Nemeth Code Basics
We will go over three worksheets in this workshop, including how they are
formatted.

Notice in the numbers below that literary numbers are in the upper part of
the cell. Nemeth numbers are in the lower part of the cell.
Literary Numbers
@g=@^=@_=@`=@a=@b=@c=@d=@e=@f=
=
0
1
2 3
4
5
6
7
8
9
=
Nemeth Numbers
=
@M=@N=@O=@P=@Q=@R=@S=@T=@U=@V=
0
1
2
3
4
5
6
7
8
9
Practice reading the numbers below.
@R=
@TUV=
@PR=C=@PS=
@NQO=
Mary Denault CTEBVI 2010
Page 1

The first portion of this worksheet shows numbers. Because Nemeth
numbers are in the lower part of the braille cell, the punctuation indicator is
needed after problem numbers and before punctuation. The punctuation
indicator is |=(dots 456).

Directions are in cell 5 with runovers in cell 3. A blank line is left before
directions unless they follow a page-change indicator. When a cell-5
heading is before directions, a blank line is required between the cell 5
heading and directions.

No blank line is left after directions unless they are followed by spatial
material.

Special typeface is ignored in directions.

In the example below, a centered heading precedes the directions. There
is a blank line after the heading.

The number to the right of the problem has been moved to the beginning
of the directions. This is a section number to reference within the chapter.
==============IG^mqz=IqbL=
=
====@TJN=Itofqb=>=mofjb=c^`qlofwIk=E=b^G=
==krj_zQ=
@N|Q=@UQ=
@O|Q=@NRM=
@P|Q=@SOR=
@Q|Q=@NQRM=
=
=
Mary Denault CTEBVI 2010
Page 2
Superscripts and Subscripts

The normal level of writing is called the baseline.

When a number or letter is elevated it is called a superscript.

When a number or letter is lowered it is called a subscript.

The baseline indicator is used to put the level of writing back to the normal
level. The indicator is not used when there is a space or punctuation
indicator following the superscript or subscript.
Indicators
?=Baseline (dot 5)
{=Superscript (dots 45)
X=Subscript (dots 56)
@T{R=
@OGT{O=
u{O=Kh=@SQ=
@RR|Q=\PSuvLNSu{O?v{P?@=
Mary Denault CTEBVI 2010
Page 3
@NMXU=
cXk=

Subscript indicators are not used when a letter from any alphabet has a
subscript of a number. The number can have a decimal point or a
comma, but cannot have a superscript or subscript of its own.

When a subscript indicator isn’t used, the baseline indicator isn’t needed,
like in the example below.
H2O
IeOIl=
Practice reading the expressions below.
u{Q=
=
@Pu{O=
=
@NMv{P=
=
I`IlP=
=
Mary Denault CTEBVI 2010
Page 4

This section shows directions followed by itemized problems. The
directions are in cell 5 with runovers in cell 3.

Problems begin in cell 1, with runovers in cell 3. The problems below are
itemized, but do not contain subdivisions.

The letters in the problems below are variables. No letter indicator is used
unless the variable stands alone and is not part of an equation.
====@TJO=IcVa=>=IId`cQ=
@R|Q=@PS=C=@SQ=
@S|Q=@OT^=C=@QR^=
@T|Q=@QUw{O=C=@NNOw{S=
=
====@TJP=IcVa=>=IIi`jQ=
@U|Q=@NU=C=@PM=
@V|Q=@P`a=C=@Ua=
@NM|Q=@R^{O=C=@O^{R=
Mary Denault CTEBVI 2010
Page 5
Fractions

Simple Fractions: When writing simple fractions, be sure to use the
opening and closing fraction indicators.

Be sure that the number sign isn’t used instead of the opening fraction
indicator.

The opening fraction indicator precedes the numerator (top of fraction),
the closing fraction indicator follows the denominator (bottom of fraction).
Simple Fraction Indicators
\=Opening Fraction Indicator (dots 1456)=
@=Closing Fraction Indicator ( dots 3456)=
L=Horizontal Simple Fraction Line (dots 34)=
=
\MLT@=
=
=
\QLP@=
@RM|Q=\VjLPSjk@=
Mary Denault CTEBVI 2010
Page 6
Practice reading the fractions below.
\NLO@=
=
\RLNM@=
=
\TLU@=
Mixed Number Indicators

A mixed number is an expression which begins with a numeral and is
followed by a simple fraction whose numerator and denominator are both
numerals.

An expression is not a mixed number if it contains any letter, even if the
expression is in the same form as a mixed number.
|\=Opening Indicator (dots 456, 1456)=
=
|@=Closing Indicator (dots 456, 3456)=
L=Fraction Line (dots 34)=
Examples:
@NM|\PLQ|@=
Mary Denault CTEBVI 2010
Page 7
=
=
\OTLNO@=Kh=@O|\PLNO|@=Kh=@O|\NLQ|@=
=
=
Practice reading the mixed fractions below.
@N|\NLO|@=
=
@NM|\PLQ|@=
=
@Q|\NLT|@=
Nemeth Comma

The Nemeth comma is made up of dot (6)

If a Literary comma (dot 2) were used, how would it be read?
,
Practice reading the numbers below.
@OUIMMM=
@NQI=@NRI=C=@NS
Mary Denault CTEBVI 2010
Page 8
Symbol of Omission

The symbol of omission is made up of dots (123456).

This symbol is used for spaces that are blank, or contain a question mark.
It is not used for blank lines in print.

It is spaced the same as what it replaces.
? + ? = 28
ZHZ=Kh=@OU=
Practice reading the problems below.
@NMHNQ=Kh=Z=
=
ZHNMM=Kh=@NOR=
Mary Denault CTEBVI 2010
Page 9
Signs of Operation
H=Plus: (dots 346)
=
J=Minus: (dots 36)
=
]G Times: (dots 4, 16)
=
G=Times: (dots 16)
=
KL=Divided by: (dots 46, 34)
=
l=Curved division sign (dots 135)
=
=
Signs of Comparison
=
=
Kh=Equals: (dots 46, 13)
=
KN=Greater than: (dots 46, 2)
=
?h=Less than: (dots 5, 13)
=
XO=Proportion (as) (dots 56, 23)
=
?N==Ratio (is to) (dots 5, 2)
=
Mary Denault CTEBVI 2010
Page 10
=
@SGu=Kh=@QO=
=
@RkJNQ=Kh=@SJRk=
@O]GQ=Kh=@Q]GO=
Practice reading the examples below.
@S]GS=Kh=@PS=
=
@SGS=Kh=@PS=
=
cfsb]G=JJJJ=Kh=cfcqbbk=
=
@NHO=Kh=Z=
=
@N=?N=@O=XO=@P=?N=@S=
=
u=?h=v=
Mary Denault CTEBVI 2010
Page 11

The symbol of omission is used for the question marks above blank lines
below.

Notice that the word with is uncontracted in directions for problems 19-21.
A word in direct contact with a sign of comparison can't be contracted.

The baseline indicator is used before the fraction line and closing fraction
in problems 17 and 18 below.

Notice the mixed fractions in problems 24 and 25.
====@TJQ=Itofqb=b^G=co^`Xk=V=ixbL=qzjpQ=
@NN|Q=\ULNO@=
@NO|Q=\VLNR@=
@NP|Q=\NULU@=
@NQ|Q=\ONLS@=
=
====@TJR=IpfjmifcvQ=
@NR|Q=\VuLNR@=
@NS|Q=\OQ_LNU_`@=
@NT|Q=\u{NR?Lu{R?@=
@NU|Q=\Vk{U?Lk{O?@=
=
=
Mary Denault CTEBVI 2010
Page 12
====@TJS=Iobmi^`b=b^G=Z=tfqe=KNI=?hI=lo=
==Kh|Q=
@NV|Q=\NLQ@=Z=\NLS@=
@OM|Q=\SLNP@=Z=\SLT@=
@ON|Q=\PLU@=Z=\TLNS@=
=
@TJT=Itofqb=b^G=co^`Xk=lo=jfuA=krj_z=
w=^=ab`fj^iQ=
@OO|Q=\QLR@=
@OP|Q=\QLNR@=
@OQ|Q=@Q|\NLS|@=
@OR|Q=@T|\NPLOM|@=
Decimal Point
 The decimal point is made up of dots (46) K=
4.75
@QKTR=
68.462
@SUKQSO=
=
.254
@KORQ=
Mary Denault CTEBVI 2010
Page 13
Line Over

When there is a single line over a number or letter, lower-case or
uncapitalized, from any alphabet, the symbol below is used. If the line is
over more than one letter, refer to the five-step rule in the Nemeth Code,
Section 86.
W=Line over (dots (156) =
=
Practice reading the problems below.
uW=
=
uvWw=
=
@KORQ=
=
uW|Dp=
=
@QKMM=
=
uWHvW=
=
@OKTRHQKOR=
=
=
Mary Denault CTEBVI 2010
Page 14
=
====@TJU=Itofqb=b^G=ab`fj^i=w=^=co^`Xk=
==lo=jfuA=krj_z=V=ixbL=qzjpQ=
@OS|Q=@MKSTO=
@OT|Q=@MKOT=
@OU|Q=@TKPW=
@OV|Q=@OKUU=
=
@PM|Q=Iplisb=MrpH=^=af^do^jP=IbfYq=
==mi^vzp=?mf`fm^qA=V=^=pHibJbifjVIk=
==qRkfp=qyok^XqQ=IV=pG=^=qyok^XqN=b^G=
==mi^vz=fp=y=^c=?l=ilppQ=Iex=|j=d^jbp=
==afa=>=G^jmflk=mi^vU=
=
====@TJV=Ibumobpp=b^G=oIk^i=krj_z=w=>=
==nrlqfRq=E=qtl=VqbdzpQ=
@PN|Q=@TKQ=
@PO|Q=J@QKOR=
@PP|Q=J@U=
@PQ|Q=@PKPW=
=
@PR|Q=Itofqb=>=krj_z=J@N=w=^=nrlqfRq=E=
==qtl=Vqbdzp=V=\obb=afSzRq=t^vpQ=
@PS|Q=I?k=\obb=oNi=krj_zp=q=[b=Oq=\NLP@=
==C=\NLO@|Q=
Mary Denault CTEBVI 2010
Page 15
Signs of Comparison


Signs of comparison are shown below.
A space is required before and after signs of comparison. The numeric
indicator is repeated after the comparison sign.
@TJNM=Ido^me=b^G=lmR=pRqXbQ=
@PT|Q=@S=Kh=uHV=
@PU|Q=@PtJU=Kh=@N=
@PV|Q=v=KNW=@RKR=
@QM|Q=j=?h=\TLU@=
=
@TJNN=Itofqb=b^G=krj_z=V=p`fRqfcf`=
klqIkQ=
@QN|Q=@MKMMMTS=
@QO|Q=@MKMMMMMPPR=
=
====Itofqb=b^G=krj_z=V=ab`fj^i=klqIkQ=
@QP|Q=@P]GNM{JR=
@QQ|Q=@QKT]GNM{JU=
Mary Denault CTEBVI 2010
Page 16
Spatial Problems

In spatial problems, the numeric indicator isn’t used.

There are blank lines above and below spatial problems, even when there
is a page change indicator above or below them.

The separation line is made up of dots 25.

There must be one blank cell between separation lines when more than
one problem is written across the page.

The separation line goes one cell to the right and left of the widest item in
the problem.

When spatial arrangements are identified by a number or letter, no symbol
of one spatial arrangement may be less than 3 cells distant from any
symbol on any line except separation lines.
Mary Denault CTEBVI 2010
Page 17
Addition and Subtraction

Plus and minus signs are placed in the cell to the left of the widest number
which appears above the separation line. If they are deliberately
misaligned, follow print.
Mary Denault CTEBVI 2010
Page 18
Multiplication

The multiplication cross is written in the cell next to the first digit above the
line.
Mary Denault CTEBVI 2010
Page 19
Practice reading the problems below.
==NR=
=HOP=
PPPPP=
=
=
==NMM=
=J=VN=
PPPPPPP=
=
=
@Q|Q===QO=
======HOV=
=====PPPPP=
=
Mary Denault CTEBVI 2010
Page 20
Mary Denault CTEBVI 2010
Page 21

The Review and Name at the top of the page are left aligned.

The heading for the worksheet is centered.

Directions are in cell 5. A blank line is required below the directions
because of the spatial material that follows.
IIobsfbt=Ij^\=I?tyq=@QJO=
IIobsfbt=IIC=IImo^`qf`b=
=
I?k=JJJJ=
=
====Ij=Ijriqfmif`Ik=C=IafsfKk=Ic^`qp=
=
====IcVa=>=molar`q=lo=nrlqfRqQ=
=
@N|Q====V===@O|Q====U===@P|Q====Q=
======IGP=========]GR=========]GV=
=====PPPPP=======PPPPP=======PPPPP=
=
@Q|Q====S===@R|Q====M===@S|Q====U=
======]GU=========]GV=========]GP=
=====PPPPP=======PPPPP=======PPPPP=
=
@T|Q====O===@U|Q====V===@V|Q====S=
======]GU=========]GN=========]GV=
=====PPPPP=======PPPPP=======PPPPP=
=
@NM|Q====U===@NN|Q=====U===@NO|Q====T=
=======]GS===========]GU==========]GV=
======PPPPP=========PPPPP========PPPPP=
=
=
@NP|Q====U===@NQ|Q====V===@NR|Q====U=
=======]GT==========]GV==========]GN=
======PPPPP========PPPPP========PPPPP=
=
@NS|Q====O===@NT|Q====Q===@NU|Q====T=
=======]GV==========]GU==========]GU=
======PPPPP========PPPPP========PPPPP=
=
@NV|Q====V===@OM|Q====T===@ON|Q====S=
=======]GQ==========]GT==========]GT=
======PPPPP========PPPPP========PPPPP=
=
Mary Denault CTEBVI 2010
Page 22
@OO|Q====V===@OP|Q====U===@OQ|Q====P=
=======]GS==========]GO==========]GV=
======PPPPP========PPPPP========PPPPP=
=
Blank Line

The blank line is used to show a space to be filled in when a blank line is
shown in print.

The blank line is spaced like what it is replacing.
JJJJ==Blank Line (dots 36, 36, 36,36)
Examples:
@S]GT=Kh=JJJJ=
Mary Denault CTEBVI 2010
Page 23

Blank lines are shown below. Notice that they are spaced away from the
sign of comparison (equals).

Two different symbols are used for division. Follow print for the symbol to
be used. (See page 10 for symbols)
@OR|Q=@UKLQ=Kh=JJJJ=
@OS|Q=@NMKLR=Kh=JJJJ=
@OT|Q=@OMKLQ=Kh=JJJJ=
@OU|Q=@PSKLQ=Kh=JJJJ=
@OV|Q=@QRKLR=Kh=JJJJ=
@PM|Q=@QMKLU=Kh=JJJJ=
=
@PN|Q=@QlPO=
@PO|Q=@QlOU=
@PP|Q=@VlPS=
@PQ|Q=@RlPM=
@PR|Q=@VlRQ=
@PS|Q=@UlRS=
@PT|Q=@TlQV=
@PU|Q=@SlQU=
===
Mary Denault CTEBVI 2010
Page 24
====I\Vh=Iu=Ilsz=
@PV|Q=Itofqb=^ii=>=c^`qlop=E>=krj_z=
==@QU|Q=Iex=`=v=O=prob=v=e=cKa=>j=^iiU=
Mary Denault CTEBVI 2010
Page 25

Itemized material with subdivisions is shown below. The main
division goes in 1/5, subdivisions are in 3/5. This is a Nemeth rule.

The dollar sign ]p=is used below. The numeric indicator isn't
used with the dollar sign.
============IImol@j=IIplisH=
===============Imo^`qf`b=
=
====Itofqb=>=io=E>=plirXkQ=
@N|Q=I?l=c[j=Pq^Vp=@QPM=^`obp=E=iCQ=Iup=
====xkz=mi^kp=Spbii=?p=E=u=^q=]pQIMMM=mz=
====^`obQ=Iex=jG=j?lv=t=>=xkz=o`s=fc=eb=
====pbiip=e^ic=U=iCU=
==X^|Q=]pUSMIMMM=
==X_|Q=@ONR=^`obp=
==X`|Q=IvbpN=eb=albpQ=
@O|Q=I>=Iibbp=C>=IpCp=b^G=xkA=@ORMJ^`ob=
====c[jpQ=I>v=b^G=_?y=^kl>o=@TR=^`obpQ=
====IqaN=>=Iibbp=e=@PRQ=^`obpQ=IWl=xkp=j=
====iCU=
==X^|Q=@OV=^`obp=j=
==X_|Q=>=IpCp=
==X`|Q=>=Iibbp=
Mary Denault CTEBVI 2010
Page 26
=
=
=
====Itofqb=^=krj_z=pRqXbN=C=plisbQ=
@P|Q=IV=@NVUOI=?>=T=@PQ=cbtz=c[jp=V=>=
==IrkfqA=IL^qbp=\^k=V=@NVUN|Q=Ifc=?>=T=
==@OIQMM=c[jp=V=@NVUOI=ex=|j=c[jp=T=?>=V=
==@NVUN|U=
@Q|Q=I>=Im[hz=c[j=e^p=@P=?qp=w=|j=`^qqib=
==w=>=ILbVt^v=c[jQ=I>=Im[hzp=e=@VM=
==`^qqibQ=Iex=|j=`^qqib=a=>=ILbVt^vp=eU=
Mary Denault CTEBVI 2010
Page 27
=
====Itofqb=>=io=E>=_bL=bLfj^qbQ=
@R|Q=I^k=^i^ph^k=Gf`hR=c[jz=pbiip=@OIQNS=
====bTp=V=?l=jlk\Q=I>=^sz^db=eR=lk=>=c[j=
====i^vp=^_=@NS=bTp=mz=jlk\Q=Iex=|j=eRp=
====albp=>=c[jz=eU=
==X^|Q=@NR=
==X_|Q=@NRM=
==X`|Q=@NIRMM=
==Xa|Q=@NRIMMM=
@S|Q=IV=@NVUPI=^=_rBbi=E=`lok=`lL=
====]pPKPM|Q=I^=_rBbi=E=WNq=`lL=]pPKRQ|Q=
====Ifc=^=c[jz=plia=@TIRMM=_rBbip=E=`lok=
====C=@O=?qp=w=jG=WNqN=^_=ex=jG=j?lv=ta=
====>=c[jz=e=o`saU=
==X^|Q=]pOUIMMM=
==X_|Q=]pRPIMMM=
==X`|Q=]pTRIMMM=
==Xa|Q=]pTTPIMMM=
Mary Denault CTEBVI 2010
Page 28
=
=
====IifL=>=VZjIk=V=>=mol@jQ=I`olpp=y=>=
==VZjIk=q=tlkDq=ebim=v=^kptz=>=?nQ=
@T|Q=Ig^plk=Im[hz=fp=il^aH=_^ibp=E=e^v=
==lkql=^=jbG^kf`^i=[jQ=I>=[j=jlsbp=>=
==@RMJmKa=_^ibp=rm=S>=e^viEqQ=Ig^plk=
==il^ap=@N=_^ib=b=@R=pb`lkapQ=Iex=|j=
==_^ibp=t=eb=il^a=V=@SM=pb`lkapU=
@U|Q=IOq=@NVTM=C=@NVUMI=|t=molar`Xk=E=
==bTp=V`oNpA=_v=@RIRSUIMMM=jbqof`=qlkpQ=
==IV=@NVUMI=molar`Xk=M=@OSITMMIMMM=
==jbqof`=qlkpQ=I^=jbqof`=qlk=bnr^ip=
==@NIMMM=hfildo^jpQ=Iex=|j=jbqof`=qlkp=E=
==bTp=T=molar`A=V=@NVTM|U=
=
=
Mary Denault CTEBVI 2010
Page 29
Reference Sheet
Nemeth Numbers
=
@M=@N=@O=@P=@Q=@R=@S=@T=@U=@V=
0
1
2 3
4
5
6
7
8
9
Level Indicators
?=Baseline (dot 5)
{=Superscript (dots 45)
X=Subscript (dots 56)
Simple Fraction Indicators
\=Opening Fraction Indicator (dots 1456)=
@=Closing Fraction Indicator ( dots 3456) =
L=Horizontal Simple Fraction Line (dots 34) =
Mixed Number Indicators
|\=Opening Indicator (dots 456, 1456)=
|@=Closing Indicator (dots 456, 3456)
L=Fraction Line (dots 34) =
Signs of Operation
H=Plus: (dots 346)
J=Minus: (dots 36)
]G Times: (dots 4, 16)
G=Times: (dots 16)
KL=Divided by: (dots 46, 34)
l=Curved division symbol (dots 135)
=
Signs of Comparison
Kh=Equals: (dots 46, 13)
KN=Greater than: (dots 46, 2)
?h=Less than: (dots 5, 13)
XO=Proportion (as) (dots 56, 23)
?N==Ratio (is to) (dots 5, 2)
Mary Denault CTEBVI 2010
Page 30