# Unit 6 Simple Fractions and Mixed Numbers

A simple fraction is a fraction whose numerator and denominator are whole numbers. It may contain numbers, letters, or expressions, but internal fractions may not appear in the numerator or denominator.

When a simple fraction occurs within Nemeth Code, an opening simple fraction indicator is place immediately in front of the numerator. The numbers are separated by a fraction line and the closing simple fraction indicator is placed immediately after the denominator. No numeric indicator is used between fraction indicators.

Opening Simple Fraction Indicator | ⠹ |

Closing Simple Fraction Indicator | ⠼ |

Horizontal Fraction Line | ⠌ |

Diagonal Fraction Line | ⠸⠌ |

Opening Mixed Number Indicator | ⠸⠹ |

Closing Mixed Number Indicator | ⠸⠼ |

# Horizontal Fraction Line

When the numerator and denominator are separated by a horizontal fraction line, the horizontal fraction line is used.

# Example:

$\frac{3}{4}$Opening Simple Fraction Indicator | Number | Horizontal Fraction Line | Number | Closing Simple Fraction Indicator |

⠹ | ⠒ | ⠌ | ⠲ | ⠍ |

⠹⠒⠌⠲⠼

# More Examples:

$\frac{2}{3}}<{\displaystyle \frac{3}{4}$⠹⠆⠌⠒⠼⠀⠐⠅⠀⠹⠒⠌⠲⠼

$\frac{a+b}{c}$⠹⠁⠬⠃⠌⠉⠼

$\frac{1}{2}}\cdot {\displaystyle \frac{2}{3}}={\displaystyle \frac{1\cdot 2}{2\cdot 3}}={\displaystyle \frac{2}{6}}={\displaystyle \frac{1}{3}$⠹⠂⠌⠆⠼⠡⠹⠆⠌⠒⠼⠀⠨⠅⠀⠹⠂⠡⠆⠌⠆⠡⠒⠼⠀⠨⠅⠀⠹⠆⠌⠖⠼⠀⠨⠅⠀⠹⠂⠌⠒⠼

* Notice that spacing follows Nemeth rules for Operations and Comparisons

$\left({\displaystyle \frac{a}{b}}\right)\left({\displaystyle \frac{a}{b}}\right)$⠷⠹⠁⠌⠃⠼⠾⠷⠹⠁⠌⠃⠼⠾

* Notice that there is no space between the parenthesis even if it looks like it in print.

$\text{We ate}\phantom{\rule{thickmathspace}{0ex}}{\displaystyle \frac{1}{2}}\phantom{\rule{thickmathspace}{0ex}}\text{of the pie already!}$⠠⠺⠑⠀⠁⠞⠑⠀⠸⠩⠀⠹⠂⠌⠆⠼⠀⠸⠱⠀⠷⠀⠮⠀⠏⠊⠑⠀⠁⠇⠗⠖

* This sentence is written with Nemeth Code switch indicators.

# Diagonal Fraction Line

When the numerator and denominator are separated by a diagonal line, the diagonal fraction line is used.

# Example:

$\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$Opening Simple Fraction Indicator | Number | Diagonal Fraction Line | Number | Closing Simple Fraction Indicator |

⠹ | ⠆ | ⠸⠌ | ⠒ | ⠼ |

⠹⠆⠸⠌⠒⠼

# More Examples:

$\raisebox{1ex}{$2x$}\!\left/ \!\raisebox{-1ex}{$y$}\right.}$⠹⠆⠭⠸⠌⠽⠼

$\text{What is}\phantom{\rule{thickmathspace}{0ex}}{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\phantom{\rule{thickmathspace}{0ex}}\text{of}\phantom{\rule{thickmathspace}{0ex}}100\text{?}$⠠⠱⠁⠞⠀⠊⠎⠀⠸⠩⠀⠹⠂⠸⠌⠒⠼⠀⠠⠄⠷⠀⠼⠂⠴⠴⠀⠸⠱⠦

* This sentence is written with Nemeth Code switch indicators.

# Mixed Numbers

A mixed number is a whole number and a fraction combined into one unspaced number where the fraction follows the whole number. The fractional part of the mixed number must be preceded by an opening mixed number indicator and followed by a closing mixed number indicator. When the numerator and denominator are separated by a horizontal fraction line, the horizontal fraction line is used. When the numerator and denominator are separated by a diagonal line, the diagonal fraction line is used.

# Example:

$1\u2064{\displaystyle \frac{3}{4}}$Whole Number | Opening Mixed Number Indicator | Number | Horizontal Fraction Line | Number | Closing Mixed Number Indicator |

⠼⠂ | ⠸⠹ | ⠒ | ⠌ | ⠲ | ⠸⠼ |

⠼⠂⠸⠹⠒⠌⠲⠸⠼

# More Examples:

$5+1\u2064{\displaystyle \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}=\phantom{\rule{thickmathspace}{0ex}}\text{?}$⠼⠢⠬⠂⠸⠹⠂⠸⠌⠆⠸⠼⠀⠨⠅⠀⠿

$6\u2064{\displaystyle \frac{p}{7}}$⠼⠖⠸⠹⠏⠌⠶⠸⠼

$\left\{0,{\displaystyle \frac{1}{2}},1,1\u2064{\displaystyle \frac{1}{2}},2\right\}$⠨⠷⠴⠠⠀⠹⠂⠌⠆⠼⠠⠀⠂⠠⠀⠂⠸⠹⠂⠌⠆⠸⠼⠠⠀⠆⠨⠾

$\text{I ran}\phantom{\rule{thickmathspace}{0ex}}2\u2064{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}\phantom{\rule{thickmathspace}{0ex}}\text{laps around the track today.}$⠠⠊⠀⠗⠁⠝⠀⠸⠩⠀⠼⠆⠸⠹⠂⠸⠌⠲⠸⠼⠀⠸⠱⠀⠇⠁⠏⠎⠀⠜⠨⠙⠀⠮⠀⠞⠗⠁⠉⠅⠀⠞⠙⠲

* This sentence is written with Nemeth Code switch indicators.

# Brain Boost

## Spatial Arrangement with Fractions

In braille, most fractions are written horizontally with the numerator, a fraction line, and the denominator all on one line. When a fraction is written out in its graphic form, the numerator and denominator line up vertically and are separated by a spatial fraction line. Unlike spatial arrangements for addition and subtraction, the numeric indicator must be used in both the numerator and the denominator.

Opening Fraction Indicator | ⠹ |

Closing Fraction Indicator | ⠼ |

Spatial Fraction Line (varying length) | ⠒⠒⠒ |

The fraction line should be only as wide as the term. It is preceded (unspaced) by an opening fraction indicator and followed (unspaced) by a closing fraction indicator.

# Example:

$\frac{3}{4}$⠀⠼⠒⠀

⠹⠒⠒⠼

⠀⠼⠲

* Notice that a numeric indicator is required because the number follows a space.

$\frac{7}{25}$⠀⠼⠶⠀⠀

⠹⠒⠒⠒⠼

⠀⠼⠆⠢

* If the numbers are an uneven number of digits, move the smaller number left.

# Cancellation Indicators

** **As with regrouping of addition and subtraction problems (Unit 5), spatial math formation often shows cancellations made when simplifying or reducing fractions. The opening cancellation symbol and closing cancellation symbol encloses the number or character to be cancelled. The new number or character is written directly above the cancelled number.

Opening Cancellation | ⠪ |

Closing Cancellation | ⠻ |

$\begin{array}{r}1\\ \underset{\_}{\phantom{0}\overline{){3}}}\\ \overline{){27}}\\ 9\end{array}$

⠀⠼⠂

⠀⠪⠒⠻

⠹⠒⠒⠒⠒⠼

⠀⠪⠆⠶⠻⠀

⠀⠀⠼⠔

$\frac{\stackrel{1}{\overline{){2}}}}{4}}\times {\displaystyle \frac{3}{\underset{1}{\overline{){2}}}}}={\displaystyle \frac{3}{4}$⠀⠼⠂

⠀⠪⠆⠻⠀⠀⠀⠀⠼⠒⠀⠀⠀⠀⠀⠀⠀⠼⠒

⠹⠒⠒⠒⠼⠈⠡⠹⠒⠒⠒⠼⠀⠨⠅⠀⠹⠒⠒⠼

⠀⠼⠲⠀⠀⠀⠀⠀⠪⠆⠻⠀⠀⠀⠀⠀⠀⠼⠲

⠀⠀⠀⠀⠀⠀⠀⠀⠼⠂