|tex}} 1|3|TEX}}|$$}}
yields the display style LaTeX
\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
afterx 2 + 1 y 3 − 1
: before {{math|{{frac|''x''{{^|2|tex}} {{op|+|tex}} 1|''y''{{^|3|tex}} {{op|-|tex}} 1|tex}}|$}} after
yields the text style LaTeX
- before 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}}|$$}}
yields the display style LaTeX
\frac{x^2 + xy + 1}{y^3 - 1}
: before {{math|{{tfrac|''x''{{^|2}} {{op|+}} ''x''{{sp|1}}''y'' {{op|+}} 1|''y''{{^|3}} {{op|-}} 1}}|&}} after
yields the text style HTML+CSS
- before
afterx 2 + x y + 1 y 3 − 1
: before {{math|{{frac|''x''{{^|2|tex}} {{op|+|tex}} xy {{op|+|tex}} 1|''y''{{^|3|tex}} {{op|-|tex}} 1|tex}}|$}} after
yields the text style LaTeX
- before after
: {{math|{{frac|''x''{{^|2}} {{op|+}} ''x''{{sp|1}}''y'' {{op|+}} 1|''y''{{^|3}} {{op|-}} 1|HTM}}|&&}}
yields the display style HTML+CSS
x 2 + x y + 1 y 3 − 1
: {{math|{{frac|''x''{{^|2|tex}} {{op|+|tex}} xy {{op|+|tex}} 1|''y''{{^|3|tex}} {{op|-|tex}} 1|TEX}}|$$}}
yields the display style LaTeX
\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
afterx 2 + √ xy+ 1y 3 − 1
: 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 LaTeX
- before after
: {{math|{{frac|''x''{{^|2}} {{op|+}} {{sqrt|''xy''}} {{op|+}} 1|''y''{{^|3}} {{op|-}} 1|HTM}}|&&}}
yields the display style HTML+CSS
x 2 + √ xy+ 1y 3 − 1
: {{math|{{frac|''x''{{^|2|tex}} {{op|+|tex}} {{sqrt|xy|tex}} {{op|+|tex}} 1|''y''{{^|3|tex}} {{op|-|tex}} 1|TEX}}|$$}}
yields the display style LaTeX
\frac{x^2 + \sqrt{xy} + 1}{ \sqrt[3]{y^3 - 1} }
: before {{math|{{frac|''x''{{^|2}} {{op|+}} {{sqrt|''x''{{sp|1}}''y''}} {{op|+}} 1|{{root|''y''{{^|3}} {{op|-}} 1|3}}}}|&}} after
yields the text style HTML+CSS
- before
afterx 2 + √ x y+ 13√ y 3 − 1
: before {{math|{{frac|''x''{{^|2|tex}} {{op|+|tex}} {{sqrt|xy|tex}} {{op|+|tex}} 1|{{root|''y''{{^|3|tex}} {{op|-|tex}} 1|3|tex}}|tex}}|$}} after
yields the text style LaTeX
- before after
: {{math|{{frac|''x''{{^|2}} {{op|+}} {{sqrt|''x''{{sp|1}}''y''}} {{op|+}} 1|{{root|''y''{{^|3}} {{op|-}} 1|3}}|HTM}}|&&}}
yields the display style HTML+CSS
x 2 + √ x y+ 13√ y 3 − 1
: {{math|{{frac|''x''{{^|2|tex}} {{op|+|tex}} {{sqrt|xy|tex}} {{op|+|tex}} 1|{{root|''y''{{^|3|tex}} {{op|-|tex}} 1|3|tex}}|TEX}}|$$}}
yields the display style LaTeX
HTML compared with rendered LaTeX
: {{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 LaTeX
-
,x 2 + x y + 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}}|$$}}
yields the display style HTML+CSS, the display style LaTeX
- ,
x 2 + x y + 1 y 3 − 1
Euler’s number
The code
: {{math|''e'' {{=|sp}} {{lim|''n''->infty|HTM}} {{(|{{sp|-1}}{{frac|''n''{{^|''n''}}|''n''!|HTM}}|)|Big}}{{^|{{^|{{^|1{{op|/}}''n''|100%}}|100%}}}} {{=|sp}} <!-- -->{{lim|''n''->infty|HTM}} {{frac|''n''|{{root|''n''!|<big>''n''</big>{{sp|1}}}}|HTM}}{{sp|1}}, |tex = e = \lim_{n \to \infty} { \left( \frac{n^n}{n!} \right) }^{1/n} = \lim_{n \to \infty} \frac{n}{ \sqrt[n]{n!} },|&&}}
yields the display style HTML+CSS
-
e =
1 / n =⎛ ⎝ n n n! ⎞ ⎠
,n n √ n!
and with the $$
option, yields the display style LaTeX
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".
LaTeX 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!