# Unit 18 Spatial Math

The following braille symbols are used for transcribing vertical math problems.

Begin horizontal line | ⠐⠒ |

Vertical line segment | ⠸ |

Numeric passage indicator | ⠼⠼ |

Numeric passage terminator | ⠼⠄ |

Sometimes math problems are arranged vertically as they are in print. In such cases, there are two optional braille formats.

## Method One

Align the numeric indicator on the left and align the numbers in columns by place value. A space may follow the number sign. A horizontal line is placed under the number columns initiated by dot 5 and followed by unspaced dots 2-5 at least as wide as the math problem.

## Method Two

Use of the numeric passage indicator followed by the numeric passage terminator. This method places the entire passage in numeric mode and the numeric indicator is not used. All letters a-j must be preceded by a grade 1 indicator. Indentation is used to set the math problem apart from the numeric indicators. The sign of operation is spaced after the first number on the first line.

## Examples:

### Addition or Subtraction

$\begin{array}{r}1231\\ \underset{\_}{+26}\\ 1257\end{array}$ |
⠀⠀⠼⠁⠃⠉⠁⠀⠀ ⠐⠖⠼⠀⠀⠃⠋⠀⠀ ⠀⠀⠐⠒⠒⠒⠒⠀⠀ ⠀⠀⠼⠁⠃⠑⠛ |
⠼⠼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠃⠉⠁⠀⠀⠐⠖ ⠀⠀⠀⠀⠃⠋⠀⠀⠀⠀ ⠀⠀⠐⠒⠒⠒⠀⠀⠀⠀ ⠀⠀⠁⠃⠑⠛⠀⠀⠀⠀ ⠼⠄ |

Method One | Method Two |

### Multiplication

$\begin{array}{r}123\\ \underset{\_}{\times 3}\\ 369\end{array}$ |
⠀⠀⠼⠁⠃⠉⠀⠀ ⠐⠦⠼⠀⠀⠉⠀⠀ ⠀⠀⠐⠒⠒⠒⠀⠀ ⠀⠀⠼⠉⠋⠊ |
⠼⠼⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠃⠉⠀⠐⠦ ⠀⠀⠀⠀⠉⠀⠀⠀ ⠀⠀⠐⠒⠒⠀⠀⠀ ⠀⠀⠉⠋⠊⠀⠀⠀ ⠼⠄ |

Method One | Method Two |

### Division

A vertical line segment is placed between the divisor and the dividend and the quotient line is placed above the dividend.

$\begin{array}{r}5\\ 5\stackrel{\_}{|25}\\ \underset{\_}{25}\end{array}$ | ⠀⠀⠀⠀⠀⠀⠼⠑ ⠀⠀⠀⠐⠒⠒⠒⠒ ⠼⠑⠀⠸⠀⠼⠃⠑ ⠀⠀⠀⠀⠀⠼⠃⠑ ⠀⠀⠀⠀⠀⠐⠒⠒ |
⠀⠼⠼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑ ⠀⠀⠀⠀⠐⠒⠒⠒ ⠀⠀⠑⠀⠸⠀⠃⠑ ⠀⠀⠀⠀⠀⠀⠃⠑ ⠀⠀⠀⠀⠀⠀⠐⠒ ⠀⠼⠄ |

Method One | Method Two |