# Lesson 3.4: Simple Fractions

## Symbols

$\text{opening fraction indicator}$

⠹

$\text{/ diagonal line or slash}$

⠌

$\text{closing fraction indicator}$

⠼

### Explanation

In print, a common way for fractions to be displayed is to have the numerator, the top number, above a horizontal fraction line and the denominator, the bottom number, below the line. However, fractions may also be displayed with the numerator the the left of a diagonal line, or slash, and the denominator to the right. Also in some cases, the numerator may be slightly raised and the denominator slightly lowered. Remember that a fraction is really only a division problem where the division has not taken place.

In braille, fraction indicators are used in order to represent the beginning and end of a fraction. They are signs of enclosure and always include a symbol indicating the beginning and a symbol indicating the end of the fraction. These symbols are unique to braille and do not exist in print. The first indicators that will be covered are the simple fraction indicator and the mixed number fraction indicator.

Simple fractions are fractions that have a numerator and denominator that are either directly above each other or slightly raised or lowered and the numbers are divided by a horizontal line or a slanted line. For simple fractions, the opening fraction indicator is dots one-four-five-six and the closing fraction indicator is dots three-four-five-six. Simple fractions cannot include fractions in the numerator or denominator. A simple fraction can contain numbers, letters, or expressions. Remember that everything to the left of the fraction line is considered the numerator and everything to the right of the fraction line is the denominator. Since the opening fraction indicator is a full cell indicator, no numeric indicator is needed at the beginning of the fraction. Fractions are numbers, so they are spaced the same as other digits.

Thus a simple division problem such as 24รท6 written as a fraction would be ((24)/6).

However, if the numerator and denominator are written in print on the same line with a diagonal slash such as twenty four slash six, the fraction indicators are not used. Instead, the numeric indicator is used and slash (dots three-four-five followed by dots three-four) is used. It would look like 24/6. This is because when problems are written this way, it usually indicates a division problem rather than a fraction.

Fractions may be added, subtracted, multiplied, and divided by other expressions in horizontal arrangements.

### Example 1

$\frac{1}{4}$

⠹⠂⠌⠲⠼

### Example 2

$\frac{2}{3}$

⠹⠆⠌⠒⠼

### Example 3

$2+\frac{3}{4}$

⠼⠆⠬⠹⠒⠌⠲⠼

### Example 4

$\frac{5}{8}-\frac{3}{8}$

⠹⠢⠌⠦⠼⠤⠹⠒⠌⠦⠼

### Example 5

$\frac{1}{2},\phantom{\rule{.3em}{0ex}}\frac{2}{4},\phantom{\rule{.3em}{0ex}}\frac{3}{6}$

⠹⠂⠌⠆⠼⠠⠀⠹⠆⠌⠲⠼⠠⠀⠹⠒⠌⠖⠼

### Example 6

$\frac{1}{2}=\frac{2}{4}$

⠹⠂⠌⠆⠼⠀⠨⠅⠀⠹⠆⠌⠲⠼

### Example 7

$\frac{1}{2}>\frac{1}{3}$

⠹⠂⠌⠆⠼⠀⠨⠂⠀⠹⠂⠌⠒⠼

### Example 8

$2+\frac{1}{2+2}$

⠼⠆⠬⠹⠂⠌⠆⠬⠆⠼

### Example 9

$\frac{\mathrm{a}}{\mathrm{b}}$

⠹⠁⠌⠃⠼