# Unit 12 Complex Fractions

A complex fraction is a fraction whose numerator, denominator, or both contain a simple fraction or mixed number. When this occurs, the simple fraction is nested inside the complex fraction indicators.

In Nemeth Code, complex fraction indicators and complex fraction lines are formed by placing a dot 6 in front of the simple fraction symbols. This distinguishes the complex fraction symbols from the embedded simple fraction symbols. No numeric indicator is used between the fraction indicators.

Complex Fraction Opening Indicator | ⠠⠹ |

Complex Fraction Closing Indicator | ⠠⠼ |

Horizontal Complex Fraction Line | ⠠⠌ |

Diagonal Complex Fraction Line | ⠠⠸⠌ |

Baseline Indicator | ⠐ |

# Example:

$\frac{{\displaystyle {\frac{2}{3}}}}{3}$Complex Fraction Indicator | Numerator | Complex Fraction Line | Denominator | Complex Fraction Indicator |

⠠⠹ | ⠹⠆⠌⠒⠼ | ⠠⠌ | ⠒ | ⠠⠼ |

⠠⠹⠹⠆⠌⠒⠼⠠⠌⠒⠠⠼

* Notice how the simple fraction in the numerator is embedded in the complex fraction.

$\frac{3}{{\displaystyle {\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}}$

Complex Fraction Indicator | Numerator | Complex Fraction Line | Denominator | Complex Fraction Indicator |

⠠⠹ | ⠒ | ⠠⠌ | ⠹⠂⠸⠌⠆⠼ | ⠠⠼ |

⠠⠹⠒⠠⠌⠹⠂⠸⠌⠆⠼⠠⠼

* Notice how the simple fraction in the denominator is embedded in the complex fraction.

# Example:

$\raisebox{1ex}{$\frac{2}{3}$}\!\left/ \!\raisebox{-1ex}{$\frac{1}{5}$}\right.}$Complex Fraction Indicator | Numerator | Complex Fraction Line | Denominator | Complex Fraction Indicator |

⠠⠹ | ⠹⠆⠌⠒⠼ | ⠠⠸⠌ | ⠹⠂⠌⠢⠼ | ⠠⠼ |

⠠⠹⠹⠆⠌⠒⠼⠠⠸⠌⠹⠂⠌⠢⠼⠠⠼** **

# More Examples:

$\frac{x+2}{\frac{x-2}{x+5}}$⠠⠹⠭⠬⠆⠠⠌⠹⠭⠤⠆⠌⠭⠬⠢⠼⠠⠼

** **

⠠⠹⠂⠸⠹⠂⠌⠆⠸⠼⠠⠌⠢⠠⠼

$\raisebox{1ex}{$5\u2064\raisebox{1ex}{$q$}\!\left/ \!\raisebox{-1ex}{$r$}\right.$}\!\left/ \!\raisebox{-1ex}{$6$}\right.}$⠠⠹⠢⠸⠹⠟⠸⠌⠗⠸⠼⠠⠸⠌⠖⠠⠼

# Baseline Indicator

If a level change occurs in a fraction, a baseline indicator is used to bring the expression to baseline by placing the baseline indicator directly after the last character affected by the level change.

# Examples:

$\frac{{2}^{a}}{\frac{a}{b}+\frac{c}{d}}$⠠⠹⠆⠘⠁⠐⠠⠌⠹⠁⠌⠃⠼⠬⠹⠉⠌⠙⠼⠠⠼

* Notice how this fraction could be misread if the baseline indicator were missing. The rest of the fraction would remain in superscript position.

$\frac{3\u2064\frac{1}{x}}{{x}^{2}{y}^{3}z}$⠠⠹⠒⠸⠹⠂⠌⠭⠸⠼⠠⠌⠭⠘⠆⠐⠽⠘⠒⠐⠵⠠⠼

Note: Fractions containing a fraction in the exponent position are **not** considered complex fractions since the fraction is attached to a whole number.

**Example:**

⠹⠁⠘⠹⠂⠌⠒⠼⠐⠌⠃⠼

Begin all complex fractions on a new braille line. See rules for runovers.