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# Lesson 4.1: Variables

## Explanation

A variable is a quantity that varies in its possible value. Letters are usually used to represent variables in mathematical expressions. Grade 1 symbol indicators may be needed in simple mathematical expressions where letters stand alone or where the letters a through j follow numerals. Grade 1 mode is needed when the symbol could be misread as a grade 2 meaning or as a numeric meaning.

In the circumstance of a sequence of letters standing alone that could represent a shortform word, grade 1 mode must be turned on by the grade 1 symbol indicator or by the use of grade 1 passage indicators for the entire expression. The choice of grade 1 indicators will be determined by the presence of any additional items within the expression that require grade 1 mode. The preference is to use the grade 1 indicator that best preserves the mathematical expression without interruption.

In Example 1, the single letter n is used as a variable. The letter stands alone and also has a grade 2 meaning therefore the grade 1 symbol indicator is required.

### Example 1

$3+5=n$
⠼⠉⠐⠖⠼⠑⠀⠐⠶⠀⠰⠝

In Example 2, the single letter a is used as a variable. The letter stands alone, however it does not have a grade 2 meaning. A grade 1 symbol indicator is not required.

### Example 2

$a=6$
⠁⠀⠐⠶⠀⠼⠋

In Example 3, a single letter is used as a variable. The letter does not stand alone, therefore it does not need a grade 1 indicator.

### Example 3

$n+4$
⠝⠐⠖⠼⠙

The numeric indicator turns on grade 1 mode. A lower-case letter a through j that immediately follows a number can be misread as a numeric meaning. The grade 1 symbol indicator is used to set grade 1 mode for the letter. The grade 1 indicator also turns off numeric mode.

### Example 4

$3b$
⠼⠉⠰⠃

### Example 5

$3n$
⠼⠉⠝

### Example 6

$5x$
⠼⠑⠭

An upper-case letter that immediately follows a number does not require the grade 1 symbol indicator. The capital indicator turns off numeric mode and prevents the letter from being misread as a numeral.

### Example 7

$3B$
⠼⠉⠠⠃

Variables in mathematical expressions should follow print for spacing and case. The capital letter indicator, dot six, is used before a single capital letter. A capital word indicator dots six, six, should precede an upper-case letter sequence that is used as a variable.

### Example 8

$\text{point}\phantom{\rule{.3em}{0ex}}D$
⠏⠕⠔⠞⠀⠰⠠⠙

### Example 9

$\text{point}\phantom{\rule{.3em}{0ex}}\mathrm{DF}$
⠏⠕⠔⠞⠀⠠⠠⠙⠋

When a sequence of letters used as a variable could be read as a shortform, a single grade 1 symbol indicator is used. This turns on grade 1 mode for the first letter of the sequence, thereby separating it from its potential shortform word meaning.

### Example 10

$\text{Line}\phantom{\rule{.3em}{0ex}}\mathrm{AB}$
⠠⠇⠔⠑⠀⠰⠠⠠⠁⠃

The letters should be spaced as the symbols they represent in the mathematical expression.

### Example 11

$C+8$
⠠⠉⠐⠖⠼⠓

### Example 12

$3x-1$
⠼⠉⠭⠐⠤⠼⠁

### Example 13

$\left(m=5\right)$
⠐⠣⠰⠍⠀⠐⠶⠀⠼⠑⠐⠜