Chapter 7 - Fractions
| Verbose | Brief | Super-Brief | |
|---|---|---|---|
| Fraction Indicators | |||
| Simple | |||
| Opening | Start Fraction | Start Frac | Frac |
| Middle | Over | Over | Over |
| Closing | End Fraction | End Frac | End Frac |
| Nested Once | |||
| Opening | Start Start Fraction | Start Start Frac | Nest Frac |
| Middle | Over Over | Over Over | Nest Over |
| Closing | End End Fraction | End End Frac | Nest End Frac |
| Nested Twice | |||
| Opening | Start Start Start Fraction | Start Start Start Frac | Nest Twice Frac |
| Middle | Over Over Over | Over Over Over | Nest Twice Over |
| Closing | End End End Fraction | End End End Frac | Nest Twice End Frac |
| Continued Fraction Indicators | |||
| Outermost Fraction | |||
| Opening | Continued Fraction | Continued Frac | Continued Frac |
| Middle | Over | Over | Over |
| Closing | [ends with ellipsis] | [ends with ellipsis] | [ends with ellipsis] |
| Inner Fractions | |||
| Opening | Start Fraction | Start Frac | Frac |
| Middle | Over | Over | Over |
| Closing | [ends with the ellipsis] | [ends with the ellipsis] | [ends with the ellipsis] |
Rule 7.1 - ID: fractions_SIM1
Applies To
Simple Fractions
Conditions
The fraction must not contain any other fractions.
Description
Simple fraction indicators are used for fractions that contain no other fractions.
Example 1 fractions_SIM1-02
Example Image:
|
verbose |
a minus StartFraction
b plus c Over
d minus e EndFraction
times f |
 |
|---|---|---|
|
brief |
a minus StartFrac
b plus c Over
d minus e EndFrac
times f |
|
|
superbrief |
a minus Frac
b plus c Over
d minus e EndFrac
times f |
|
Example 2 fractions_SIM1-01
Example Image:
|
verbose |
StartFraction
1 Over
x EndFraction
|
|
|---|---|---|
|
brief |
StartFrac
1 Over
x EndFrac
|
|
|
superbrief |
Frac
1 Over
x EndFrac
|
|
Rule 7.2 - ID: fractions_NES1
Applies To
Nested Once Fractions
Conditions
The fraction must contain one or more simple fractions in the numerator or denominator, but no fractions that contain further fractions.
Description
Nested once or complex fraction indicators are used for fractions that contain one or more simple fractions in the numerator and/or denominator.
Example 1 fractions_NES1-01
Example Image:
|
verbose |
StartStartFraction
StartFraction
x Over
y EndFraction
OverOver
z EndEndFraction
not-equals StartStartFraction
x OverOver
StartFraction
y Over
z EndFraction
EndEndFraction
|
|
|---|---|---|
|
brief |
StartStartFrac
StartFrac
x Over
y EndFrac
OverOver
z EndEndFrac
not-equals StartStartFrac
x OverOver
StartFrac
y Over
z EndFrac
EndEndFrac
|
|
|
superbrief |
NestFrac
Frac
x Over
y EndFrac
NestOver
z NestEndFrac
not-equals NestFrac
x NestOver
Frac
y Over
z EndFrac
NestEndFrac
|
|
Rule 7.3 - ID: fractions_NESX1
Applies To
Nested Fractions
Description
For fractions that contain nested fractions, fraction indicators are used that convey the largest depth of nested fractions contained.
Example 1 fractions_NESX1-01
Example Image:
|
verbose |
StartStartStartFraction
StartStartFraction
left-parenthesis 1 minus x right-parenthesis StartFraction
d Over
d x EndFraction
left-parenthesis 2 x right-parenthesis minus 2 x StartFraction
d Over
d x EndFraction
left-parenthesis 1 minus x right-parenthesis OverOver
left-parenthesis 1 minus x right-parenthesis squared EndEndFraction
OverOverOver
1 plus left-parenthesis StartFraction
2 x Over
1 minus x EndFraction
right-parenthesis squared EndEndEndFraction
|
|
|---|---|---|
|
brief |
StartStartStartFrac
StartStartFrac
left-p'ren 1 minus x right-p'ren StartFrac
d Over
d x EndFrac
left-p'ren 2 x right-p'ren minus 2 x StartFrac
d Over
d x EndFrac
left-p'ren 1 minus x right-p'ren OverOver
left-p'ren 1 minus x right-p'ren squared EndEndFrac
OverOverOver
1 plus left-p'ren StartFrac
2 x Over
1 minus x EndFrac
right-p'ren squared EndEndEndFrac
|
|
|
superbrief |
NestTwiceFrac
NestFrac
L p'ren 1 minus x R p'ren Frac
d Over
d x EndFrac
L p'ren 2 x R p'ren minus 2 x Frac
d Over
d x EndFrac
L p'ren 1 minus x R p'ren NestOver
L p'ren 1 minus x R p'ren squared NestEndFrac
NestTwiceOver
1 plus L p'ren Frac
2 x Over
1 minus x EndFrac
R p'ren squared NestTwiceEndFrac
|
|
Example 2 fractions_NESX1-02
Example Image:
|
verbose |
a 0 plus StartStartStartStartFraction
1 OverOverOverOver
a 1 plus StartStartStartFraction
1 OverOverOver
a 2 plus StartStartFraction
1 OverOver
ellipsis plus StartFraction
1 Over
a Subscript
n Baseline
EndFraction
EndEndFraction
EndEndEndFraction
EndEndEndEndFraction
|
|
|---|---|---|
|
brief |
a 0 plus StartStartStartStartFrac
1 OverOverOverOver
a 1 plus StartStartStartFrac
1 OverOverOver
a 2 plus StartStartFrac
1 OverOver
ellipsis plus StartFrac
1 Over
a Sub
n Base
EndFrac
EndEndFrac
EndEndEndFrac
EndEndEndEndFrac
|
|
|
superbrief |
a 0 plus Nest3Frac
1 Nest3Over
a 1 plus NestTwiceFrac
1 NestTwiceOver
a 2 plus NestFrac
1 NestOver
ellipsis plus Frac
1 Over
a Sub
n Base
EndFrac
NestEndFrac
NestTwiceEndFrac
Nest3EndFrac
|
|
Rule 7.4 - ID: fractions_NUM1
Applies To
Numeric Fractions
Conditions
The numerator must be an integer in the range of 1 to 9 the denominator must be an integer in the range of 1 to 99.
Description
The fraction is pronounced naturally, such as one-half or two-thirds. The name of the number is spoken for the numerator, which is followed by the ordinal name of the denominator. The ordinal name is spoken in it's singular form if the numerator is the integer 1, otherwise the plural form is used.
Example 1 fractions_NUM1-03
Example Image:
|
verbose |
StartFraction
20 Over
5 EndFraction
times StartFraction
1 Over
100 EndFraction
equals one-twenty-fifth |
|
|---|---|---|
|
brief |
StartFrac
20 Over
5 EndFrac
times StartFrac
1 Over
100 EndFrac
equals one-twenty-fifth |
|
|
superbrief |
Frac
20 Over
5 EndFrac
times Frac
1 Over
100 EndFrac
equals one-twenty-fifth |
|
Example 2 fractions_NUM1-02
Example Image:
|
verbose |
one-half plus two-halves plus three-halves plus four-halves plus ellipsis equals sigma-summation Underscript
n equals 1 Overscript
infinity EndScripts
StartFraction
n Over
2 EndFraction
|
|
|---|---|---|
|
brief |
one-half plus two-halves plus three-halves plus four-halves plus ellipsis equals sigma-summation Underscript
n equals 1 Overscript
infinity EndScripts
StartFrac
n Over
2 EndFrac
|
|
|
superbrief |
one-half plus two-halves plus three-halves plus four-halves plus ellipsis equals sigma-summation Underscript
n equals 1 Overscript
infinity EndScripts
Frac
n Over
2 EndFrac
|
|
Example 3 fractions_NUM1-01
Example Image:
|
verbose |
StartFraction
three-fifths Over
8 EndFraction
equals three-fifths times one-eighth |
|
|---|---|---|
|
brief |
StartFrac
three-fifths Over
8 EndFrac
equals three-fifths times one-eighth |
|
|
superbrief |
Frac
three-fifths Over
8 EndFrac
equals three-fifths times one-eighth |
|
Note: This example is particularly difficult to transcribe directly to Nemeth Code. The next specification will include a setting that is beneficial for transcription.
Rule 7.5 - ID: fractions_NUM2
Conditions
There must be a number followed by a numeric fraction.
Description
The word "and" is inserted between a number and the following numeric fraction.
Example 1 fractions_NUM2-10
Example Image:
|
verbose |
3 and five-eighths equals StartFraction
29 Over
8 EndFraction
|
|
|---|---|---|
|
brief |
3 and five-eighths equals StartFrac
29 Over
8 EndFrac
|
|
|
superbrief |
3 and five-eighths equals Frac
29 Over
8 EndFrac
|
|
Rule 7.6 - ID: fractions_CON1
Applies To
Continued Fractions
Description
Continued fractions use the continued fraction indicators. The outermost fraction uses different indicators than the contained fractions. The ellipsis symbol ends all the fractions.
Example 1 fractions_CON1-01
Example Image:
|
verbose |
a 0 plus ContinuedFraction
b 1 Over
a 1 plus StartFraction
b 2 Over
a 2 plus StartFraction
b 3 Over
a 3 plus ellipsis equals a 0 plus StartFraction
b 1 Over
a 1 EndFraction
plus StartFraction
b 2 Over
a 2 EndFraction
plus ellipsis |
|
|---|---|---|
|
brief |
a 0 plus ContinuedFrac
b 1 Over
a 1 plus StartFrac
b 2 Over
a 2 plus StartFrac
b 3 Over
a 3 plus ellipsis equals a 0 plus StartFrac
b 1 Over
a 1 EndFrac
plus StartFrac
b 2 Over
a 2 EndFrac
plus ellipsis |
|
|
superbrief |
a 0 plus ContinuedFrac
b 1 Over
a 1 plus Frac
b 2 Over
a 2 plus Frac
b 3 Over
a 3 plus ellipsis equals a 0 plus Frac
b 1 Over
a 1 EndFrac
plus Frac
b 2 Over
a 2 EndFrac
plus ellipsis |
|