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# Lesson 4.2: Simple Fractions

## Symbols

$\text{simple numeric fraction line}$

$\text{general fraction opening}$

$\text{general fraction closing}$

$\text{general fraction line}$
⠨⠌

$/\phantom{\rule{.3em}{0ex}}\text{forward slash}$
⠸⠌

## Explanation

A simple fraction is one whose numerator and denominator are both numerals consisting of only digits, decimal points, commas or separator spaces, and whose fraction line is drawn between two vertically or nearly vertically arranged numerals. The numeric indicator is used with the numerator followed by the simple numeric fraction line and the denominator numeral. The simple numeric fraction line continues numeric mode therefore the numeric indicator is not repeated with the denominator in a simple fraction. The simple numeric fraction line is formed with dots three four.

When two digits are written on the same line of print with a diagonal slash between them as in 20/20 (twenty forward slash twenty), it is not considered a fraction. The expression is written as it appears in print using the forward slash. The forward slash is formed with two cells; dots four five six in the first cell and dots three four in the second cell. The forward slash terminates numeric mode therefore the numeric indicator is repeated with the second numeral.

### Example 1

$\frac{1}{2}$
⠼⠁⠌⠃

### Example 2

$\frac{3}{4}$
⠼⠉⠌⠙

### Example 3

$\frac{1}{2},\phantom{\rule{.3em}{0ex}}\frac{2}{4},\phantom{\rule{.3em}{0ex}}\frac{3}{6}$
⠼⠁⠌⠃⠂⠀⠼⠃⠌⠙⠂⠀⠼⠉⠌⠋

### Example 4

$3+\frac{1}{4}$
⠼⠉⠐⠖⠼⠁⠌⠙

### Example 5

$\frac{2}{3}+\frac{1}{2}$
⠼⠃⠌⠉⠐⠖⠼⠁⠌⠃

### Example 6

$20/20$
⠼⠃⠚⠸⠌⠼⠃⠚

## General Fraction Indicator

When the numerator or denominator are not entirely numeric as defined above, general fraction indicators must be used. The numerator and denominator are written between general fraction indicators and the general fraction line is used. The opening general fraction indicator is formed with dots one two three five six and the closing general fraction indicator is formed with dots two three four five six. The general fraction line is two cells; dots four six in the first cell and dots three four in the second cell. The opening and closing fraction indicators have a contracted (grade 2) meaning, therefore grade 1 mode must be used to prevent the fraction indicator from being misread as its grade 2 meaning. Grade 1 mode is set by the grade 1 symbol indicator, the numeric indicator, and the grade 1 word or passage indicators. The entire expression must be evaluated for choice of indicators.

The examples below illustrate how the grade 1 indicators and numeric indicator affect the subsequent symbols to set grade 1 mode.

In Example 7, numerator a over denominator four, general fraction indicators are required because the numerator is not a digit. In this example, the opening and closing general fraction indicators are identified as symbols that have a potential grade 2 meaning. Grade 1 mode must be turned on for the opening fraction indicator. Grade 1 mode is turned on by the numeric indicator in the denominator and remains in effect until the end of the symbol sequence, therefore no additional indicator is needed with the closing fraction symbol.

### Example 7

$\frac{a}{4}$
⠰⠷⠁⠨⠌⠼⠙⠾

Example 8, numerator two plus three over denominator six, requires general fraction indicators because the numerator contains something other than a digit ‐ the plus sign. The general fraction indicators must be in grade 1 mode. The grade 1 symbol indicator turns on grade 1 for the opening fraction indicator. The numeric indicator places the closing fraction indicator in grade 1 mode.

### Example 8

$\frac{2+3}{6}$
⠰⠷⠼⠃⠐⠖⠼⠉⠨⠌⠼⠋⠾

In a fraction where the numerator and denominator are both letters, grade 1 mode must be set for both the opening and closing general fraction indicators. It is best to avoid interrupting the expression, therefore use of the grade 1 word indicator is preferred. The grade 1 word indicator sets grade 1 mode for the remainder of the symbol sequence. Although grade 1 symbol indicators can be used with each fraction indicator, doing so is considered more intrusive and interrupts the mathematical expression.

### Example 9

$\frac{a}{b}$
⠰⠰⠷⠁⠨⠌⠃⠾

The numeric indicator sets grade 1 mode for the remainder of the symbol sequence. Grade 1 mode when set by the numeric indicator is terminated by a space, hyphen, dash, or grade 1 terminator. The numeric indicator is the first symbol of the expression in Example 10. The fraction requires the general fraction indicators because the numerator contains a plus sign. No grade 1 indicators are required because grade 1 mode is set by the numeric indicator and continues through the entire expression.

### Example 10

$3+\frac{1+1}{4}$
⠼⠉⠐⠖⠷⠼⠁⠐⠖⠼⠁⠨⠌⠼⠙⠾

In Examples 11 and 12, a grade 1 passage indicator and terminator are used because multiple symbols within the expression have alternate grade 2 meanings. Using individual grade 1 symbol indicators would interrupt the mathematical expression. The general fraction indicators and any letters that stand alone must be in grade 1 mode. An expression that consists of three or more symbol sequences meets the criteria for a passage. The expression is set in grade 1 mode by placing the passage indicator before its first symbol and a grade 1 terminator after its final symbol.

### Example 11

$\frac{2+3}{10}=\frac{x}{2}$
⠰⠰⠰⠷⠼⠃⠐⠖⠼⠉⠨⠌⠼⠁⠚⠾⠀⠐⠶⠀⠷⠭⠨⠌⠼⠃⠾⠰⠄

### Example 12

$x=\frac{a+b}{c}$
⠰⠰⠰⠭⠀⠐⠶⠀⠷⠁⠐⠖⠃⠨⠌⠉⠾⠰⠄